CN104460594A - Dispatching optimization method based on two-layer nest structure - Google Patents

Abstract

The invention relates to a dispatching optimization method based on a two-layer nest structure and belongs to the technical field of industrial automation. A nest optimization algorithm structure is adopted for the problem of mixed integral non-linear programming (MINLP) existing in the production dispatching of most of manufacturing enterprises, global search is conducted by means of continuous updating of multiple solutions without the gradient information of a solution space, a feasible coarse judgment model is added and constructed, the feasibility of a solution is coarsely and fast judged before the solution evaluation, so that it is ensured that the true satisfactory solution of the dispatching model is obtained with a high probability, the calculated amount is small, the optimizing process is simple, and the application range is wide.

Description

A Scheduling Optimization Method Based on Two-Layer Nested Structure

technical field

The invention relates to a scheduling optimization method based on a two-layer nested structure, which is suitable for solving mixed integer non-linear programming (Mixed Integral Non-Linear Programming, hereinafter referred to as MINLP) problems encountered in production scheduling, and belongs to the technical field of industrial production automation.

Background technique

With the increasing production scale of the manufacturing industry, the increasingly complex production process, and the increasingly fierce market competition, production scheduling is an important tool to improve the management level of enterprises and obtain greater economic benefits. The generalized production scheduling problem is aimed at the decomposable production process. Under the condition of satisfying the constraint conditions, how to arrange the raw material resources, processing control variables, processing time and sequence occupied by each decomposition process to achieve production benefits (for production Comprehensive evaluation of cost and product quality) maximization. Scheduling optimization problems are similar to general optimization problems, but they also have new characteristics, such as large-scale problems, complex descriptions of production processes, difficult constraints and objective functions, and so on. The mathematical model of the scheduling optimization problem is mainly described by the mathematical programming description method, that is, using discrete variables to represent discrete decision states such as arrangement order and production plan selection, using continuous variables to represent continuous operating conditions, and using algebraic equations or inequalities to describe the objective function and constraints , so the problem is abstracted into a MINLP model. This description is intuitive and easy to understand, and it is also conducive to measuring the complexity of the model.

The two-level optimization method is a special algorithm for solving MINLP problems. It utilizes the type characteristics of the optimization variables and uses a two-level structure to solve the problem. The two-level optimization algorithm can be divided into "interval approximation" algorithm and "nested optimization" algorithm. The former obtains the lower boundary and upper boundary of the original MINLP optimization problem by iteratively solving a series of MILP main problems and NLP sub-problems until the interval difference between the two boundaries is less than the set range, so it is called "interval approximation" algorithm. The latter simplifies the model into an NLP model for each fixed discrete variable candidate solution, so NLP optimization can be regarded as a sub-optimization problem when the value of the discrete variable has been determined, and the optimal value obtained by the sub-optimization problem is used as a pair The evaluation of discrete variable solutions is regarded as the basis for optimizing discrete variables. In this way, the original MINLP optimization problem is transformed into a nested optimization problem of the outer MIP model and the inner NLP model, so it is called the "nested optimization" algorithm. How to improve the solution efficiency is the main problem faced by the "nested optimization" algorithm, because each discrete variable candidate solution in the outer combinatorial optimization process corresponds to an inner NLP optimization problem. If it is required to obtain the optimal value of these NLP models, it will take a lot of time to solve. At present, most "nested optimization" algorithms use a random-accurate two-layer structure, because when the inner NLP model is a convex optimization problem, the exact The search algorithm has obvious advantages in solving efficiency than the random search algorithm.

Contents of the invention

The purpose of the present invention is to propose a scheduling optimization method based on a two-layer nested structure. For the MINLP problems existing in the production scheduling of most manufacturing enterprises, the method can ensure that the real satisfactory solution of the scheduling model is obtained with a higher probability. The quantity is small, and the optimization process is simple, and the application range is wide.

The scheduling optimization method of the nested structure that the present invention proposes, comprises the following steps:

Step 1) Initialize parameters:

Set the parameters of the outer GA algorithm and the inner PSO algorithm, including population size N _s , N _f , PSO speed update weighting coefficients ω, φ _p , φ _g , GA crossover probability p _c and mutation probability p _m , and the maximum number of iteration steps

Step 2) probability selection stage;

Step 2.1 Set the outer layer optimization iteration step k _s =0, initialize discrete variable candidate solutions s(1,k _s ),…,s(n _s ,k _s ),…,s(N _s ,k _s );

Step 2.2 If the number of iteration steps k _s of the outer layer optimization does not exceed For s(n _s ,k _s )(n _s =1,...,N _s ) corresponding N _s NLP optimization sub-models Using the inner layer optimization algorithm (PSO algorithm) to iteratively calculate to step, and record historical optimization data $e\left(k_f\right){|}_{\mathrm{the\; s}({\mathrm{no}}_{\mathrm{the\; s}},k_{\mathrm{the\; s}})},p^{\′}\left(k_f\right){|}_{\mathrm{the\; s}({\mathrm{no}}_{\mathrm{the\; s}},k_{\mathrm{the\; s}})}(k_f=1,...,K_f^{\mathrm{FM}});$

Step 2.3 For s(n _s ,k _s )(n _s =1,...,N _s ), use its historical minimum penalty value and Feasibility Rough Decision Model Estimation Then determine the feasibility of s(n _s , k _s ), that is, to determine

Step 2.4 If s(n _s ,k _s ) is not feasible, keep as rough penalty If s(n _s , k _s ) is feasible, iteratively optimize the sub-model with the inner optimization algorithm (PSO algorithm) to step, record historical optimization data Estimated by rough evaluation model Keep estimates rough evaluation

Step 2.5 According to the obtained rough evaluation value and rough penalty value, use the outer layer optimization algorithm (GA algorithm) and the feasibility rule method to update the rough optimal set

In this step, according to the feasibility rough judgment model of the discrete variable candidate solution, the rough penalty value corresponding to the discrete variable combination s is quickly obtained and feasibility estimates Then judge whether to continue to evaluate s; if feasible, further implement rough evaluation to obtain rough evaluation value Based on the above evaluation results, the outer stochastic optimization algorithm solves the following combinatorial optimization problems:

Obtain the former through the outer stochastic optimization algorithm An estimated optimal and feasible discrete variable candidate solution, namely

Save it in the rough premium collection middle. Through the feasibility rule method, the optimal update operation of the outer stochastic optimization algorithm is performed under rough evaluation conditions;

Step 2.6 The number of iteration steps of outer layer optimization k _s =k _s +1, if the number of iteration steps of outer layer optimization k _s is less than Return to step 2.2, if the number of iteration steps k _s of the outer layer optimization exceeds Then go to step 3);

Step 3) Accurate evaluation stage:

Solve N _s NLP optimization sub-models corresponding to s(n _s ,K _s )(n _s =1,...,N _s ) Using the inner layer optimization algorithm (PSO algorithm) to iteratively calculate to Step to get accurate evaluation value and the corresponding optimal continuous variable solution $f^{*}{|}_{\mathrm{the\; s}({\mathrm{no}}_{\mathrm{the\; s}},K_{\mathrm{the\; s}})}({\mathrm{no}}_{\mathrm{the\; s}}=1,...,N_{\mathrm{the\; s}});$

Step 4) determine the final satisfactory solution:

Compare the exact evaluation values of each NLP optimization sub-model According to the following feasibility rules, the optimal group is selected as the satisfactory solution of the scheduling model:

${\mathrm{<span\; class="notranslate">\; f</span>}}^{\mathrm{<span\; class="notranslate">\; g</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; f</span>}}^{<span\; class="notranslate">\; *</span>}{<span\; class="notranslate">\; |</span>}_{{\mathrm{<span\; class="notranslate">\; the\; s</span>}}^{\mathrm{<span\; class="notranslate">\; g</span>}}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 9</span>}<span\; class="notranslate">\; )</span>$

The final satisfactory solution is ${\mathrm{the\; s}}^g=\mathrm{the\; s}(G,K_{\mathrm{the\; s}}^{\max }),f^g=f^{*}{|}_{\mathrm{the\; s}(G,K_{\mathrm{the\; s}}^{\max })},$ in $G=\arg {\min }_{{\mathrm{no}}_{\mathrm{the\; s}}\&Element;\{1,...,N_{\mathrm{the\; s}}\}}{e}^{*}{|}_{\mathrm{the\; s}({\mathrm{no}}_{\mathrm{the\; s}},K_{\mathrm{the\; s}})}.$

3. A scheduling optimization method based on a two-layer nested structure as claimed in claim 1, characterized in that: in said step 2.2), the key step of inner layer optimization is to use a feasibility rough judgment model and a rough evaluation model The screening and evaluation of the solution is essentially to predict the convergence results of the penalty value and the evaluation value, that is, to use the numerical information (internal optimization history data) obtained by the limited number of iterations to estimate the exact convergence obtained after the infinite iteration calculation The specific implementation method is to use the negative power function curve to fit the iterative descent process of the penalty value (evaluation value) to obtain the final convergence result. The specific steps are as follows:

A.1 The inner layer optimizes the acquisition of historical data

The acquisition process of inner optimization historical data is the iterative calculation process of inner optimization algorithm. The present invention adopts particle swarm optimization algorithm (PSO algorithm) to solve The cost of any individual f in the population is defined as $f\left(f\right)=J(f,\stackrel{\&OverBar;}{\mathrm{the\; s}}){|}_{\stackrel{\&OverBar;}{\mathrm{the\; s}}=\mathrm{the\; s}},$ The calculation process of the algorithm is:

Among them, K _f is the maximum number of inner layer optimization iteration steps used to obtain historical data, w, φ _p , φ _g are the speed update weighting coefficients of the PSO algorithm;

A.2 Solution of Rough Evaluation Model

Since the negative power function can better describe and _predict the _change trend of e(k _f )| _s , use the optimized historical data e(k _f ) _| Power function, and then estimate e(∞)| _s :

$\begin{array}{c}\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; e</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&theta;</span>}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; f</span>}}<span\; class="notranslate">\; )</span>{<span\; class="notranslate">\; |</span>}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; A</span>}<span\; class="notranslate">\; \&CenterDot;</span>{{\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; f</span>}}}^{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; B</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; C</span>}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; f</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; ,</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; ,</span><span\; class="notranslate">\; \&infin;</span>\\ \mathrm{<span\; class="notranslate">\; \&theta;</span>}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; A</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; B</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; C</span>}<span\; class="notranslate">\; )</span>\end{array}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 10</span>}<span\; class="notranslate">\; )</span>$

Further adopt the recursive fitting algorithm, when the inner stochastic optimization algorithm obtains new data e(k _f ) _| Parameter θ, until the inner layer algorithm iterates to the number of steps K _f , so that the amount of data meets the fitting accuracy:

in, express The weight coefficient in; Indicates that when the algorithm iterates to k _f steps, the fitting function value and the mean square error between observations e(k _f )| _s :

The initial value of the recursive algorithm is set as follows:

θ ₀ =(A ₀ ,B ₀ ,C ₀ )=(0,0.5,e(1)| _s ) (14)

${<span\; class="notranslate">\; \{</span>\frac{{<span\; class="notranslate">\; \&PartialD;</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}{{<span\; class="notranslate">\; \&PartialD;</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}\mathrm{<span\; class="notranslate">\; \&theta;</span>}}{\mathrm{<span\; class="notranslate">\; J</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&theta;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; \}</span>}^{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; \&epsiv;</span>}<span\; class="notranslate">\; \&Center\; Dot;</span>\mathrm{<span\; class="notranslate">\; I</span>}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 15</span>}<span\; class="notranslate">\; )</span>$

Among them, ε represents a very small constant;

Using optimized historical data e(k _f )| _s , k _f =1,2,...,K _f , the estimated value of e(∞)| _s is obtained as:

$\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; e</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{{\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; f</span>}}}<span\; class="notranslate">\; ,</span><span\; class="notranslate">\; \&infin;</span><span\; class="notranslate">\; )</span>{<span\; class="notranslate">\; |</span>}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; C</span>}}_{{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; f</span>}}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 16</span>}<span\; class="notranslate">\; )</span>$

The rough evaluation process for the discrete variable candidate solution s ∈ S to be evaluated in the outer layer can be summarized as, using the PSO algorithm to solve its corresponding inner sub-model to No. step To obtain historical optimization data e(k _f )| _s , Then use formula (11) and formula (12) to recursively fit the parameter θ of the negative power function (10), and as the final evaluation value of s

4. A scheduling optimization method based on a two-layer nested structure as claimed in claim 1, characterized in that: in said step 2.3), the key step is to calculate the historical minimum penalty value p'(k _f )| _s , And use the feasibility rough judgment model to calculate Then determine the feasibility of s(n _s ,k _s ), the specific implementation steps are as follows:

B. Determination of the feasibility rough judgment model:

Note that e(k _f )| _s is a fixed discrete variable s∈S, the inner stochastic optimization algorithm solves the sub-model And iterate to the evaluation value of step k _f , decompose e(k _f )| _s into the sum of target value and penalty value:

e(k _f )| _s ＝o(k _f )| _s +p(k _f )| _s (17)

Among them, o(k _f )| _s and p(k _f )| _s represent the objective function value and penalty value of the inner stochastic optimization iteration to the k _fth step, respectively.

When the parameters are selected properly and the number of iteration steps tends to infinity, the stochastic optimization algorithm will converge to the global optimal solution with probability 1. Therefore, e(∞)| _s is the optimal target value of the sub-model, that is, the exact evaluation value e ^* | _s of the discrete variable s:

Define the historical minimum penalty value p′(k _f )| _s ,k _f =1,2,...,K _f as:

For the historical minimum penalty value of the discrete variable s p′(∞)| _s , by finding the historical minimum penalty value p′(∞)| _s , the feasibility of the optimal solution in the solution subspace corresponding to the discrete variable s can be determined This is the working process of the feasibility determination model. The calculation process of p′(∞)| _s is similar to that of e(∞)| _s , except that The evaluation value in the expression is replaced by the historical minimum penalty value, and the modified formula (13) is:

The rough decision process for the feasibility of the discrete variable candidate solution s∈S to be evaluated in the outer layer can be summarized as, using the PSO algorithm to solve the corresponding inner sub-model to No. step To obtain historical minimum penalty value data p′(k _f )| _s , Then use formula (11) and formula (12) to recursively fit the parameter θ of the negative power function (10), and As the final historical minimum penalty value p′(∞)| _s of s, then judge its feasibility.

5, a kind of scheduling optimization method based on two-layer nested structure as claimed in claim 1, is characterized in that: in described step 2.5), the key step of outer layer optimization is to utilize outer layer optimization algorithm (GA algorithm) and Feasibility rule method updates the rough preservation set, the specific steps are as follows:

C. Calculation of Outer Layer Optimization

The outer layer optimization uses the inner layer optimization as an evaluation tool for candidate solutions of discrete variables, and uses the basic genetic algorithm (GA algorithm) to solve min _s∈S J(s). The cost of any individual s in the population is defined as The population is continuously updated through iterative calculations with a fixed number of steps, and finally obtained A high-quality discrete variable candidate solution. Its algorithm calculation process is:

Among them, K _s is the maximum number of iteration steps of outer layer optimization, p _c , _pm are the crossover probability and mutation probability of GA algorithm.

6. A scheduling optimization method based on a two-layer nested structure as claimed in claim 1, characterized in that: in said step 3), the key step is to solve s(n _s , K _s )(n _s =1 ,...,N _s ) corresponding to N _s NLP optimization sub-models ${\min }_{f\&Element;f}J(f,\stackrel{\&OverBar;}{\mathrm{the\; s}}){|}_{\stackrel{\&OverBar;}{\mathrm{the\; s}}=\mathrm{the\; s}({\mathrm{no}}_{\mathrm{the\; s}},K_{\mathrm{the\; s}})},$ The specific steps are as follows:

D. Accurately evaluate the solution algorithm

In the stage of accurate evaluation, particle swarm optimization algorithm (PSO algorithm) is used to solve the problem The cost of any individual f in the population is defined as The calculation process of the algorithm is:

in, is the maximum number of optimization iteration steps in the accurate evaluation stage, w, φ _p , φ _g are the speed update weighting coefficients of the PSO algorithm;

Using the above algorithm to accurately solve the current rough optimal set NLP submodel And then get continuous variable solution And the corresponding optimal evaluation value is

The present invention proposes a scheduling optimization method based on a two-layer nested structure, which has the following characteristics and advantages:

(1) The method of the present invention adopts a two-layer nested structure, and the combined optimization problem of the outer layer is solved by the discrete GA algorithm; the non-convex optimization problem of the inner layer is solved by the continuous PSO algorithm.

(2) The method of the present invention adopts two-stage steps. In the rough evaluation stage, the outer discrete GA algorithm finds several optimal candidate solutions from the discrete variable solution space based on the evaluation values obtained by the inner rough evaluation model, and saves them in the rough optimal set. In the precise evaluation stage, the inner continuous PSO algorithm performs precise evaluation on each candidate solution in the rough preservation set through sufficient iterations, and takes the group with the best evaluation value as the final solution of the problem.

(3) The method of the present invention requires the rough model to have a faster evaluation speed, and the evaluation results allow a certain range of noise or deviation. Therefore, the recursive fitting algorithm uses the limited iterative data of the continuous PSO algorithm in the inner layer to estimate the optimal target value of the inner layer sub-model, which can be regarded as a rough evaluation process of the candidate solution of the corresponding discrete variable in the outer layer, and the more sufficient the amount of iterative data , the evaluation result is more accurate but the evaluation efficiency is lower.

(4) The probability of obtaining a satisfactory solution is improved by replacing the conventional optimization algorithm with a single optimal solution with a high-quality rough set. The larger the size of the preserved set, the higher the probability value, but at the same time it will increase the amount of calculation in the accurate evaluation stage.

(5) The method of the present invention adopts the rough judgment model of feasibility and can quickly eliminate infeasible solutions with a high probability, combined with the rough "evaluation" and "optimum" means based on the order optimization thought, the optimization algorithm based on the two-layer structure proposed by the present invention It can ensure that the real satisfactory solution of the scheduling model is obtained with a high probability.

Description of drawings

FIG. 1 is a flow chart of a scheduling optimization method based on a two-level nested structure proposed by the present invention.

Detailed ways

The proposed two-level structure optimization method belongs to a kind of "nested optimization" algorithm. The outer layer of this type of method solves the MIP problem, which is suitable for the stochastic optimization method. Its characteristic is to use the continuous update of multiple solutions for global search without relying on the gradient information of the solution space. The update process of the solution depends on the optimal value obtained by solving the NLP problem of the inner structure, as the basis for screening old solutions and generating new solutions. Essentially, the goal of the screening process is to find better individuals in the target group, and does not care about the precise evaluation value of each individual, only to ensure that the screening results are correct. Therefore, the present invention introduces the idea of order optimization and uses rough evaluation to obtain satisfactory screening results with a relatively high probability. Ordinal optimization is a soft optimization method proposed for stochastic simulation optimization problems. It is proposed to solve stochastic simulation optimization problems that are very time-consuming to evaluate. The purpose is to obtain a satisfactory solution with a higher probability under rough evaluation conditions. The design idea of the ordinal optimization algorithm is to construct a rough evaluation model, imprecisely but quickly evaluate the candidate solutions sampled from the solution space, and select the top few solutions based on the rough evaluation value and the idea of "order" comparison. Satisfactory solutions are estimated as candidate solutions. Since the "sequence" converges at an exponential speed and is robust to bias and noise, there will be at least one true satisfactory solution among the candidate solutions with a high probability.

In the method proposed by the present invention, only the optimal target value of the NLP problem about the continuous variable of the original problem is estimated, instead of finding its global optimal solution, as a rough evaluation of the value of the corresponding discrete variable of the original problem, only the A higher probability results in at least one satisfactory candidate solution for the discrete variable. In this way, after a certain number of iterative steps, the precise evaluation is carried out to obtain the final satisfactory solution. In addition, constrained order optimization was proposed as a means of constraint processing. Its core idea is to construct a rough feasibility judgment model. Before the solution evaluation, the feasibility of the solution is roughly but quickly judged. For the estimated infeasible solution , do not continue to evaluate. Therefore, this method can eliminate infeasible solutions in a probabilistic sense, thereby further saving computation.

For ease of expression, at first illustrate the general form of the MINLP model of the scheduling optimization problem that the present invention aims at:

$\begin{array}{cc}\underset{\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}}{\mathrm{<span\; class="notranslate">\; min</span>}}& \mathrm{<span\; class="notranslate">\; Z</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; )</span>\end{array}$

stg _p (x,y)≤0 p=1,...,P(1)

h _q (x,y)=0 q=1,...,Q

x∈X,y∈Y

Among them, x∈X represents a continuous variable, y∈Y represents a discrete variable, g _p ( ) is an inequality constraint expression, h _q ( ) is an equality constraint expression, f( ), g _p ( ) and There is at least one nonlinear function in h _q (·). For the convenience of explanation, the MINLP model is abbreviated as

$\underset{\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; \&Element;</span>\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; \&Element;</span>\mathrm{<span\; class="notranslate">\; S</span>}}{\mathrm{<span\; class="notranslate">\; min</span>}}\mathrm{<span\; class="notranslate">\; J</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>$

Among them, the optimization variables are discrete quantities s=[s ₁ ,...,s _t ,...,s _T ] and continuous quantities f=[f ₁ ,...,f _p ,...,f _P ], S and F are the solution spaces of two groups of variables respectively. For the above model, the two-layer nested optimization structure is

$\underset{\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; \&Element;</span>\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; \&Element;</span>\mathrm{<span\; class="notranslate">\; S</span>}}{\mathrm{<span\; class="notranslate">\; min</span>}}\mathrm{<span\; class="notranslate">\; J</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&DoubleLeftRightArrow;</span>\underset{\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; \&Element;</span>\mathrm{<span\; class="notranslate">\; S</span>}}{\mathrm{<span\; class="notranslate">\; min</span>}}<span\; class="notranslate">\; (</span>\underset{\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; \&Element;</span>\mathrm{<span\; class="notranslate">\; f</span>}}{\mathrm{<span\; class="notranslate">\; min</span>}}\mathrm{<span\; class="notranslate">\; J</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; ,</span>\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; the\; s</span>}}<span\; class="notranslate">\; )</span>{<span\; class="notranslate">\; |</span>}_{\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; the\; s</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; the\; s</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 3</span>}<span\; class="notranslate">\; )</span>$

In the case of a fixed discrete variable s, the original model degenerates into a relatively simple inner non-convex NLP submodel Only the continuous variable f is left as the decision variable to be optimized. To solve the submodel, the optimal target value is the extreme optimal value corresponding to the discrete variable s

${\mathrm{<span\; class="notranslate">\; e</span>}}^{<span\; class="notranslate">\; *</span>}{<span\; class="notranslate">\; |</span>}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}<span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; \&Element;</span>\mathrm{<span\; class="notranslate">\; f</span>}}{\mathrm{<span\; class="notranslate">\; min</span>}}\mathrm{<span\; class="notranslate">\; J</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; ,</span>\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; the\; s</span>}}<span\; class="notranslate">\; )</span>{<span\; class="notranslate">\; |</span>}_{\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; the\; s</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; the\; s</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 4</span>}<span\; class="notranslate">\; )</span>$

Through the inner optimization solution, each discrete variable candidate solution in the outer discrete space can obtain a limit optimal value. Using the discrete stochastic optimization algorithm to solve the outer combinatorial optimization problem based on the limit optimal value, the global optimal solution s ^* can be obtained:

${\mathrm{<span\; class="notranslate">\; the\; s</span>}}^{<span\; class="notranslate">\; *</span>}<span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; \&Element;</span>\mathrm{<span\; class="notranslate">\; S</span>}}{\mathrm{<span\; class="notranslate">\; min</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; e</span>}}^{<span\; class="notranslate">\; *</span>}{<span\; class="notranslate">\; |</span>}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 5</span>}<span\; class="notranslate">\; )</span>$

The optimal solution of its corresponding sub-model That is, the global optimal value corresponding to the continuous variable.

However, finding the optimal solution of the inner sub-model is very time-consuming, and each discrete variable candidate solution corresponds to an inner sub-model, which makes it impractical to directly solve the two-level optimization problem. If the inner continuous variable optimization problem is regarded as the evaluation problem of the outer discrete variable, then the scheduling optimization problem can be transformed into the inner "evaluation" and outer "optimum" problem of the discrete variable. "Evaluation" accuracy to improve the efficiency of "excellent selection". Specifically, using a rough evaluation model, only a small amount of computing resources are consumed to obtain an estimate of the optimal value of the sub-optimization problem, that is, a rough "evaluation". By comparing the rough evaluations of different discrete variable candidate solutions, the candidate solutions are "optimized". Furthermore, in order to deal with the constraints, a feasibility judgment model is established. Before the evaluation of the discrete variable candidate solutions, the feasibility is roughly but quickly judged. For the candidate solutions that are estimated to be infeasible, the evaluation is not continued. Therefore, infeasible candidate solutions can be eliminated in a probabilistic sense, thereby further saving computation.

The optimization algorithm based on the two-layer nested optimization structure proposed by the present invention includes two main stages of probability selection and accurate evaluation. The probabilistic optimal stage is the key innovation of the present invention. In the probabilistic optimal stage, inner and outer layers of optimization are set. In the inner layer optimization, rough evaluation and screening are carried out for each discrete variable candidate solution, while in the outer layer optimization, the discrete variables are continuously updated. A collection of variable candidate solutions. The inner and outer layers of the algorithm are nested for calculation until the number of update calculations in the outer layer reaches the preset value, and the algorithm enters the stage of precise evaluation. In the accurate evaluation stage, the commonly used continuous optimization method is used to optimize the continuous variables on the basis of a limited number of determined discrete variable candidate solutions, and accurately solve the NLP sub-problems corresponding to each discrete variable candidate solution. Find the final solution to the scheduling optimization problem.

The flow chart of the optimization algorithm based on the two-layer nested structure proposed by the present invention is shown in FIG. 1 .

Specific steps are as follows:

Step 1) Initialize parameters.

Set the parameters of the outer GA algorithm and the inner PSO algorithm, including population size N _s , N _f , PSO speed update weighting coefficients ω, φ _p , φ _g , GA crossover probability p _c and mutation probability p _m , and the maximum number of iteration steps

Step 2) Probability selection stage.

Step 2.1 Set the outer layer optimization iteration step k _s =0, initialize discrete variable candidate solutions s(1,k _s ),...,s(n _s ,k _s ),...,s(N _s ,k _s ).

Step 2.2 If the number of iteration steps k _s of the outer layer optimization does not exceed For s(n _s ,k _s )(n _s =1,...,N _s ) corresponding N _s NLP optimization sub-models Using the inner layer optimization algorithm (PSO algorithm) to iteratively calculate to step, and record historical optimization data $e\left(k_f\right){|}_{\mathrm{the\; s}({\mathrm{no}}_{\mathrm{the\; s}},k_{\mathrm{the\; s}})},p^{\&prime;}\left(k_f\right){|}_{\mathrm{the\; s}({\mathrm{no}}_{\mathrm{the\; s}},k_{\mathrm{the\; s}})}(k_f=1,...,K_f^{\mathrm{FM}}).$

Step 2.3 For s(n _s ,k _s )(n _s =1,...,N _s ), use its historical minimum penalty value and Feasibility Rough Decision Model Estimation Then determine the feasibility of s(n _s , k _s ), that is, to determine

Step 2.4 If s(n _s ,k _s ) is not feasible, keep as rough penalty If s(n _s , k _s ) is feasible, iteratively optimize the sub-model with the inner optimization algorithm (PSO algorithm) to step, record historical optimization data Estimated by rough evaluation model Keep estimates rough evaluation

Step 2.5 According to the obtained rough evaluation value and rough penalty value, use the outer layer optimization algorithm (GA algorithm) and the feasibility rule method to update the rough optimal set

In this step, according to the feasibility rough judgment model of the discrete variable candidate solution, the rough penalty value corresponding to the discrete variable combination s is quickly obtained and feasibility estimates Then it is judged whether to continue to evaluate s. If feasible, further implement rough evaluation to obtain rough evaluation value Based on the above evaluation results, the outer stochastic optimization algorithm solves the following combinatorial optimization problems:

Obtain the former through the outer stochastic optimization algorithm An estimated optimal and feasible discrete variable candidate solution, namely

Save it in the rough premium collection middle. Through the feasibility rule method, the optimal update operation of the outer stochastic optimization algorithm is performed under rough evaluation conditions.

Step 2.6 The number of iterative steps for outer layer optimization k _s =k _s +1. If the number of iteration steps k _s of the outer layer optimization is less than Return to step 2.2. If the number of iteration steps k _s of the outer layer optimization exceeds Then go to step 3).

Step 3) Accurate evaluation stage.

Solve N _s NLP optimization sub-models corresponding to s(n _s ,K _s )(n _s =1,...,N _s ) Using the inner layer optimization algorithm (PSO algorithm) to iteratively calculate to Step to get accurate evaluation value and the corresponding optimal continuous variable solution $f^{*}{|}_{\mathrm{the\; s}({\mathrm{no}}_{\mathrm{the\; s}},K_{\mathrm{the\; s}})}({\mathrm{no}}_{\mathrm{the\; s}}=1,...,N_{\mathrm{the\; s}}).$

Step 4) Determine the final satisfactory solution.

Compare the exact evaluation values of each NLP optimization sub-model According to the following feasibility rules, the optimal group is selected as the satisfactory solution of the scheduling model:

${\mathrm{<span\; class="notranslate">\; f</span>}}^{\mathrm{<span\; class="notranslate">\; g</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; f</span>}}^{<span\; class="notranslate">\; *</span>}{<span\; class="notranslate">\; |</span>}_{{\mathrm{<span\; class="notranslate">\; the\; s</span>}}^{\mathrm{<span\; class="notranslate">\; g</span>}}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 9</span>}<span\; class="notranslate">\; )</span>$

The final satisfactory solution is ${\mathrm{the\; s}}^g=\mathrm{the\; s}(G,K_{\mathrm{the\; s}}^{\max }),f^g=f^{*}{|}_{\mathrm{the\; s}(G,K_{\mathrm{the\; s}}^{\max })},$ in $G=\arg {\min }_{{\mathrm{no}}_{\mathrm{the\; s}}\&Element;\{1,...,N_{\mathrm{the\; s}}\}}{e}^{*}{|}_{\mathrm{the\; s}({\mathrm{no}}_{\mathrm{the\; s}},K_{\mathrm{the\; s}})}.$

In the step 2.2), the key step of the inner layer optimization is to use the feasibility rough judgment model and the rough evaluation model to screen and evaluate the solutions, which is essentially to predict the convergence results of the penalty value and the evaluation value, that is, to use the finite step The numerical information (inner optimization history data) obtained by several iterations is used to estimate the precise convergence value obtained after infinite step iterative calculation. The specific implementation method is to use the negative power function curve to fit the iterative descent process of the penalty value (evaluation value) to obtain the final convergence result. The steps are as follows:

A.1 The inner layer optimizes the acquisition of historical data

The acquisition process of inner optimization historical data is the iterative calculation process of inner optimization algorithm. The present invention adopts particle swarm optimization algorithm (PSO algorithm) to solve The cost of any individual f in the population is defined as $f\left(f\right)=J(f,\stackrel{\&OverBar;}{\mathrm{the\; s}}){|}_{\stackrel{\&OverBar;}{\mathrm{the\; s}}=\mathrm{the\; s}},$ The calculation process of the algorithm is:

Among them, K _f is the maximum number of inner layer optimization iteration steps used to obtain historical data, and w, φ _p , φ _g are the speed update weighting coefficients of the PSO algorithm.

A.2 Solution of Rough Evaluation Model

Since _the negative power function can better describe and predict the variation trend _{of e (} k _{f )} | Fit a negative power function to estimate e(∞)| _s :

$\begin{array}{c}\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; e</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&theta;</span>}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; f</span>}}<span\; class="notranslate">\; )</span>{<span\; class="notranslate">\; |</span>}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; A</span>}<span\; class="notranslate">\; \&Center\; Dot;</span>{{\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; f</span>}}}^{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; B</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; C</span>}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; f</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; ,</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; ,</span><span\; class="notranslate">\; \&infin;</span>\\ \mathrm{<span\; class="notranslate">\; \&theta;</span>}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; A</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; B</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; C</span>}<span\; class="notranslate">\; )</span>\end{array}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 10</span>}<span\; class="notranslate">\; )</span>$

Further adopt the recursive fitting algorithm, when the inner stochastic optimization algorithm obtains new data e(k _f ) _| Parameter θ, until the inner layer algorithm iterates to the number of steps K _f , so that the amount of data meets the fitting accuracy:

in, express The weight coefficient in; Indicates that when the algorithm iterates to k _f steps, the fitting function value and the mean square error between observations e(k _f )| _s :

The initial value of the recursive algorithm is set as follows:

θ ₀ =(A ₀ ,B ₀ ,C ₀ )=(0,0.5,e(1)| _s ) (14)

${<span\; class="notranslate">\; \{</span>\frac{{<span\; class="notranslate">\; \&PartialD;</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}{{<span\; class="notranslate">\; \&PartialD;</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}\mathrm{<span\; class="notranslate">\; \&theta;</span>}}{\mathrm{<span\; class="notranslate">\; J</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&theta;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; \}</span>}^{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; \&epsiv;</span>}<span\; class="notranslate">\; \&Center\; Dot;</span>\mathrm{<span\; class="notranslate">\; I</span>}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 15</span>}<span\; class="notranslate">\; )</span>$

Among them, ε represents a very small constant.

Using optimized historical data e(k _f )| _s , k _f =1,2,...,K _f , the estimated value of e(∞)| _s is obtained as:

$\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; e</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{{\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; f</span>}}}<span\; class="notranslate">\; ,</span><span\; class="notranslate">\; \&infin;</span><span\; class="notranslate">\; )</span>{<span\; class="notranslate">\; |</span>}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; C</span>}}_{{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; f</span>}}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 16</span>}<span\; class="notranslate">\; )</span>$

The rough evaluation process for the discrete variable candidate solution s ∈ S to be evaluated in the outer layer can be summarized as, using the PSO algorithm to solve its corresponding inner sub-model to No. step To obtain historical optimization data e(k _f )| _s , Then use formula (11) and formula (12) to recursively fit the parameter θ of the negative power function (10), and as the final evaluation value of s

In the step 2.3), the key step is to calculate the historical minimum penalty value p′(k _f )| _s , and use the feasibility rough judgment model to calculate Then determine the feasibility of s(n _s , k _s ), the specific implementation steps are as follows.

B. Determination of Feasibility Rough Judgment Model

Note that e(k _f )| _s is a fixed discrete variable s∈S, the inner stochastic optimization algorithm solves the sub-model And iterate to the evaluation value of step k _f . Decompose e(k _f )| _s into the sum of target value and penalty value:

e(k _f )| _s ＝o(k _f )| _s +p(k _f )| _s (17)

Among them, o(k _f )| _s and p(k _f )| _s represent the objective function value and penalty value of the inner stochastic optimization iteration to the k _fth step, respectively.

When the parameters are selected properly and the number of iteration steps tends to infinity, the stochastic optimization algorithm will converge to the global optimal solution with probability 1. Therefore, e(∞)| _s is the optimal target value of the sub-model, that is, the exact evaluation value e ^* | _s of the discrete variable s.

Define the historical minimum penalty value p′(k _f )| _s ,k _f =1,2,...,K _f as:

For the historical minimum penalty value of the discrete variable s p′(∞)| _s , by finding the historical minimum penalty value p′(∞)| _s , the feasibility of the optimal solution in the solution subspace corresponding to the discrete variable s can be determined Judgment, this is the working process of the feasibility judgment model. The calculation process of p′(∞)| _s is similar to that of e(∞)| _s , except that The evaluation value in the expression is replaced by the historical minimum penalty value, and the modified formula (13) is:

The rough decision process for the feasibility of the discrete variable candidate solution s∈S to be evaluated in the outer layer can be summarized as, using the PSO algorithm to solve the corresponding inner sub-model to No. step To obtain historical minimum penalty value data p′(k _f )| _s , Then use formula (11) and formula (12) to recursively fit the parameter θ of the negative power function (10), and As the final historical minimum penalty value p′(∞)| _s of s, then judge its feasibility.

In described step 2.5, the key step of outer layer optimization is to utilize outer layer optimization algorithm (GA algorithm) and feasibility rule method to update the rough optimization set, and concrete steps are as follows:

C. Calculation of Outer Layer Optimization

The outer layer optimization uses the inner layer optimization as an evaluation tool for candidate solutions of discrete variables, and uses the basic genetic algorithm (GA algorithm) to solve min _s∈S J(s). The cost of any individual s in the population is defined as The population is continuously updated through iterative calculations with a fixed number of steps, and finally obtained A high-quality discrete variable candidate solution. Its calculation process is as follows:

Among them, K _s is the maximum number of iteration steps of outer layer optimization, p _c , _pm are the crossover probability and mutation probability of GA algorithm.

In the step 3), the key step is to solve the N _s NLP optimization sub-models corresponding to s(n _s ,K _s )(n _s =1,...,N _s ) ${\min }_{f\&Element;f}J(f,\stackrel{\&OverBar;}{\mathrm{the\; s}}){|}_{\stackrel{\&OverBar;}{\mathrm{the\; s}}=\mathrm{the\; s}({\mathrm{no}}_{\mathrm{the\; s}},K_{\mathrm{the\; s}})},$ The specific steps are as follows:

D. Accurately evaluate the solution algorithm

In the stage of accurate evaluation, particle swarm optimization algorithm (PSO algorithm) is used to solve the problem The cost of any individual f in the population is defined as The calculation process of the algorithm is:

in, is the maximum optimization iteration steps in the accurate evaluation stage, w, φ _p , φ _g are the speed update weighting coefficients of the PSO algorithm.

Using the above algorithm to accurately solve the current rough optimal set NLP submodel And then get continuous variable solution And the corresponding optimal evaluation value is

Claims (5)

1. A scheduling optimization method of a nested structure is characterized by comprising the following steps:

step 1) initializing parameters:

setting parameters of an outer GA algorithm and an inner PSO algorithm, including a population size N_s,N_fPSO velocity update weighting factor ω, φ_p,φ_gGA crossover probability p_cAnd the probability of variation p_mMaximum number of iteration stepsK_s，

Step 2) probability optimization stage;

step 2.1 setting outer optimization iteration step number k_sInitializing a discrete variable candidate solution s (1, k) when equal to 0_s),…,s(n_s,k_s),…,s(N_s,k_s)；

Step 2.2 if the outer layer optimizes the iteration step number k_sNot exceedFor s (n)_s,k_s)(n_s＝1,...,N_s) Corresponding to N_sNLP optimization submodelIterative computation to by inner layer optimization algorithm (PSO algorithm)Step and record historical optimization data

Step 2.3 for s (n)_s,k_s)(n_s＝1,...,N_s) Using its historical minimum penalty value And feasibility coarse decision model estimationAnd then determining s (n)_s,k_s) Determination of feasibility of

Step 2.4 ifs(n_s,k_s) Infeasible, reserveAs a coarse penalty valueIf s (n)_s,k_s) Feasible, iterative optimization submodel with inner layer optimization algorithm (PSO algorithm)ToStep, recording historical optimization dataEstimation using a coarse evaluation modelPreserving estimatesAs roughness evaluation value

Step 2.5, according to the obtained rough evaluation value and rough penalty value, updating a rough guarantee set by utilizing an outer layer optimization algorithm (GA algorithm) and a feasibility rule method

In the step, according to a feasibility rough judgment model of a discrete variable candidate solution, a rough penalty value corresponding to a discrete variable combination s is quickly obtainedAnd feasibility estimationFurther judging whether to continue evaluating s; if the evaluation is feasible, further performing rough evaluation to obtain a rough evaluation valueBased on the above evaluation results, the outer layer random optimization algorithm optimizes the problem by solving the following combinations:

(6)

before obtaining by outer layer random optimization algorithmA candidate solution of a discrete variable that estimates the best and feasible, i.e.

(7)

And is

Store it in the rough keep-good setIn (1). Is carried out under rough evaluation conditions by a feasibility rule methodPerforming optimization updating operation on the outer layer random optimization algorithm;

step 2.6 outer optimization iteration step number k_s＝k_s+1 if outer optimization iteration step number k_sIs less thanReturning to step 2.2, if the outer layer optimizes the iteration step number k_sExceedStep 3) is entered;

step 3) accurate evaluation stage:

solving for s (n)_s,K_s)(n_s＝1,...,N_s) Corresponding to N_sNLP optimization submodelIterative computation to by inner layer optimization algorithm (PSO algorithm)Step of obtaining an accurate evaluation valueAnd corresponding optimal continuous variable solution

Step 4) determining a final satisfactory solution:

comparing the accurate evaluation values of each NLP optimization submodelAnd taking an optimal group as a satisfactory solution of the scheduling model according to the following feasibility rule method:

and is

(8)

Wherein,

the final satisfactory solution isWherein

2. The scheduling optimization method based on the two-layer nested structure as claimed in claim 1, wherein: in the step 2.2), a key step of inner layer optimization is to utilize a feasible rough judgment model and a rough evaluation model to perform solution screening and evaluation, and essentially predict convergence results of penalty values and evaluation values, that is, numerical information (inner layer optimization historical data) obtained by finite step number iteration is used to estimate an accurate convergence value obtained after infinite step iteration calculation, and a specific implementation means is to fit an iterative descending process of the penalty values (evaluation values) with a negative power function curve to obtain a final convergence result, and the specific steps are as follows:

a.1 acquisition of inner-layer optimization historical data

The process of obtaining the inner optimization historical data is a process of iterative calculation of an inner optimization algorithm. The invention adopts Particle Swarm Optimization (PSO) algorithm to solveCost definition of any individual f in a populationIs composed ofThe algorithm calculation process is as follows:

wherein, K_fOptimizing iteration steps, w, phi, for a maximum inner layer for obtaining historical data_p,φ_gUpdating the weighting coefficient for the speed of the PSO algorithm;

a.2 solving of the coarse evaluation model

Because the negative power function can better describe and predict e (k)_f)|_sUsing the optimization history data e (k)_f)|_s,k_f＝1,2,...,K_fFitting a negative power function to estimate e (∞) luminance_s：

(10)

θ＝(A,B,C)

Further adopting a recursion fitting algorithm, and obtaining new data e (k) in each iteration of the inner-layer random optimization algorithm_f)|_sThe fitting parameter θ is then analytically updated with minimal computation by the following recursions (11) and (12) until the inner-layer algorithm iterates to the number of steps K_fSo that the data amount satisfies the fitting accuracy:

k_f＝1,2,...,K_f

k_f＝1,2,...,K_f

wherein,to representThe weight coefficient of (1);indicates when the algorithm iterates to k_fStep time, fit function valueAnd the observed value e (k)_f)|_sMean square error between:

the initial value of the recursion algorithm is set according to the following method:

θ₀＝(A₀,B₀,C₀)＝(0,0.5,e(1)|_s) (14)

wherein, a very small constant is represented;

using optimized historical data e (k)_f)|_s,k_f＝1,2,...,K_fObtaining the current information of e (∞)_sThe estimated values of (c) are:

aiming at the S-belonged discrete variable candidate solution S of the outer layer to be evaluatedThe rough evaluation process can be summarized as that the corresponding inner layer submodel is solved by utilizing the PSO algorithmTo the firstStep by stepTo obtain historical optimization dataFitting parameters theta of the negative power function (10) by recursion of an equation (11) and an equation (12), and performing the fittingFinal evaluation value as s。

3. The scheduling optimization method based on the two-layer nested structure as claimed in claim 1, wherein: in said step 2.3), the key step is to calculate the historical minimum penalty value p' (k)_f)|_sAnd calculating by using a feasibility rough judgment modelAnd then determining s (n)_s,k_s) The method comprises the following specific implementation steps:

B. determination of feasibility rough decision model:

note e (k)_f)|_sSolving the sub-model by the inner-layer random optimization algorithm under the condition that the fixed discrete variable S belongs to SAnd iterate to the kth_fEvaluation value of step e(k_f)|_sThe sum of the target value and the penalty value is decomposed as:

e(k_f)|_s＝o(k_f)|_s+p(k_f)|_s (17)

wherein, o (k)_f)|_sAnd p (k)_f)|_sRespectively representing the inner layer random optimization iteration to the k < th >_fObjective function value and penalty value of step.

When the parameters are selected properly and the iteration step number tends to be infinite, the random optimization algorithm converges to the global optimal solution with the probability of 1. Thus, e (∞) ventilation_sAs an optimal target value for the submodel, i.e. an accurate evaluation value e for a discrete variable s^*|_s：

Defining a historical minimum penalty value p' (k)_f)|_s,k_f＝1,2,...,K_fComprises the following steps:

historical minimum penalty value for discrete variable s is p' (∞) & gt_sBy solving for historical minimum penalty value p' (∞) & gtluminance_sThe feasibility determination of the optimal solution in the solution subspace corresponding to the discrete variable s can be carried out, namely the working process of the feasibility determination model, p' (∞) · survival_sCalculating process of (1) and e (∞) luminance_sIs similar to but only willThe evaluation value in the expression is replaced by a historical minimum penalty value, and the modified expression (13) is as follows:

the feasibility rough judgment process aiming at the discrete variable candidate solution S belonging to S to be evaluated at the outer layer can be summarized as that the corresponding inner layer sub-model is solved by utilizing the PSO algorithmTo the firstStep by stepTo obtain historical minimum penalty value dataFitting parameters theta of the negative power function (10) by recursion of an equation (11) and an equation (12), and performing the fittingFinal historical minimum penalty value p' (∞) as s_sThen, the feasibility of the test piece is determined.

4. The scheduling optimization method based on the two-layer nested structure as claimed in claim 1, wherein: in the step 2.5), the key step of outer layer optimization is to update a rough guarantee set by using an outer layer optimization algorithm (GA algorithm) and a feasibility rule method, and the specific steps are as follows:

C. calculation of skin optimization

The outer layer optimization and the inner layer optimization are used as evaluation tools of discrete variable candidate solutions, and a basic genetic algorithm (GA algorithm) is adopted to solve min_s∈SJ(s), the cost of any individual s in the population is defined asContinuously updating the population by iterative calculation of fixed step number to finally obtainAnd (4) solving the high-quality discrete variable candidate solution. The algorithm calculation process is as follows:

wherein, K_sOptimizing the number of iteration steps, p, for the maximum skin_c,p_mCross probability and mutation probability of the GA algorithm.

5. The scheduling optimization method based on the two-layer nested structure as claimed in claim 1, wherein: in the step 3), the key step is to solve s (n)_s,K_s)(n_s＝1,...,N_s) Corresponding to N_sNLP optimization submodelThe method comprises the following specific steps:

D. precise evaluation solving algorithm

Solving by adopting Particle Swarm Optimization (PSO) algorithm in the accurate evaluation stageThe cost of any individual f in the population is defined asThe algorithm calculation process is as follows:

wherein,maximum number of iteration steps, w, phi, for the precise evaluation phase_p,φ_gUpdating the weighting coefficient for the speed of the PSO algorithm;

accurately solving the current rough optimization-preserving set by utilizing the algorithmNLP submodel Further obtainSolution to continuous variableAnd a corresponding optimum evaluation value of