CN110348576A

CN110348576A - A kind of decision-making technique for improving multiple target bacterial chemotaxis algorithm based on index

Info

Publication number: CN110348576A
Application number: CN201910633804.8A
Authority: CN
Inventors: 卢志刚; 姚伟涛
Original assignee: Yanshan University
Current assignee: Yanshan University
Priority date: 2019-07-15
Filing date: 2019-07-15
Publication date: 2019-10-18

Abstract

The invention discloses a kind of decision-making techniques that multiple target bacterial chemotaxis algorithm is improved based on index, belong to system optimization decision domain.The present invention is first to I_sde+Index solves non-convex problem and is improved, and proposes a kind of fusion I_sde+Improvement MOBCC algorithm -- the BIMOBCC of index.The improvement strategy of this method mainly has: using domination concept as main criteria, I in disaggregation selects_sde+Index value is as secondary criterion；Using the relatively middle non-domination solution generated of external archival storage disaggregation and the new non-domination solution generated using NDX crossover operator, the search capability of algorithm is increased；Using I_sde+The foundation that index is updated as external archival, and next-generation solution is updated using external archival.The validity of improved method is demonstrated finally by ZDT series of functions, demonstrates the practicability of improved method by solving electric heating integrated dispatch problem.The present invention is of great significance to the multi-objective optimization question solved in practical application.

Description

Decision-making method for improving multi-target bacteria chemotaxis algorithm based on indexes

The technical field is as follows:

the invention relates to the field of system optimization decision-making, in particular to a decision-making method for improving a multi-target bacterial chemotaxis algorithm based on indexes.

Background art:

the complexity of global optimization problems has increased significantly over the past few decades and has expanded into multi-objective optimization problems. In the multi-objective optimization problem, the nature of the optimization problem is extremely complex, and a plurality of targets which are optimized simultaneously are interactive and conflict with each other, such as in enterprise production activities, product quality and production cost are two conflicting targets. The calculation amount of multi-objective solution is greatly increased, and the traditional deterministic optimization methods such as linear programming, nonlinear programming, iteration methods, gradient methods and the like can not meet the requirements of actual calculation. The intelligent evolutionary algorithm is a random search algorithm simulating biological natural selection and natural planning, for example: evolutionary algorithms, group intelligence algorithms, simulated annealing algorithms, tabu search algorithms, neural network algorithms, and the like. The method is widely applied to solving of highly complex nonlinear problems, has good universality, and fully embodies the advantages of the evolutionary intelligent algorithm when solving the complex system optimization problem with only a single target, so that a series of multi-target intelligent evolutionary algorithms appear for the optimization problems of a plurality of targets. Due to the unique advantages and mechanisms of the algorithms, the algorithms are widely concerned by scholars at home and abroad, the research enthusiasm is raised, and the algorithms are successfully applied to a plurality of fields such as signal processing, image processing, production scheduling, task allocation, mode recognition, automatic control, mechanical design and the like.

The multi-objective evolutionary intelligent algorithm can be classified into a polymerization function type, an index evaluation type and a pareto domination type according to different evolutionary modes. Most of the traditional intelligent algorithms at present are mostly based on the pareto dominance type, but the solution capability of the pareto dominance type to the high-dimensional multi-target problem is insufficient, and the index evaluation-based method becomes a research hotspot. In addition, research for improving the performance of the evolutionary algorithm by a method based on the fusion of a pareto mechanism and an index mechanism is made.

The bacterial chemotaxis algorithm (BC) is a group intelligent optimization algorithm which is proposed by doctor M ü according to different movement laws of bacteria under different chemical attractant concentrations in 2002, is widely applied to single-target optimization problems such as power grid fault first-aid repair, micro-grid planning and reactive power optimization of a power system and has good effect as a novel group intelligent algorithm, and has certain research significance for solving multi-target problems.

The invention content is as follows:

the invention provides a decision-making method for improving a multi-target bacteria chemotaxis algorithm based on indexes, which is based on I_sde+The method of indexes is introduced into the MOBCC algorithm based on a domination framework and aims at the defect of the method on non-convex problems to I_sde+The value is perfected, and new I is provided_sde+Value calculation method, then on the basis of the basic BCC search, using I_sde+The value is used as evaluation index, the pareto dominance is used as the primary criterion of individual comparison, and I_sde+The value is used as a secondary criterion for individual comparison; preserving the non-dominated individuals generated in the comparison process, and generating new individuals by using a normal distribution crossover operator (NDX); the convergence rate of the multi-target problem solved by the multi-target bacterial chemotaxis algorithm (MOBCC) is further improved, the convergence and diversity of the solution set are finally obtained, and the applicability of the algorithm in the multi-target problem is improved.

In order to solve the technical problems, the technical scheme provided by the invention is as follows: an optimization method for improving a multi-target bacterial chemotaxis algorithm based on indexes is characterized in that basic data are obtained in a system to establish a system model; determining a plurality of objective functions based on a system model, and optimizing the objective functions by adopting an index-based improved multi-objective bacterial chemotaxis algorithm; using the optimized solution in a system model to make system decision; the method is characterized in that: the index-based multi-target bacteria chemotaxis improvement algorithm comprises the following steps:

1) setting basic parameters and generating an initialized population P;

2) executing a basic BCC search strategy on each individual in the population P in the step 1), obtaining two to-be-determined positions of individual movement and population movement, and executing feasibility verification and adjustment on the two to-be-determined positions;

3) according to the function values corresponding to the two to-be-positioned positions searched in the step 2), the functions are dominated by pareto and improved I_sde+Index (I)For comparison criteria: if the positions are mutually dominant, the non-dominant position is taken as a new position, if the positions are not mutually dominant, the position corresponding index value is larger than the new position, and the smaller position is stored in an external archive EXA 1; if the function value corresponding to the new position is dominated by the function value corresponding to the original position, taking the original position as the new position; executing the judging method for each individual to obtain a new group position and an external archive EXA 1;

4) updating the archive EXA1 obtained in the step 3) to an external archive; selecting part of individuals with excellent corresponding index values from the new group obtained in the step 3), executing an NDX (named data reduction) crossing strategy to obtain a new position, executing feasibility verification and adjustment, and updating the new position into an external file; if the number of external archives is larger than the upper limit, executing the step 5), otherwise executing the step 6);

5) executing an external archive update policy: firstly, performing non-dominance comparison on external archives, deleting an archive individual corresponding to a dominance solution, if the non-dominance comparison is still larger than an upper limit, calculating a corresponding index value, and deleting an individual with a small value until the requirement of the number of the external archives is met;

6) updating the new population P obtained in the step 3) according to individuals in an external archive to obtain a new generation population Q;

7) and (5) judging whether the termination condition is met, if so, outputting a result, and if not, performing the step 2).

After improvement I_sde+The calculation formula of the index is shown as the following formula:

in the formula: p, q' represent individuals in the population; dist (p, q)_i') denotes the individual p, and the individual q_i' similarity is Euclidean distance, where p, q_i' belongs to P and P ≠ q_i', P is a population set; and q is_i' is q_iShifted solution, a solution q_iMove to a new location q_iThe formula of' is as follows:

in the formula, p (j), q (j), and q '(j) represent target values of the individuals p, q, and q' in the j-th dimension, respectively, and m is a target dimension;

P_SB(P)set of individuals representing the sum of function values for which the sum of objective function values in the population P is less than the sum of function values for P, if SB (q)<SB (P), then q ∈ P_SB(p)；N_SB(p)For the number of individuals in the set, the objective function value and solving formula for individual x are as follows

In the formula, f_i(x) Is the function value of the individual x on the ith question, and m is the total number of sub-targets.

The invention adopts the technical scheme and has the beneficial effects that: the invention builds a basic framework of the algorithm, the algorithm takes a pareto mechanism as a primary criterion of solution comparison, and if the pareto mechanism and the pareto mechanism are mutually non-dominant solutions, improved I is used_sde+Selecting a better solution by using the index value as a secondary criterion, wherein the improved I_sde+The index solves the defect of non-convex problem; an external archiving strategy is adopted, and the externally archived individuals are mainly composed of I_sde+The variation of the index difference is generated, suboptimal solutions in non-dominated solutions are formed, each generation of individuals are compared and updated by using external files, and the distribution and convergence of an optimal solution set can be improved; simulation tests prove that the BIMOBCC based on indexes can solve the problem that the solution sets obtained by the MOBCC algorithm in the multi-target problem are not uniformly distributed and the applicability of the MOBCC algorithm in the high-dimensional multi-target problem is high.

Description of the drawings:

FIG. 1 is a flow chart of an optimization method for improving a multi-target bacterial chemotaxis algorithm based on indexes according to the invention;

FIG. 2 is a simulation result of the algorithm of the present invention at test function ZDT 1;

FIG. 3 is a simulation result of the algorithm of the present invention at test function ZDT 2;

FIG. 4 is a simulation result of the algorithm of the present invention at test function ZDT 3;

FIG. 5 is a simulation result of the algorithm of the present invention at test function ZDT 4;

FIG. 6 is a simulation result of the algorithm of the present invention at test function ZDT 6;

FIG. 7 is a simulation result of the algorithm of the present invention at test function CONVEX 60;

FIG. 8 is a schematic diagram of an electrothermal model of an actual solution case used in the present invention;

FIG. 9 is a simulation result of the algorithm of the present invention in a practical electro-thermal scheduling application;

the specific implementation mode is as follows:

the invention discloses an optimization method for improving a multi-target bacteria chemotaxis algorithm based on indexes, wherein in a system, basic data are obtained to establish a system model; determining a plurality of objective functions based on a system model, and optimizing the objective functions by adopting an index-based improved multi-objective bacterial chemotaxis algorithm; using the optimized solution in a system model to make system decision; the method is characterized in that: the index-based multi-target bacteria chemotaxis improvement algorithm comprises the following steps:

1) setting basic parameters and generating an initialized population P;

3) according to the function values corresponding to the two to-be-positioned positions searched in the step 2), the functions are dominated by pareto and improved I_sde+The indexes are comparison criteria: if the positions are mutually dominant, the non-dominant position is taken as a new position, if the positions are not mutually dominant, the position corresponding index value is larger than the new position, and the smaller position is stored in an external archive EXA 1; if the function value corresponding to the new position is dominated by the function value corresponding to the original position, taking the original position as the new position; executing the judging method for each individual to obtain a new group position and an external archive EXA 1;

Preferred embodiment of the invention, modified I_sde+The calculation formula of the index is shown as the following formula:

in the formula: p, q' represent individuals in the population; dist (p, q)_i') denotes the individual p, and the individual q_i' similarity, i.e. Euclidean distance (where p, q_i' belongs to P and P ≠ q_i', P is a population set); and q is_i' is q_iShifted solution, a solution q_iMove to a new location q_iThe formula of' is as follows:

P_SB(P)set of individuals representing the sum of function values for which the sum of objective function values in the population P is less than the sum of function values for P (if SB (q))<SB (P), then q ∈ P_SB(p))，N_SB(p)For the number of individuals in the set, the objective function value and solving formula for individual x are as follows

The invention introduces a basic bacterial chemotaxis algorithm searching method; then, an applied improvement strategy and an applied step are explained in detail, and a flow framework of a BIMOBCC algorithm is built; finally, the improved algorithm and other multi-target algorithms are compared by using a plurality of standard test functions and evaluation indexes, and the effectiveness of the algorithm is proved. The method comprises the following specific steps:

1. introduction of basic bacterial chemotaxis algorithm

The BCC algorithm is an advanced intelligent optimization algorithm developed in recent years, has excellent solving capability, can solve not only a single-target problem, but also a complex n-dimensional multi-target problem, namely the single-target problem when n is 1, is actually unique in solution to the single-target function problem, and finally, the problem is also explained by the convergence of all bacteria on the same point of the single-target BCC algorithm. When n >1 all bacteria will no longer converge to the same point, but there are many different solutions, the set of these solutions is usually called Pareto solution set, when n 2, the Pareto solution appears as a curve; when n is 3, the Pareto solution should be distributed on a curved surface, and so on. For the judgment of the convergence of the algorithm, the convergence speed, the convergence accuracy and the solution uniformity are usually adopted for measurement.

The BCC algorithm flow is as follows:

(1) the location of the bacteria is initialized and randomly distributed at different locations within the feasible domain.

(2) Initialization of parameters, determining initial precision epsilon_beginFinal precision ε_endAnd an update constant alpha.

(3) Determining a system parameter T₀、b、τ_c。

T₀＝ε^0.30·10^-1.73 (1)

b＝T₀(T₀ ^-1.54·10^0.60) (2)

(4) The velocity of the bacteria is set to a constant value, and v is generally 1.

(5) The values of the movement time τ of the bacteria in the new direction are calculated following the following distribution:

the parameter T is determined by:

wherein, T₀＝ε^0.03·10^-1.73，T₀＝ε^0.03·10^-1.73，b＝T₀·(T₀ ^-1.54·10^0.6)。T₀For a given travel time, f_prIs the difference between the function values of the current iteration and the previous iteration,/_prB is a fixed parameter representing the modulus of the vector between the current generation bacterial site and the previous generation bacterial site.

(6) The bacteria movement direction was calculated. The new direction deviates to the left or right from the original trajectory respectively, following the following gaussian probability distribution:

wherein their desired μ ═ e (x) and varianceAre respectively given as follows:

if it is notμ＝62°(1-cos(θ))，σ＝26°(1-cos(θ))，τ_prThe duration of a motion trajectory on the bacteria; if it is notμ＝62°，σ＝26°。

(7) Calculating the new position of the bacteria in the current generationWhereinIs a new position of the bacteria,is the position of the bacteria on the last iteration process,is the direction vector of the new track, l is the length of the new track.

(8) Assuming that each bacterium can sense the position of all other bacteria, for the k-th generation of bacterium i, the better surrounding bacteria were explored, and the center points of these better bacteria were calculatedAnd a random length of travel toward the central storeDetermining positionWhere rand () is a random number situated between (0,2) subject to uniform distribution, the center point of the partner with better position around bacterium i is defined byDetermined by the following formula:

wherein,is the distance between bacterium i and bacterium j.

(9) For the bacteria i at the k generation position, determining a new position at the step number k +1 according to BC algorithm based on the position information of the last steps memorized by the bacteria i

(10) ComparisonAndif it isThen the bacteria move to step k +1Otherwise move toTo obtain

(11) ComparisonAndif it isThen the bacteriumMove to step k +1Otherwise, move to pointTo obtain

(12) And (5) repeating the steps (3) - (10) until the termination condition is met.

The BCC algorithm gives consideration to the search of single bacteria and the mutual perception among the bacteria, has good local search and global perception capability, and has certain advantages for solving a multi-target problem. At present, the multi-objective BCC algorithm is widely applied to reactive power optimization of a power distribution network, reactive power optimization of a power system, daily active power dispatching of a generator set, fault rush-repair of the power distribution network and the like, and good application results are obtained. The BCC algorithm is an inherent excellent algorithm, has a value of continuous research and has strong application potential.

2. Improved policy introduction and application

The basic mocbc algorithm is a method belonging to the pareto mechanism, that is, besides the pareto dominance criterion, a secondary criterion must be used for non-dominance solution selection to ensure the diversity of the final solution set; inspired by research based on fusion of index framework and pareto dominant framework, the invention introduces I_sde+The index is used as a criterion for comparing the non-dominant solutions; in order to fully utilize the advantages of the BCC algorithm, adding a non-dominant solution in the comparison process into an external archive; and partial individuals are selected to execute the NDX crossover operator, so that the solving speed of the algorithm is further improved. The improvement strategy employed by the present invention is described in detail below.

2.1、I_sde+Establishment and improvement of index

In the process of comparing and searching new positions generated in the flow of the attached figure 1, indexes are introduced as the criterion of non-dominant solution comparison, but due to the influence of an index calculation rule, the value of a non-convex solution set individual cannot represent the quality of the individual, so the index calculation rule is firstly perfected to be suitable for the non-convex problem, and then the basic MOBCC algorithm is applied. The following is a detailed description and perfection of the calculation index, and the specific application steps of the present invention.

2.1.1, moving Density estimation strategy SDE

I_sde+The index is developed by a density estimation method SDE based on movement, and different from other density estimation strategies, the SDE simultaneously contains distribution information and convergence information of individuals. The method has good effect on solving the problems of low dimension and high dimension and multiple targets.

When density estimation is carried out on an individual P in a population, the convergence of other individuals and the convergence of P on a target in each dimension is compared, whether other individuals are moved to the position of the P in the dimension is judged, and if the performance of one or some individuals on the target in the dimension is better than that of the individual P, the individuals are moved to the position of the individual P in the target in the dimension; otherwise, the positions of other individuals are kept unchanged;

for minimization problems, the density D' (P, P) of an individual P in a population can be expressed as

D′(p，P)＝SF{dist(p,q₁′),dist(p,q₂′)…dist(p,q_N-1′)} (9)

In the formula: n represents the size of P, dist (P, q)_i') denotes the individual p, and the individual q_i' similarity (p, q)_i' belongs to P and P ≠ q_i'), SF, represents a functional relationship. And q is_i' is q_iShifted solution, a solution q_iMove to a new location q_iThe formula of' is as follows:

in the formula, p (j), q (j), and q '(j) represent target values of p, q, and q' in the j-th dimension, respectively, and m is the target dimension

2.1.2, sub-targeting function and

in solving a multi-objective optimization problem (MOP), in order to be able to use scalar values for direct comparisons between individuals, fitness assignments need to be made to map to one spatial dimension. Goal Sum (SB) is a special case of sub-goal weight assignment, all weights are set to 1, and normalization of the goal values is a necessary condition for making the goal function and independent. The mass of the individual x is represented by the sum of the multi-objective function values, and the calculation formula is as follows

In the formula: f. of_i(x) Is the function value of x on the ith problem, and m is the total number of sub-targets

2.1.3、I_sde+Value solving

Fusing the sum of the targets into SDE, a new index (I) is generated_sde+) When solving for MOP with m minimum targets, to obtain I_sde+Indexes, and the solutions in the population are sorted according to the target sum. If the evaluation index of one solution is required, only the target sum of the other solutions is less than the sum of the function values of the solution, and the calculation complexity is reduced to a certain extent. One solution of p to I_sde+The calculation formula is shown below

In the formula: p_SB(P)A set of individuals representing a sum of function values in the population P for which the sum of objective function values is less than P, N_SB(p)Is the number of individuals in the set, has the highest value I_sde+The solution of (a) is considered to be better.

I_sde+Is a fusion of the objective function and the SDE, each with improved convergence and density estimation capabilities. The function sum is fused into the SDE index, and the selection pressure of the solution is utilized while the diversity of population members is kept, so that the solution is developed towards the front direction of the optimal pareto.

2.1.4 for I_sde+Improvement of

As can be seen from equation (12), if a comparison set P of individuals is present_SB(P)Is an empty set, i.e. there is no functional sum ofSmall individuals, then the_sde+A value of 0 can easily be eliminated during the selection process. If the solution is a non-convex problem, for the optimal solution of a sub-target, the solution's I_sde+A value of 0 is very easy to replace during the update, and the solution is exactly what we want to keep. So we are right to I_sde+The improvement is carried out, if the solving problem is a non-convex problem, a larger value 1 is assigned to the sub-target optimal solution, so that the sub-target optimal solution can be reserved in the comparison process, and the diversity of results is ensured. Then I_sde+The calculation formula of the index is shown as the following formula:

2.1.5 applications to improve MOBCC

In the invention, the individual position x obtained by executing BCC algorithm is obtained firstly_i,new1And group perception position x_i,new2Using the pareto mechanism as a main criterion, I_sde+And (3) as a secondary criterion, carrying out comparison selection on the solution set to generate a next generation solution, wherein the selection process of the solution is shown as Algorithm 1

After the BCC search strategy is executed in the flow of the attached figure 1, a new position of bacteria is determined according to the obtained position obtained by interaction between the self moving position of an individual and a group, in addition, a non-dominant solution can be reserved, and the advantages of a BCC algorithm are fully utilized; the concrete description is as follows

1) For an individual, firstly calculating a function value corresponding to a position obtained by interaction of the self moving position of the individual and a group, if the function value is dominant to each other, turning to the step 2), and if not, turning to the step 3);

2) selecting non-dominant individuals as new positions of the bacterial individuals, deleting dominant individuals, and turning to step 4);

3) calculating I corresponding to two non-dominant solutions according to formula (13)_sde+Selecting an individual with a large index value as a new position of the bacterial individual, storing another non-dominant individual to an external archive, and turning to the step 4);

4) if the function value of the new position is governed by the original position, the new position is the original position, and the comparison process is ended;

this comparison criterion was performed on all individuals, resulting in new locations after the movement of the bacterial population, and the retention of non-dominated external archives (denoted as EXA 1).

2.2, NBX Cross operator update

In order to further improve the convergence speed and the convergence performance of the algorithm, a part of individuals are selected to execute the NDX crossing strategy. In the flow of the attached figure 1, new positions of bacterial colonies are generated, and the method selects individuals from the new positions for cross updating to obtain the new positions, so that the convergence rate of the algorithm can be improved. The principles of the crossover strategy are described in detail below, as well as specific applications within the present invention.

The classical SBX operator (simulatedBinary crossbar) Crossover operator can transmit excellent individual genes in a father body to a certain substring of the next generation, so that the substring has the characteristic superior to that of the father string, the convergence of a genetic algorithm to a global optimal solution is ensured, the strategy has the advantage of excellent genes of the substring genetic father string, but the strategy has the limitation that the global search performance of the Crossover operator is relatively weak, and the population diversity cannot be well ensured; the related literature uses a normal distribution crossover operator, and a new crossover operator is provided:

a) and a normal distribution crossover operator (NDX) is introduced to enhance the space searching capability of the algorithm. Suppose the parent is p₁、p₂Generating a sub-generation of x using NDX₁、x₂. For the ith variable, the interleaving procedure is as follows:

(a) a random number te (0,1) is generated.

(b) If t is less than or equal to 0.5, then

(c) If t is greater than or equal to 0.5, then

Wherein: selecting an elite particle as one of the parents, wherein N (0,1) is a normal distribution random variable;

in the present invention, I is used_sde+Partial individuals are selected by indexes to carry out NDX cross calculation, a set EXA2 is obtained and added into an external archive, the convergence and diversity of the multi-target solution set are improved, and the specific steps are shown in Algorithm 2.

The method can generate more excellent new individuals by utilizing better bacteria individuals after generating the new group positions obtained by comparison in the flow of the attached figure 1, and further improves the searching capability of the algorithm; the specific application steps are as follows:

1) i corresponding to the new position of the group obtained by calculation_sde+Indexes are obtained, sequencing is carried out, and N1 larger bacteria individuals are selected;

2) respectively calculating the offspring individuals of the selected individuals according to formulas (14) and (15);

3) performing feasibility verification and adjustment on the filial generation individuals: if the individual exceeds the upper limit or the lower limit, taking the corresponding limit value;

4) comparing the verified filial generations, if the two filial generations are dominant to each other, deleting the dominant filial generation, and recording the non-dominant filial generation into an external archive (EXA 2); if two children do not dominate each other, the 2 children are all logged into an external archive (EXA 2);

2.3 external archive update policy

In order to limit the number of external archives generated by the retention comparison of the non-dominant solution and the NDX crossover in the flow of fig. 1, and reduce the computational complexity, the external archives must be compared and updated, and the detailed description of the external archives and the external archive updating strategy applied by the present invention are as follows.

Another reason for studying group intelligence is redundancy. For example, if there is only one robot in the Mars mission, the action is ended if the robot is broken. If a plurality of robots are provided, other robots can replace the missing robots to work, and the stability of the whole system is improved. In addition, for many tasks, the efficiency of the several agents is much higher, and if regional search and collection tasks are to be performed on mars, the search process can be greatly accelerated by adopting multi-robot collaborative search.

An external archive (EXA) is a set for storing mutually independent solutions obtained by respective generations.

A series of mutually independent solutions constitutes a Pareto Optimal Front (POF). The set of mutually independent solutions is stored in an external storage archive.

The non-dominant solution of the external archive record is directly operated to obtain the available non-dominant solution, so as to achieve the aim of making the solution distributed at the front edge of the pareto more uniform. The sources of the externally archived individuals in the present invention are mainly from non-dominant solution comparisons and based on I_sde+The variation of the index and the updating process of the external archive are shown as Algorithm 3:

the method updates archives (EXA1, EXA2) generated by retaining and comparing non-dominated solutions and NDX intersection to an external archive (EXA), and comprises the following specific steps:

1) initializing external archives, and defining the number limit EXA of the archives;

2) if the non-dominated solution retains individuals in the generated archive EXA1, independent of the EXA individuals, adding the EXA1 individuals to the EXA;

3) if the individuals in the file EXA2 generated by the crossover strategy are independent of the EXA individuals, adding the EXA2 individuals to the EXA;

4) if the number of archives is larger than the upper limit EXA, calculating I corresponding to the EXA individual_sde+Index values are ranked, and better limitrexa individuals are selected as new external archives;

building of BIMOBCC Algorithm framework

By combining the above methods, the invention provides a new BCC Algorithm-BIMOBCC based on index improvement by using indexes on the basis of the basic MOBCC Algorithm, and the flow chart of the frame of the provided Algorithm is shown as Algorithm4, and the specific steps are as follows:

1) setting basic parameters and generating an initialized population P;

2) executing a basic BCC search strategy on each individual in the population to obtain two to-be-determined positions of individual movement and population movement, and executing feasibility verification and adjustment on the two to-be-determined positions;

3) according to the function values corresponding to the two to-be-positioned positions searched in the step 2), using the pareto dominance and I_sde+The indexes are comparison criteria: if the positions are mutually dominant, the non-dominant position is taken as a new position, if the positions are not mutually dominant, the position corresponding index value is larger than the new position, and the position with smaller value is stored in an external archive EXA 1; if the function value corresponding to the new position is dominated by the function value corresponding to the original position, taking the original position as the new position; executing the judging method for each individual to obtain a new group position and an external archive EXA 1;

4) updating the archive EXA1 obtained in the step 3) to an external archive; selecting part of individuals with excellent corresponding index values from the new group obtained in the step 3), executing an NDX (named data interchange) crossing strategy to obtain a new position, carrying out feasibility verification and adjustment, and updating the new position into an external archive; if the number of external archives is larger than the upper limit, executing the step 5), otherwise executing the step 6);

7) judging whether a termination condition is met, if so, outputting a result, and if not, performing the step 2);

4. comparing the test result with the evaluation index

The performance test of the modified BCC algorithm will be done here by running it to solve 6 standard test functions. These 6 functions include 5 dual target standard test functions (ZDT series) and 1 triple target standard test function (Convex 60). Details of these test functions are shown in table 1. Meanwhile, in order to verify the effectiveness of the improved algorithm, the section compares and analyzes the result obtained by BIMOBCC and the result obtained by basic MOBCC, NSGA-II and GBCC algorithms through evaluation indexes by testing 5 ZDT series standard functions, and finally verifies the effectiveness of the improved method.

4.1 test function and evaluation index

TABLE 1 Standard test function

In order to make a reasonably effective assessment of the performance of an algorithm, a number of algorithm evaluation criteria are proposed. In this section, the performance of the algorithm is evaluated by using the reverse generation distance as an evaluation index. An Inverse Generation Distance (IGD) is an index for evaluating overall performance. The method mainly evaluates the convergence performance and the distribution performance of the algorithm by calculating the minimum distance sum of each point (individual) on the real Pareto frontier to an individual set acquired by the algorithm. The smaller the value, the better the overall performance of the algorithm, including convergence and distribution performance. The calculation formula is as follows:

in the formula: p is a set of points uniformly distributed on the real Pareto surface, | P | is the number of individuals of the set of points distributed on the real Pareto surface. Q is an optimal Pareto optimal solution set obtained by the algorithm. And d (v, Q) is the minimum Euclidean distance of individual v in P to population Q.

Therefore, IGD is to evaluate the overall performance of the algorithm by calculating the average of the minimum distances from the set of points on the true Pareto surface to the acquired population. Through the above formula, it can be known that when the convergence performance of the algorithm is relatively good, d (v, Q) is relatively small, so that the convergence performance of the algorithm can be evaluated; however, when the distribution performance of the algorithm is poor, most individuals in the population are concentrated in a narrow area, and d (v, Q) of many individuals is large according to the formula, so that the distribution performance of the algorithm is evaluated.

4.2 simulation results and comparative analysis

In order to ensure the fairness of the algorithm, the population size, the initial precision, the number of non-dominant solutions and the operation times of the algorithm in the comparison algorithm are set to be the same. The specific parameters of each algorithm are set as follows.

NSGA-II: the population number is set to 100; the crossing and variation indexes are both set to be 20; the final solution number is set to 100; the algorithm iterates 100 times.

MOEA/D: the initial population is set to 100; the number of times of simulating binary crossover operators is set to 20, and polynomial mutation operators are set to 20; the crossing rate is set to be 1.00, and the variation rate is 0.01; the final solution number is set to 100; the algorithm iterates 100 times.

MOBCC: initial population set to 100, initial precision set to 2.0, and final precision set to 10^-8The precision update constant is 1.2; the number of precision updating iterations is set to 5; the final solution number is set to 100 and the algorithm iterates 100 times.

BIMOBCC: initial population settings100, initial precision set to 2.0, final precision set to 10^-8The precision update constant is 1.2; the number of precision updating iterations is set to 5; the external profile size for each bacterium was set to 200 storage units, the final solution number was set to 100, and the algorithm was iterated 100 times.

For the same standard test function, a real PF curve is taken as 500 points, each algorithm is independently operated 30 times, and the IGD index average value and variance data pair ratio of each algorithm is shown in table 2:

TABLE 2 IGD index for solving test function

As is clear from Table 2, the improved pareto solution IGD index of the multi-objective bacterial chemotaxis algorithm (BIMOBCC) proposed by the present invention is superior to NSGA-II, MOEA/D and the basic MOBCC algorithm in the five standard test functions; the result proves that the algorithm adopts an index selection and external archiving based strategy, which is beneficial to improving the convergence and diversity of the multi-target solution set, so as to obtain a better pareto solution set.

When the problems of multi-objective optimization such as reactive power optimization of a power distribution network, reactive power optimization of a power system, daily active power scheduling of a generator set, fault rush-repair of the power distribution network and the like are involved, based on the table 2, it can also be expected that the method can well complete system decision and achieve the expected effect.

For real life problems such as engineering application and the like, the system consists of a plurality of objective functions which are mutually conflicted and influenced, so that the practical problems are complicated, and the system can exactly solve the life problems and solve the multi-objective optimization problem.

5. Practical case application

The wind energy resources in the three-north (northeast, northwest and north China) area of China are rich, the wind power installation is concentrated, and the problem of wind power consumption is particularly serious. In the 'three north' area, the thermal power generating units with poor regulating capability account for 89.3% of the total installed power supply, and the regulating capability of the system is poor. Especially in the heating period in winter, the Combined Heat and Power (CHP) unit has the operating characteristic of 'fixing the Power with Heat', so that the adjusting capability of the CHP unit is greatly limited, the wind Power receiving capability of the system is further reduced, and the problem of wind abandon is more prominent. Therefore, the operation constraint of 'fixing the power with heat' in the 'three north' area is decoupled, the peak regulation capability of the system is improved, and the method is an important means for improving the wind power consumption level of the system and ensuring the healthy and continuous development of the wind power industry in China. Under the low-carbon economic background, with the rapid development of new energy wind power, the low-carbon economic development requirement of China is met, and the problem of wind power consumption caused by heat supply is urgently needed to be solved. The electric heating energy is used as a basic component of an energy internet, the comprehensive scheduling of the electric heating energy in the winter heating period is researched, the efficient consumption of wind power is realized, the social and economic benefits are improved, the environmental cost is reduced, and the electric heating energy has important social significance.

The comprehensive electric heating scheduling model comprising the heat storage device and the carbon capture device is established, and the lowest total power generation coal consumption cost and CO of the system are considered₂The two goals of minimum emission are solved by the improved method provided by the invention, and the effectiveness and practicability of the method are proved.

5.1 modeling

Aiming at the problems that the consumption level of new energy wind power is reduced and the social comprehensive cost is improved in order to meet the heat supply requirement in the area with large proportion of a cogeneration unit, an electric heating comprehensive scheduling model is established by considering thermoelectric coupling elements such as a heat storage device, an electric boiler and the like, and the schematic diagram of the electric heating scheduling model is shown in an attached figure 8, so that the operation defect of deciding electricity by heat is relieved, and the social economic cost and the environmental cost are improved. With minimum total power generation coal consumption cost and CO of the system₂And establishing a dual-target optimization model according to the two targets with the minimum discharge amount and the existing documents.

A) Objective function

At a minimum system operating cost F₁And carbon emission cost F₂The minimum is the objective function.

1. Economic dispatch cost

The economic dispatching of the electric heating integrated energy system takes the minimum coal consumption cost and the minimum wind abandon punishment of the system as dispatching targets, and the economic dispatching target function can be expressed as

In the formula: t is a scheduling time interval, h; n is a radical of_m，N_g，N_chpThe number of the conventional thermal power generating units, the carbon capturing units and the cogeneration units are respectively; p is a radical of_mi，t，p_zi，tThe power generation power of the conventional thermal power generating unit i and the power generation power of the carbon capture unit i at the moment t are respectively; p is a radical of_chpi，t，q_chpi，tThe generating power and the heating power of the ith cogeneration unit at the moment t are respectively; f. of_mi，f_gi，f_chpiThe cost functions of the ith conventional thermal power generating unit, the carbon capture unit and the cogeneration unit are quadratic functions which can be expressed as

In the formula, a_i，b_i，c_iRespectively are coefficients of a coal consumption function of the unit i; p is a radical of_i，tGenerating power of the unit i at the time t;

2. cost of environment scheduling

In the formula: e.g. of the type_mi、e_gi、e_chpiThe carbon emission functions of the ith thermal power generating unit, the ith carbon collecting unit and the ith cogeneration unit are quadratic functions like the coal consumption function, and the correlation coefficient is u_i，v_i，w_i；E_cCapturing CO for a carbon capture plant₂Amount can be expressed as

In the formula: p is a radical of_i，0For capturing CO units for a carbon capture plant i₂Consumed electrical power, MW; p is a radical of_ci，tAnd (4) collecting energy consumption, MW of the carbon collecting unit i at the moment t.

B) Constraint condition

1. Constraint condition of power system

(1) Power balance constraint

In the formula: p is a radical of_gi，tThe net generated power, MW, of the carbon capture unit i at the moment t; p is a radical of_wi，tWind power, MW, scheduled for the wind turbine generator i at the moment t; p is a radical of_l，tThe power load of the system at the moment t, MW;

(2) constraints of conventional thermal power generating units

And (3) restraining an upper limit and a lower limit of output:

in the formula:the minimum generating power and the maximum generating power of the conventional thermal power generating unit i at the moment t are respectively represented as MW.

Unit climbing restraint:

in the formula:the maximum upward and downward climbing work of the minimum generating power of the conventional thermal power generating unit iRate, MW.

(3) Carbon capture unit constraints

p_zi，t＝p_gi，t+p_ci，t (25)

In the formula:the minimum generating power, the maximum generating power and the MW of the carbon capture unit i at the moment t are respectively.

And (3) climbing restraint of the carbon capture unit:

in the formula:the minimum generating power of the carbon capture unit i is the maximum upward and downward climbing power MW.

Trapping device constraints

In the formula:the maximum upward and downward climbing power and MW of the energy consumption of the carbon capture unit equipment in unit time are respectively.

(4) Constraint of cogeneration unit

Thermal output constraint of cogeneration unit

In the formula:the maximum and minimum thermal power and MW of the cogeneration unit are respectively.

Electric output constraint of cogeneration unit

In the formula:respectively the maximum and minimum electric output, MW, of the cogeneration unit under the pure condensation working condition; c_viThe amount of reduction of the power generation power by the unit heating load of the multi-extraction when the total steam inlet amount of the cogeneration group i is not changed; c_miThe elastic coefficients of electric power and thermal power when the cogeneration unit i operates in a backpressure mode; c_kiIs a constant

Hot ramp restraint

In the formula:the maximum upward and downward thermal power ramp rates, MW, of the unit i are respectively.

And (3) electric climbing restraint of the cogeneration unit:

in the formula:the maximum upward and downward electric power ramp rates, MW, of the unit i, respectively.

(5) Power flow constraint of power grid

In the formula:is the power flow, MW, of branch j at time t;respectively, the upper and lower bounds of the power flow, MW, of branch j.

2. Thermodynamic system constraints

(1) Heat supply balance restraint

Heat supply balance restraint

In an actual heat network, there is no heat exchange between the plurality of zones, and the heat load is balanced within the respective zones. Matrix H used herein_MNRepresents the supply relationship of heat sources and zones:

in the formula: m, I are the number of heating areas and the number of heat sources respectively; h is_mi1 denotes that the region m is supplied with heat by the heat source i; h is_mi0 means that the region m is not heated by the heat source i.

And (3) thermal power balance constraint of the region m:

in the formula:the heat supply relations of the cogeneration unit, the heat storage device and the area m are respectively set;for the heat storage device i at the time t-tau_hsHeat storage and discharge power, MW; h is_lm,tIs the thermal load, MW, of region m at time t.

(2) Thermal storage device restraint

Heat storage and release process model of heat storage device

0≤S_hsi,t≤S_hsi,max (42)

In the formula: s_hsi,t、S_hsi,t-1The heat storage amount of the heat storage device i at the time t and the time t-1 is MW & h respectively; the heat storage power and the heat release power of the heat storage device i at the moment t are respectively MW; s_hsi,maxThe maximum heat storage capacity of the heat storage device i, MW · h.

Heat storage and release rate constraints

In the formula:maximum storage and discharge power, MW, of heat storage device i

5.2 simulation data

In the case, a six-unit system is adopted for simulation, the system comprises two back pressure type thermoelectric units, two steam extraction type thermoelectric units and two conventional thermal power units, the conventional units are additionally provided with carbon capture equipment to form the carbon capture units, and the installation proportion of various power supplies is based on the actual installation proportion of a certain area. The coal consumption cost coefficient, the carbon emission coefficient and the electric heat output operation parameter of each unit are respectively shown in a table 3 and a table 4; carbon capture unit CO capture₂The energy consumption of the heat and power cogeneration unit is 0.269MWh/t, and the coefficients of the heat and power cogeneration unit are respectively 0.75, 0 and 0.15; taking 24 hours a day as a scheduling cycle and 1 hour as a time interval, the system load and the wind power prediction power select data from 9:00 of a certain day to 8:00 of the next day, see table 5; the heat load of the system remains substantially unchanged throughout the day, set at 1000 MW.

TABLE 3 coal consumption cost coefficient and carbon emission coefficient of each unit

Machine set	a_i(Yuan/MW)²*h)	b_i(Yuan/MW h)	c_i(Yuan/h)	u_i(t/MW^2*h)	v_i(t/MW^*h)	w_i(t/h)
							1	0.0532	190.12	13175.4	0.001689	0.897	28.17
2	0.1197	189.35	8075.9	0.001576	0.837	26.29
							3	0.0504	160.44	10232.6	0.001689	0.897	28.17
4	0.0504	160.44	10232.6	0.001689	0.897	28.17
							5	0.1197	189.35	8075.9	0.001576	0.837	26.29
6	0.0266	190.12	26351.5	0.001125	0.6	18.77

TABLE 4 Upper and lower limits of electric and thermal power and climbing parameters of unit

System active load and wind power prediction power at moment 524

5.3 improved Algorithm solution model

Let us assume that the carbon capture device and the heat storage device are used simultaneously in the electric heating model, and if the update position exceeds the constraint, the update position is taken as the upper and lower limit values. Substituting the related data to obtain a dual-target actual model of the system, and solving by using an improved algorithm; each bacterium represents a scheduling strategy, the electric power, the heating power and the carbon capture power of a unit are used as control variables, the whole system is divided into T time sections, an initial bacterium group is generated, and the dimension of each bacterium is N_c*T,N_cIs the number of variables. The algorithm parameters are set as follows: the number of bacterial colonies was 50, the number of external archives was 200, the initial accuracy was 2,the final precision is 10e-06, the precision update constant is 1.25, the maximum number of iterations is 100, and the single bacteria movement speed v is 1.

The specific solving steps are as follows:

1) setting basic parameters and generating an initialized population P;

2) executing a basic BCC search strategy on each individual in the population P in the step 1) to obtain two to-be-determined positions of individual movement and population movement, performing feasibility test and adjustment on the to-be-determined positions, and if the to-be-determined positions do not meet the constraint, acquiring corresponding upper and lower limit values;

4) updating the archive EXA1 obtained in the step 3) to an external archive; selecting partial individuals with excellent corresponding index values from the new group obtained in the step 3), executing an NDX (named data reduction) crossing strategy to obtain a new position, carrying out feasibility inspection and adjustment on the position to be positioned, and if the position to be positioned does not meet the constraint, taking corresponding upper and lower limit values and updating the corresponding upper and lower limit values into an external archive; if the number of external archives is larger than the upper limit, executing the step 5), otherwise executing the step 6);

8) Selecting a solution from the obtained pareto curve by using a TOPSIC evaluation method;

the pareto solution set obtained by solving is shown in fig. 9, and the bacterial positions corresponding to the solution are the corresponding scheduling schemes. We obtained coal consumption cost and carbon emission data for 3 typical scheduling schemes according to the pareto solution set, and the related data are shown in Table 6

TABLE 6 coal consumption cost and carbon emission data for three scheduling schemes

Scheme(s)	Cost/dollar in coal consumption	Carbon emission per ton
			Minimum coal solution	8718002.71	44120.16
Minimum carbon emissions solution	9262794.44	38586.10
			Solutions of compromise	8919307.69	41349.63

As is known, the cost of coal consumption and the cost of carbon emissions are two mutually limiting, interacting quantities. In the scheme of improving BIMOBCC solution, the carbon emission corresponding to the scheduling scheme with the minimum coal consumption cost is larger, and the coal consumption corresponding to the scheduling scheme with the minimum carbon emission cost is also larger. The weights of the coal consumption cost and the carbon emission discharge amount are set to be 0.5, a compromise solution is obtained to balance the contradiction relationship between the coal consumption cost and the carbon emission amount, and a balanced scheduling scheme is obtained. However, in actual production life, the development level varies from place to place, and the decision scheme should also vary.

The improved MOBCC algorithm can provide a group of more accurate, rapid and more uniformly distributed schemes for the actual multi-objective optimization problem, such as a series of pareto solutions shown in figure 9, so that a decision maker can select the schemes according to actual conditions, actual production and life needs are met, and the improved MOBCC algorithm has certain actual application value.

Claims

1. A decision-making method for improving a multi-target bacteria chemotaxis algorithm based on indexes is characterized by comprising the following steps: in the system, acquiring basic data to establish a system model; determining a plurality of objective functions based on a system model, and optimizing the objective functions by adopting an index-based improved multi-objective bacterial chemotaxis algorithm; using the optimized solution in a system model to make system decision; the index-based multi-target bacteria chemotaxis improvement algorithm comprises the following steps of:

1) setting basic parameters and generating an initialized population P;

2. The decision method according to claim 1, characterized in that: