CN108470237B - Multi-preference high-dimensional target optimization method based on co-evolution - Google Patents

Multi-preference high-dimensional target optimization method based on co-evolution Download PDF

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CN108470237B
CN108470237B CN201810143899.0A CN201810143899A CN108470237B CN 108470237 B CN108470237 B CN 108470237B CN 201810143899 A CN201810143899 A CN 201810143899A CN 108470237 B CN108470237 B CN 108470237B
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王丽萍
邱飞岳
杜洁洁
章鸣雷
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Zhejiang University of Technology ZJUT
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Abstract

A multi-preference high-dimensional target optimization method based on co-evolution comprises the following steps: step 1, initializing parameters; step 2, updating; step 3, mapping an ideal solution in the evolution population to a target space by using an ASF (automatic sequence Format) expansion function, taking the ideal solution as a preference vector to guide the reference direction of population evolution, then obtaining two temporary reference points by using a preference region selection strategy to further construct a region of interest (ROI) of a decision maker, determining an upper and lower bound range generated by a preference vector set, and guiding the population to converge towards the preference region by using a coevolution mechanism; step 4, optimizing the objective function by utilizing a coevolution mechanism, and selecting N candidate solutions with the maximum adaptation value from the candidate solutions in the ROI area range to enter next generation evolution; step 5, judging whether the termination condition is met, if not, returning to the step 2; if so, outputting the optimal solution set, and finishing the operation of the algorithm. The solution set has better convergence, stronger portability and better implementation.

Description

Multi-preference high-dimensional target optimization method based on co-evolution
Technical Field
The invention relates to a co-evolution-based multi-preference high-dimensional target optimization method, which is used for trying to solve the situation that the non-dominant solution proportion is too high in a high-dimensional target optimization problem from the viewpoint of preference of a decision maker.
Background
A Multi-Objective Evolutionary Algorithm (MOEA) is one of effective approaches to solve the Multi-Objective optimization problem. Representative algorithms are NSGA-II by Deb, SPEA2 by Ziegler, and PAES by Knowles. However, as practical problems are complicated, the problem solution needs to satisfy many common constraints, making the otherwise relatively simple two-or three-target problem evolve into a high-dimensional target problem. With the increase of the target dimension, the proportion of non-dominated solutions in the population is rapidly increased, so that when a classical algorithm is used for processing a high-dimensional target optimization problem, the selection pressure is insufficient, and the performance of the algorithm is sharply reduced. In view of this, Wang et al introduces the co-evolution idea into a multi-objective algorithm, and utilizes an adaptive value assignment method to realize co-evolution of a candidate solution set and a preference vector set, so as to guide the population to approach to a Pareto frontier. In practice, decision makers are usually only interested in a solution set that fits their preferences. Therefore, how to integrate preference information of a decision maker into a multi-objective evolutionary algorithm to obtain a candidate solution which is interested by the decision maker is a research hotspot in the field of multi-objective evolutionary computation in recent years.
Disclosure of Invention
In order to overcome the defect that the algorithm convergence is poor when the existing multi-target evolutionary algorithm solves the high-dimensional target optimization problem, the invention provides a co-evolutionary-based multi-preference high-dimensional target optimization method.
The technical scheme adopted by the invention for solving the technical problems is as follows:
a multi-preference high-dimensional target optimization method based on co-evolution comprises the following steps:
step 1, initializing parameters: setting the scale of the evolution population P as N, the scale of the preference vector set G as Ngoal, the maximum evolution algebra as MaxGen, and generating an initialization population P ═ P (P1,P2,...,PN) Generating an initialization preference vector set G ═ (G)1,G2,...,GNgoal)；
And step 2, updating: evolving the population P, generating a new offspring population Pc by genetic variation operation, and updating the upper and lower preference bounds and the upper bound of the preference vector set G
Figure BDA0001578292270000021
Lower bound
Figure BDA0001578292270000022
Wherein j is 1, 2.. times.M,m is the target number;
generating a new preference vector Gc in a random generation mode according to the updated upper and lower bounds, and updating the external set QtRespectively mixing the parent-child population and the preference vector set to obtain a mixed population JointP and a mixed preference vector set JointG, calculating respective fitness values of the mixed population JointP and the mixed preference vector set JointG, and generating a new child population and a new preference vector set by truncation selection;
step 3, determining a preference area: mapping an ideal solution in the evolution population to a target space by using an ASF (automatic sequence Format) expansion function, taking the ideal solution as a preference vector to guide the reference direction of population evolution, then obtaining two temporary reference points by using a preference region selection strategy to further construct a region of interest (ROI) of a decision maker, determining an upper and lower bound range generated by a preference vector set, and guiding the population to converge towards the preference region by using a coevolution mechanism;
and 4, optimizing: optimizing the objective function, and selecting N candidate solutions with the maximum adaptive value from the candidate solutions in the ROI region range to enter next generation evolution;
step 5, stopping judging: judging whether the termination condition is met, if not, returning to the step 2; if so, outputting the optimal solution set, and finishing the operation of the algorithm.
Further, in step 2, the calculation formula of the individual fitness value is as follows:
Figure BDA0001578292270000023
wherein n isgIs the number of candidate solutions satisfying the preference vector g, and if the candidate solution s does not satisfy any of the preference vectors g, the adaptive value F of the candidate solution ssIs 0, and:
Figure BDA0001578292270000024
Figure BDA0001578292270000031
where N is the number of solution candidates.
Still further, in step 3, a solving process of mapping the ideal solution in the evolutionary population to the target space by the ASF spreading function is as follows:
Figure BDA0001578292270000032
where p > 0, p is a small positive number, called the magnification factor,
Figure BDA0001578292270000033
the ASF expansion function can convert a multi-target problem into a single-target problem as a reference point, and obtain a reference point meeting the preference of a decision maker, and the decision maker continuously changes the reference point obtained by the ASF function through an interactive process to obtain a candidate solution most desired by the decision maker.
Further, in the step 3, the solution process of constructing the decision maker region of interest ROI by using the preference region selection strategy is as follows: in the early stage of algorithm evolution, obtaining the ideal solution z of the current population*And carrying out orthogonal decomposition on the reference points to find two temporary reference points which are respectively recorded as
Figure BDA0001578292270000038
And
Figure BDA0001578292270000039
and respectively calculating ASF function values between the two temporary reference points and each individual, finding two individuals closest to the temporary reference points, determining a preference area, determining an upper limit golalUpper and a lower limit golLower of a preference vector set range, and using more search resources for solution sets in the decision maker interested area.
In the step 3, the solving process for constructing the decision maker interesting region by using the preference region selection strategy comprises the following steps:
step 31: in the population P (t) with the current generation number t, the ideal solution is recorded as z*Calculating each individual and ideal solution z*Finding the individual with the smallest ASF value, and recording asSmin；
Step 32: for vector
Figure BDA0001578292270000034
Orthogonal decomposition is carried out to obtain two temporary references which are respectively marked as
Figure BDA0001578292270000035
And
Figure BDA0001578292270000036
step 33: respectively calculating each individual in the current population
Figure BDA0001578292270000037
ASF value of, find out from the temporary reference point
Figure BDA0001578292270000041
The two most recent individuals, denoted xcloset,i；
Step 34: according to the formula
Figure BDA0001578292270000042
And determining which is a preference solution in the current population, and eliminating population individuals not belonging to the area so as to determine the size of the preference area.
The invention has the following beneficial effects: the invention aims at solving the challenge encountered by the high-dimensional target optimization problem, namely, the non-dominant solution proportion in the population is too high as the dimension of the target increases. By utilizing a computing framework of coevolution of the population and the preference vector set, the bottleneck of over-high dominant solution ratio is effectively reduced. Meanwhile, an ASF expansion function is used for mapping an ideal solution in the evolution population to a target space, the target space is used as a preference vector to guide the reference direction of population evolution, then a preference region selection strategy is used for obtaining two temporary reference points to further construct a region of interest (ROI) of a decision maker, the range generated by a preference vector set is determined, and the population is guided to converge towards the preference region through a coevolution mechanism. The method is not limited by target dimensionality, can be combined with various multi-target evolutionary algorithms, and has strong transportability.
Drawings
FIG. 1 is a flow chart of a co-evolution-based multi-preference high-dimensional target optimization method of the present invention;
FIG. 2 is a diagram of the (μ + λ) elite selection framework;
FIG. 3 is a schematic diagram of a preference area selection policy, in which (a) represents a diagram of an earlier stage of population evolution, (b) represents a diagram of an earlier stage of a preference area selection policy, and (c) represents a diagram of a later stage of a preference area selection policy;
FIG. 4 is a multi-stage green supply chain network schematic;
FIG. 5 is a schematic illustration of a transport network chromosome decode with 3 sources and 4 depots;
FIG. 6 is a schematic diagram of multi-stage supply network chromosome decoding;
FIG. 7 is a schematic diagram of a fragment-based uniform crossover process;
FIG. 8 is a schematic diagram of a fragment-based mobile mutation method;
FIG. 9 shows the "4-4-4-4" green supply chain network model specific parameters;
fig. 10 is a flowchart.
Detailed Description
The following examples of the present invention are described in detail to give detailed embodiments and specific procedures.
As shown in fig. 10, a method for optimizing a multi-preference high-dimensional target based on co-evolution includes the following steps:
step 1: and (4) modeling the problem. A three-stage green supply chain network model is provided by taking a product production enterprise as a prototype and taking the production cost, the service quality, the production utilization rate and the green degree of a supply chain as optimization targets, and the market demand and the production capacity limit are met by selecting a proper supply chain partner and a proper logistics warehouse. As shown in fig. 4. The model has the following three assumptions: (1) the customer demand and the number of supply chain partners are known; (2) the supply chain partner requirements required for each stage are known; (3) the direction of transport of the stages is unidirectional.
The green supply chain model is divided into three supply chain stages of suppliers, manufacturers, logistics warehouses and customers, each stage having four selectable partners, and its mathematical model is shown in equations (1-10). The evaluation criteria for this green supply chain partner selection primarily considers the following four goals: (1) the total cost of product and transportation costs minimizes (2) the total time taken for transportation; (3) maximization of average product quality; (4) the green rating score is maximized.
Figure BDA0001578292270000051
min f2＝∑l∑kBTlkLQlk+∑k∑jBTkjLQkj+∑j∑iBTjiLQji (2)
min f3＝∑lPQlSl+∑kPQkMk+∑jPQjWj (3)
min f4＝∑lGlSl+∑kGkMk+∑jGjWj (4)
s.t.∑lSl＝s,∑kMk＝m,∑jWj＝w (5)
∑kLQlk＝∑jLQkj＝∑iLQji＝∑iDi (6)
∑lLQlk≤CPl,∑kLQkj≤CPk,∑jLQji≤CPj (7)
LQlk≥0,LQkj≥0,LQji≥0 (8)
Figure BDA0001578292270000052
Figure BDA0001578292270000061
Figure BDA0001578292270000062
Equations (1-4) represent the four targets to be optimized for the green supply chain partner selection problem. For convenience, f3And f4The optimization objective has been translated into a minimization problem, where:
1)f1represents the total cost of the supply chain network, including both production and transportation costs;
2)f2representing a total transit time of the supply chain network;
3)f3representing the total production quality of the supply chain network;
4)f4representing the total greenness of the supply volume network.
Equations (5-11) represent constraints for the green supply chain partner selection problem, where:
1)Slis a variable from 0 to 1 indicating whether supplier l is selected;
2)Mkis a variable from 0 to 1, indicating whether manufacturer k is selected;
3)Wjis a 0-1 variable indicating whether warehouse j is selected;
4)Direpresenting the requirements of customer i;
5)Gl(k,j)represents the greenness of supplier l (manufacturer k, warehouse j);
6)MCl(k,j)represents the production cost of supplier l (manufacturer k, warehouse j);
7)PQl(k,j)represents the product quality of supplier l (manufacturer k, warehouse j);
8)CPl(k,j)represents the capacity of a supplier l (manufacturer k, warehouse j);
9)LQlk(kj,ji)is a real variable representing supplier l to manufacturer k (manufacturer k to warehouse j, warehouse j to customer)i) The flow rate of the object;
10)TClk(kj,ji)represents the unit transportation cost of the supplier l to the manufacturer k (manufacturer k to warehouse j, warehouse j to customer i);
11)BTlk(kj,ji)the unit transportation time of the supplier l to the manufacturer k (manufacturer k to warehouse j, warehouse j to customer i) is represented.
Determining an objective function: setting three test problems, wherein the test problem is a two-target optimization problem, and considering the operation cost (f1) and the transportation time (f 2); the second test problem is a three-target optimization problem, and simultaneously the operation cost (f1), the transportation time (f2) and the product quality (f3) are considered; the third test problem is a four-target optimization problem and a high-dimensional target optimization problem, and comprehensively considers the operation cost (f1), the transportation time (f2), the product quality (f3) and the green degree (f 4).
Step 2: chromosome representation. The essence of the supply chain network model is a multi-level transport network problem. The chromosome of the transport network problem can be represented as a string of freely arranged natural numbers: and v ═ 64815273, the length of which is equal to the sum of the number of Sources (K) and the number of Depots (J), the values at each locus indicate the priority of Sources and Depots. By giving chromosomes, sequentially selecting the Source (or depth) with the highest priority and connecting the Source (or depth) with the lowest transportation cost, thereby forming a transportation network.
And step 3: and (5) decoding the chromosome. FIG. 5 shows a schematic of the transport network chromosome decoding between 3 suppliers and 4 manufacturers for a given transport cost, customer demand, and production capacity. Table 1 is a specific procedure of priority-based chromosome decoding in the context of the transport network (K ═ 3, and J ═ 4) shown in fig. 5. Taking the first cycle as an example: firstly, determining a gene position l with the highest priority as 2; then, because l is less than or equal to K and equal to 3, selecting source K and equal to l and equal to 2, simultaneously selecting depot j and equal to 2 with the lowest transportation cost, and determining the object flow rate LQ22＝min{P2,D2100 }; subsequently updating the production capacity P2100-2150-; finally, due to the production capacity P2Renewed dyeing when the dye is equal to 0Color volume v (2) ═ 0. The circulation is carried out until the user demand D is equal to phi, the circulation is stopped, and the product flow LQ is outputkj. Table 1 shows a specific process of chromosome decoding based on priority;
Figure BDA0001578292270000071
TABLE 1
The multi-level supply chain network model shown in fig. 4 can be divided into three phases: supplier l to manufacturer k, manufacturer k to warehouse j, warehouse j to customer i. Therefore, the chromosome of the supply chain network is composed of three parts, each part corresponds to the transportation network of the corresponding stage, and the decoding steps are shown in fig. 6:
first, the third stage is decoded according to the warehouse capacity CPWUser demand D and priority v3Determining a warehouse j to be selected and the object flow rate LQ thereofji；
Then, decoding the second stage, and taking the warehouse object flow as a warehouse demand DWAnd according to manufacturer production capacity CPMAnd priority v2Determining a manufacturer k to be selected and its mass flow rate LQkj；
Finally, decoding the first stage, and taking the manufacturer commodity flow as the manufacturer demand DMProduction capacity CP according to the supplierSAnd priority v1Determining a supplier l to be selected and a flow rate LQ thereoflk。
And 4, step 4: and (4) performing a crossover operation. The chromosome is crossed by adopting a fragment-based uniform crossing method, and the method has the main idea that: randomly selecting chromosome fragments of the parent as chromosome composition of the offspring, as shown in fig. 7: firstly, randomly generating a binary code, wherein the length of the binary code is equal to the number of stages of a supply chain network; then, the parent is interleaved according to the binary code: "0" indicates that the chromosome fragment of the corresponding stage is selected from parent 1, and "1" indicates that the chromosome fragment of the corresponding stage is selected from parent 2. This crossover approach is advantageous in retaining good gene segments of the parents.
And 5: and (5) performing mutation operation. The chromosome is subjected to mutation operation by adopting a fragment-based mobile mutation method, and the main idea is as follows: each chromosome segment of the parent is independently mutated, and each chromosome segment adopts a mobile mutation mode, as shown in fig. 8: firstly, randomly generating a binary code, wherein the length of the binary code is equal to the number of stages of a supply chain network; then, mutation operation is carried out on the parent according to the binary code: "0" indicates that the chromosome fragment at the corresponding stage is not mutated, and "1" indicates that the chromosome fragment at the corresponding stage is mutated by movement. This variation approach is advantageous for maintaining the independence of the individual segments of the chromosome.
Step 6: experimental data preparation and specific parameter settings.
The data of the simulation experiment adopts a '4-4-4-4' green supply chain network model which comprises four parts of a supplier, a manufacturer, a warehouse and a client. There are 4 candidates per section, in addition to the customer, from which a decision maker is required to pick the appropriate partner to meet the capacity and customer requirements of the supply network. Wherein the specific parameters of production capacity, production cost, product quality, shipping cost, shipping time, greenness and customer requirements for each stage are known, as shown in fig. 9.
And 7: optimization is carried out by applying multi-preference high-dimensional target optimization algorithm based on co-evolution
Step 71: algorithm-related parameters are initialized. When the optimization target dimension is 2-dimensional, setting the scale of the evolution population P as 100, the scale of the preference vector set G as 100, the maximum evolution generation number as 100, and generating the initialization population P (P ═ P-1,P2,...,P100) Generating an initialization preference vector set G ═ (G)1,G2,...,G100) (ii) a When the optimization target dimension is 3-dimensional, setting the scale of the evolution population P as 100, the scale of the preference vector set G as 100, the maximum evolution generation number as 200 generations, and generating the initialization population P (P ═ P-1,P2,...,P100) Generating an initialization preference vector set G ═ (G)1,G2,...,G100) (ii) a When optimizing the target dimensionIn 4 dimensions, the scale of the evolving population P is set to 150, the scale of the preference vector set G is set to 150, the maximum evolution generation number is 300, and the initial population P is generated (P ═ P1,P2,...,P150) Generating an initialization preference vector set G ═ (G)1,G2,...,G150). The cross probability of the algorithm is 0.9, and the mutation probability is 0.1.
See table 2 for details;
Figure BDA0001578292270000091
TABLE 2
Step 72: and updating and evolving. Evolving the population P, generating a new offspring population Pc by using cross mutation operation, and updating the upper and lower preference boundaries and the upper boundary aiming at the preference vector set G
Figure BDA0001578292270000092
Lower bound
Figure BDA0001578292270000093
Wherein j is 1,2, and M is the target number; generating a new preference vector Gc in a random generation mode according to the updated upper and lower bounds, and updating the external set QtAnd respectively mixing the parent-child population and the preference vector set to obtain a mixed population JointP and a mixed preference vector set JointG, calculating respective fitness values of the mixed population JointP and the mixed preference vector set JointG, and generating a new child population and a new preference vector set by truncation selection.
According to the fitness value calculation formula of the coevolution algorithm:
Figure BDA0001578292270000101
wherein n isgIs the number of candidate solutions satisfying the preference vector g, and if the candidate solution s does not satisfy any of the preference vectors g, the adaptive value F of the candidate solution ssIs 0, and:
Figure BDA0001578292270000102
Figure BDA0001578292270000103
where N is the number of solution candidates. And mixing the child-parent population and the child-parent preference vector set, calculating respective fitness values, sorting through the fitness values, and selecting excellent population and preference vector set by truncation for next-generation genetic operation.
Step 73: a preference area is determined. In the early stage of algorithm evolution, obtaining the ideal solution z of the current population*(i.e. z)r) Using ASF spread functions
Figure BDA0001578292270000104
Where ρ > 0, ρ is a small positive number called the magnification factor. Calculating each individual and ideal solution z*Finding the individual with the smallest ASF value, and recording as Smin. For vector
Figure BDA0001578292270000105
Orthogonal decomposition is carried out to obtain two temporary references which are respectively marked as
Figure BDA0001578292270000106
And
Figure BDA0001578292270000107
respectively calculating each individual in the current population
Figure BDA0001578292270000108
ASF value of, find out from the temporary reference point
Figure BDA0001578292270000109
The two most recent individuals, denoted xcloset,i. According to the formula
Figure BDA00015782922700001010
Determining which of the preferred solutions in the current population does not belong to the regionThe population individuals are eliminated, and thus the preference area range is determined. Determining the upper and lower boundaries of the preference vector set generation range, golalupper and lower, golallower, uses more search resources for the solution set of the ROI in the region of interest of the decision maker.
Step 74: and (6) optimizing. Optimizing the objective function, and selecting a candidate solution with a larger adaptive value from the candidate solutions in the ROI area range to enter next generation evolution;
step 75: and judging a stop condition. And judging whether the optimization process meets the stop requirement or not according to the preset stop condition, if so, exiting the optimization process and outputting an optimization result, and if not, returning to the step 72.
And 8: from the simulation experiment results obtained in step 7, the IGD was as shown in Table 3*Indexes, Pareto optimal solution average number and average running time;
Figure BDA0001578292270000111
TABLE 3
The utility value of the individual on the target expansion function is considered in the process of evaluating the individual, the Pareto domination relation between the individual and the preference vector is considered, the individual with stronger convergence capability and more optimal solutions is provided, and good solving performance is shown in the green supply chain partner selection problem. Compared with the traditional MOGA algorithm, the multi-objective optimization problem is converted into the single-objective optimization problem by randomly distributing weights to different optimization targets in the green supply chain partner selection problem, so that only one optimal solution can be given in each solving process, and a decision maker is not facilitated to select a satisfactory scheme from the optimal solution; or a group of Pareto dominant solutions can be obtained only by carrying out multiple operations, so that the calculation cost is greatly increased. The solution set obtained by the method has better convergence, is more beneficial for decision makers to make selections, and obviously improves the calculation efficiency.

Claims (1)

1. A multi-preference high-dimensional target optimization method based on co-evolution is characterized by comprising the following steps:
step 1: problem modeling, namely providing a three-stage green supply chain network model by taking a product production enterprise as a prototype and taking production cost, service quality, production utilization rate and green degree of a supply chain as optimization targets, and meeting the limitation of market demand and production capacity by selecting supply chain partners and logistics warehouses; the model has the following three assumptions: (1) the customer demand and the number of supply chain partners are known; (2) the supply chain partner requirements required for each stage are known; (3) the transport direction of each stage is unidirectional;
the green supply chain model is divided into three supply chain stages of suppliers, manufacturers, logistics warehouses and customers, each stage has four selectable partners, the mathematical model of the green supply chain model is shown in formulas (1) to (10), and the evaluation standard selected by the green supply chain partners considers the following four targets: the total cost formed by the product cost and the transportation cost is minimized, the total time occupied by the transportation time is minimized, the average product quality is maximized, and the green degree evaluation score is maximized;
Figure FDA0003233101630000011
minf2＝∑l∑kBTlkLQlk+∑k∑jBTkjLQkj+∑j∑iBTjiLQji (2)
minf3＝∑lPQlSl+∑kPQkMk+∑jPQjWj (3)
minf4＝∑lGlSl+∑kGkMk+∑jGjWj (4)
s.t.∑lSl＝s，∑kMk＝m，∑jWj＝w (5)
∑kLQlk＝∑jLQkj＝∑iLQji＝∑iDi (6)
∑lLQlk≤CPl，∑kLQkj≤CPk，∑jLQji≤CPj (7)
LQlk≥0，LQkj≥0，LQji≥0 (8)
Figure FDA0003233101630000012
Figure FDA0003233101630000013
Figure FDA0003233101630000014
equations (1) - (4) represent the four targets to be optimized for the green supply chain partner selection problem, f3And f4The optimization objective has been translated into a minimization problem, where:
f1represents the total cost of the supply chain network, including both production and transportation costs;
f2representing a total transit time of the supply chain network;
f3representing the total production quality of the supply chain network;
f4representing a total greenness of the supply volume network;
equations (5) - (11) represent constraints for the green supply chain partner selection problem, where:
Slis a variable from 0 to 1 indicating whether supplier l is selected;
Mkis a variable from 0 to 1, indicating whether manufacturer k is selected;
Wjis a 0-1 variable indicating whether warehouse j is selected;
Direpresenting the requirements of customer i;
Gl(k，j)represents the greenness of supplier l, supplier l including manufacturer k and warehouse j;
MCl(k,j)represents the production cost of supplier l;
PQl(k,j)indicating the product quality of supplier l;
CPl(k,j)indicating the production capacity of supplier l;
LQlk(kj,ji)is a real variable representing the flow of items from supplier l to manufacturer k, i.e., manufacturer k to warehouse j, warehouse j to customer i;
TClk(kj,ji)represents the unit transportation cost of the supplier l to the manufacturer k, i.e., the manufacturer k to the warehouse j, the warehouse j to the customer i;
BTlk(kj,ji)represents the unit transit time of supplier l to manufacturer k, i.e., manufacturer k to warehouse j, warehouse j to customer i;
determining an objective function: setting three test problems, wherein the test problem is a two-target optimization problem, and considering the operation cost (f1) and the transportation time (f 2); the second test problem is a three-target optimization problem, and simultaneously the operation cost (f1), the transportation time (f2) and the product quality (f3) are considered; the third test problem is a four-target optimization problem and a high-dimensional target optimization problem, and comprehensively considers the operation cost (f1), the transportation time (f2), the product quality (f3) and the green degree (f 4);
step 2: the chromosome represents that the essence of the supply chain network model is a multi-stage transportation network problem, and the chromosome of the transportation network problem can be represented as a string of freely arranged natural numbers: v ═ 64815273, the length of which is equal to the sum of the number of Sources (K) and the number of Depots (J), the values at each locus representing the priorities of Sources and Depots, the highest priority Source or Depot being selected in turn by giving a chromosome and being connected to the Depot or Source with the lowest transportation cost to form a transportation network;
and step 3: chromosome decoding: firstly, determining a gene position l with the highest priority as 2; then, as l is less than or equal to K and is equal to 3, source K and l are equal to 2, and the transportation cost is selected simultaneouslyThe lowest depot j is 2, and the object flow rate LQ is determined22＝min{P2,D2100 }; subsequently updating the production capacity P2100-2150-; finally, due to the production capacity P2When the chromosome v (2) is updated to be 0, the process is circulated until the user demand D is equal to phi, the circulation is stopped, and the output flow LQ is outputkj；
The multi-stage supply chain network model may be three stages: a first stage of supplier l to manufacturer k, a second stage of manufacturer k to warehouse j, a third stage of warehouse j to customer i; therefore, the chromosome of the supply chain network is composed of three parts, each part corresponds to the transportation network of the corresponding stage, and the decoding method comprises the following specific steps:
first, the third stage is decoded according to the warehouse capacity CPWUser demand D and priority v3Determining a warehouse j to be selected and the object flow rate LQ thereofji；
Then, decoding the second stage, and taking the warehouse object flow as a warehouse demand DWAnd according to manufacturer production capacity CPMAnd priority v2Determining a manufacturer k to be selected and its mass flow rate LQkj；
Finally, decoding the first stage, and taking the manufacturer commodity flow as the manufacturer demand DMProduction capacity CP according to the supplierSAnd priority v1Determining a supplier l to be selected and a flow rate LQ thereoflk；
And 4, step 4: performing crossover operation, namely performing crossover operation on chromosomes by adopting a fragment-based uniform crossover method, randomly selecting chromosome fragments of a parent as chromosomes of offspring to form, and firstly, randomly generating a binary code, wherein the length of the binary code is equal to the number of stages of a supply chain network; then, the parent is interleaved according to the binary code: "0" represents the selection of the chromosome fragment of the corresponding stage from parent 1, and "1" represents the selection of the chromosome fragment of the corresponding stage from parent 2;
and 5: performing mutation operation, namely performing mutation operation on chromosomes by adopting a fragment-based mobile mutation method, independently performing mutation operation on each chromosome fragment of a parent, and randomly generating a binary code with the length equal to the number of stages of a supply chain network by adopting a mobile mutation mode for each chromosome fragment; then, mutation operation is carried out on the parent according to the binary code: "0" indicates that the chromosome fragment at the corresponding stage is not mutated, and "1" indicates that the chromosome fragment at the corresponding stage is subjected to movement mutation;
step 6: experimental data preparation and specific parameter settings
The data of the simulation experiment adopts a '4-4-4-4' green supply chain network model, which comprises four parts of a supplier, a manufacturer, a warehouse and a client, wherein each part except the client has 4 candidates, and a decision maker is required to select a proper partner from the candidates so as to meet the production capacity and the client requirement of a supply network, wherein specific parameters of the production capacity, the production cost, the product quality, the transportation cost, the transportation time, the greenness and the client requirement of each stage are known;
and 7: optimization is carried out by applying multi-preference high-dimensional target optimization algorithm based on co-evolution
Step 71: initializing relevant parameters of an algorithm, setting the scale of the evolutionary population P as 100 when the optimization target dimension is 2-dimensional, setting the scale of the preference vector set G as 100, setting the maximum evolutionary algebra as 100 generations, and generating the initialized population P (P ═ P-1,P2,...,P100) Generating an initialization preference vector set G ═ (G)1,G2,...,G100) (ii) a When the optimization target dimension is 3-dimensional, setting the scale of the evolution population P as 100, the scale of the preference vector set G as 100, the maximum evolution generation number as 200 generations, and generating the initialization population P (P ═ P-1,P2,...,P100) Generating an initialization preference vector set G ═ (G)1,G2,...,G100) (ii) a When the optimization target dimension is 4 dimensions, the scale of the evolution population P is set to be 150, the scale of the preference vector set G is set to be 150, the maximum evolution generation number is 300, and the initialization population P is generated (P ═ P-1,P2,...,P150) Generating an initialization preference vector set G ═ (G)1,G2,...,G150) Cross over summary of algorithmThe rate is 0.9, and the mutation probability is 0.1;
step 72: updating evolution, evolving population P, generating new filial population Pc by using cross variation operation, and updating upper and lower bounds and upper bound of preference vector set G
Figure FDA0003233101630000031
Lower bound
Figure FDA0003233101630000032
Wherein j is 1,2, and M is the target number; generating a new preference vector Gc in a random generation mode according to the updated upper and lower bounds, and updating the external set QtRespectively mixing the parent-child population and the preference vector set to obtain a mixed population JointP and a mixed preference vector set JointG, calculating respective fitness values of the mixed population JointP and the mixed preference vector set JointG, and generating a new child population and a new preference vector set by truncation selection;
according to the fitness value calculation formula of the coevolution algorithm:
Figure FDA0003233101630000033
wherein n isgIs the number of candidate solutions satisfying the preference vector g, and if the candidate solution s does not satisfy any of the preference vectors g, the adaptive value F of the candidate solution ssIs 0, and:
Figure FDA0003233101630000034
Figure FDA0003233101630000035
n is the number of candidate solutions, the child-parent population and the child-parent preference vector set are mixed, the respective fitness values are calculated, and excellent populations and preference vector sets are selected by truncation through the ranking of the fitness values to perform genetic operation of the next generation;
step 73: determining a preference area, and acquiring an ideal solution z of the current population at the early stage of algorithm evolution*(i.e. z)r) Using ASF spread functions
Figure FDA0003233101630000036
Where ρ > 0, ρ is a small positive number called the magnification factor; calculating each individual and ideal solution z*Finding the individual with the smallest ASF value, and marking as Smin, and counting the vectors
Figure FDA0003233101630000037
Orthogonal decomposition is carried out to obtain two temporary references which are respectively marked as
Figure FDA0003233101630000041
And
Figure FDA0003233101630000042
respectively calculating each individual in the current population
Figure FDA0003233101630000043
ASF value of, find out from the temporary reference point
Figure FDA0003233101630000044
The two most recent individuals, denoted xcloset,iAccording to the formula fi(y)≤fi(xclosest,i),
Figure FDA0003233101630000045
Determining which are preference solutions in the current population, and eliminating population individuals not belonging to the region so as to determine a preference region range, determining an upper limit golalupper and a lower limit golallower of a preference vector set generation range, and using more search resources for a solution set of ROI in a decision maker interested region;
step 74: optimizing the target function, and selecting a candidate solution with a larger adaptive value from the candidate solutions in the ROI area range to enter next generation evolution;
step 75: judging a stopping condition, judging whether the optimization process meets the stopping requirement according to a preset stopping condition, if so, quitting the optimization process and outputting an optimization result, and if not, returning to the step 72;
and 8: and (5) obtaining a simulation test result according to the step 7.
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