CN116151303A - Method for predicting optimal migration opportunity in multi-task multi-objective optimization problem - Google Patents
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Abstract
The invention provides a method for predicting optimal migration opportunity in a multi-task multi-target optimization problem, and belongs to the technical field of evolution calculation. Firstly, a single-task multi-target evolutionary algorithm is used for independently optimizing a target task and a migration task, and decision variables of individuals in a target population are stored at intervals of a certain algebra. And then, taking the final optimized population with good convergence and diversity of the migration task as a source of constant migration information, and hybridizing the final optimized population with the target task with the population stored at regular evolutionary algebra. After information migration, the generated child individuals are evaluated by performing on the target task. When the population quality is optimal, the corresponding evolution generation is the optimal migration generation, and the generation mark is output. The method has effectiveness and reliability, can generate more accurate prediction of the optimal migration occurrence time, and effectively improves the efficiency of multi-task and multi-objective optimization.
Description
Technical Field
The invention belongs to the technical field of evolution calculation, and relates to a method for predicting optimal migration opportunity in a multi-task multi-objective optimization problem. The technology can be widely applied to various multi-task and multi-target optimization cloud platforms such as a cloud-based multi-task process parameter optimization cloud platform, a multi-task financial optimization cloud platform, a multi-task traffic scheduling optimization and platform and the like.
Background
The evolutionary algorithm is a random optimization method based on population. The algorithm starts from a randomly generated population, iteratively generates new offspring through crossover, mutation and other evolution operations, and reserves more excellent individuals. When a predetermined condition is satisfied, the final population is output as a solution to the problem. Due to its flexible representation and powerful searching capabilities, evolutionary algorithms have been advancing in many complex optimization fields in recent years, including multi-objective optimization, expensive optimization, combinatorial optimization, robust optimization, etc., and have been successfully applied to solve the problems of realistic optimization in many fields such as national defense and network security, biometrics and bioinformatics, finance and economy, sports and games, etc.
The problem of multi-objective optimization is widespread in scientific and engineering applications, aiming at simultaneously optimizing a plurality of mutually conflicting objective functions. The multi-objective evolutionary algorithm has proven to be an effective method for solving the multi-objective optimization problem, and the method can be used for forming an approximate Pareto optimal solution set with high convergence speed and uniform distribution, and two indexes for judging the excellent multi-objective evolutionary algorithm are provided: (1) ensuring the convergence of the algorithm, namely that an approximate Pareto optimal solution set obtained in a target space is as close as possible to a real Pareto optimal solution set; (2) the diversity of the evolutionary population is maintained, so that the obtained approximate Pareto optimal solution set has good distribution characteristics (such as uniform distribution) in a target space, the distribution range is as wide as possible, and it is very difficult to simultaneously meet the two targets, so far, the problems are improved intensity Pareto evolutionary algorithm SPEA2, non-dominant ranking genetic algorithm NSGA-II and decomposition-based multi-target evolutionary algorithm MOEA/D in second generation MOEAs marked by elite retention strategies at home and abroad. SPEA2 utilizes an external population to store a current non-dominant solution set, and obtains good solution distribution uniformity by introducing environment selection based on neighbor rules; the NSGA-II is typically characterized in that mechanisms such as rapid non-dominant solution ordering, crowding distance, elite reservation and the like are adopted, so that a good solution effect is obtained in multi-class multi-objective optimization problems; the MOEA/D is typically characterized by a low computational complexity due to the adoption of a weight vector to transform the multi-objective optimization problem into a single-objective optimization problem.
Inspired by multi-task learning, the evolution computing field provides a concept of multi-task optimization. And (3) multi-task optimization, namely simultaneously optimizing a plurality of tasks, and finding out the optimal solution corresponding to each task. Each task may be a different optimization problem, either single-objective or multi-objective. When the multi-objective optimization problem exists in the simultaneously optimized task, the problem is called a multi-objective optimization problem. Multitasking optimizations consider that if there is similarity or complementarity between tasks that are optimized simultaneously, then knowledge between these tasks can be reused. When multiple task solutions are coded into a unified decision space, the optimal solutions for similar tasks are close, and even the optimal solution for a task performs well in similar tasks. Compared with the traditional evolutionary algorithm, the method solves only one task at a time, simultaneously solves a plurality of tasks and multiplexes the knowledge in the related tasks, can save computing resources, accelerates convergence, and improves the overall optimization efficiency.
With the gradual penetration of research on the optimization problem and the enhancement of modeling capability, the optimization problem is more and more complex, and the required time cost and the calculation cost are more and more expensive. With the promotion of cloud computing capability and popularization of cloud services, the problem of simultaneously solving a plurality of optimization problems for a plurality of users by fully utilizing the parallelism of cloud computing in the future has become a research consensus of partial experts in the field of evolution computing. Therefore, research multi-task optimization can provide technical support for optimizing a plurality of optimization tasks in parallel on a large scale in the future, and has research value and practical significance.
However, due to the optimal points, iteration trends and adaptability landscapes of the target task and the migration task in the multitasking environment, there is often a problem of negative migration, that is, the target task has a worse optimization effect than the target task alone after receiving migration information of the simultaneous optimization task. Therefore, the migration opportunity is particularly important, and the success rate and the efficiency of information migration can be greatly improved by carrying out information migration when the local optimal points of the target task and the migration task are similar, the iteration trend is similar or the adaptability is similar. However, due to the evolutionary randomness of the evolutionary algorithm, the optimal migration opportunities are still not determined at present.
The problem of determining the optimal migration opportunity is a key problem which is urgently needed to be solved in the current multi-task multi-objective optimization research. How to determine the best opportunity for a target task to receive migration task information in a multitasking environment is a difficulty of this problem. With the continued depth of multi-objective optimization research, the importance of the best migration opportunity determination problem is increasingly prominent, which to some extent determines the future of multi-objective optimization.
Disclosure of Invention
The invention aims to predict the mutual migration time of knowledge between tasks in the process of solving the optimal solution set by using the current multi-task multi-objective optimization algorithm, avoid negative migration, solve only one task at a time in the optimal migration time compared with the traditional evolutionary algorithm, solve a plurality of tasks and multiplex the knowledge in the related tasks at the same time, save computing resources, accelerate convergence and improve the overall optimization efficiency.
A method of predicting an optimal migration opportunity in a multitasking, multitasking optimization problem, comprising the steps of: s1, the method comprises the steps of (1),Koptimizing each task simultaneously, traversing all tasks, taking the task currently being solved as a target task, randomly assigning one task from other tasks as a migration task to assist in optimizing the target task, and performing target task pairThe corresponding population is a target population, and the population corresponding to the migration task is a migration population;
set up migration task populationQScale ofN Q The dimension number of the migration task decision variable is set to beD Q Target task populationPScale ofN P The dimension number of the target task decision variable is set to beD P The maximum evolution generation numbers of the target task and the migration task areE;
S2, independently optimizing the assigned migration task populations by using a single-task multi-objective evolutionary algorithm, reserving the final populations for mating and analysis, reserving the final populations after each E generation of the migration task populations is evolved, and repeating the optimization processTRecord the first timetThe final population of the multiple iterations is saved asQ t ,t∈{1,2,3…,T};
S3, independently optimizing migration task populations by using single-task multi-objective evolutionary algorithmTSecondary final migration task populationQ t Averaging according to decision variable bits in the migration task population to generate an average final migration task population, which is recorded as ,/>The j-th decision variable of the i-th individual +.>The calculation formula of (2) is shown in the formula;
wherein the method comprises the steps ofRepresent the firsttIn the final migration task population of the multiple iterations +.>First, theiIndividual firstjThe bit decision variable is used to determine,representation ofTSecond->Average value of (2);
s4, independently optimizing the current target task population by using a single-task multi-target evolution algorithm, wherein each evolution of the target task populatione 0 The intermediate population is saved after generation, and the optimization process is repeatedHRecord the first timehSecond repeat optimizationeThe generation-saved population isWhereine 0 Parameters set manually for saving the intermediate evolution results of the target population,eto preserve the number of evolutionary passages in the middle of the target population,/->;
S5, toHThe first to be savedeGeneration populationAveraging according to decision variable bits of the target task population to generate an averageeThe generation target task population is marked as +.>,/>The j-th decision variable of the i-th individual +.>The calculation formula of (2) is shown as formula (3); />
Wherein the method comprises the steps ofRepresent the firsthSubsampled firsteGeneration target task populationi*Individual firstj*Bit decision variable +_>Representation ofHSecond->Average value of (2);
s6, willAnd->Using SBX crossover operator for information migration and generating offspring populations +.>Wherein β represents a distribution index in the SBX operator as shown in formula (4); then use the objective function to group +. >All individuals in (1) are evaluated and the population +.>Evaluation index O (>);
S7, comparing O%) When O (+)>) When the optimal value is taken, the information migration generation is indicatedeWhen information migration is performed, the best performance can be achieved, and records are recordedeObtaining the optimal time for information migration;
s8, outputting the generation numbere。
Advantageously, after the migration task is assigned in step S1, the solutions of the migration task and the target task are encoded into a unified decision space; the migration task and the target task are optimized through the step S2 and the step S4 respectively to obtain respective optimal solutions, the optimal solutions of similar tasks are close, and even the optimal solution of one task performs well in the similar tasks. Through step S6, the knowledge in the related tasks is simultaneously solved and multiplexed, then the fitness after the knowledge of the related tasks is multiplexed is evaluated, the fitness is compared, the time at which the knowledge of the similar tasks is multiplexed can be known, the computing resource can be saved, the convergence is accelerated, and the overall optimization efficiency is improved.
Preferably, the step of individually optimizing the optimized task by the single-task multi-objective evolutionary algorithm includes:
s21, initializing the generation number of evolutione1 is shown in the specification;
s22, initializing individual numbers in the optimized task population i ' 1, indicating traversal from the first individual;
s23, mutating the first task population in the current optimized task populationi ' individualsx i' Variant generation offspring is marked asx i' *;
S24, if offspring individualsx i' *Can dominate the parent individualsx i' Step S25 is performed, otherwise step S26 is performed, wherein the dominant finger: if the offspring is individualx i' *All target solutions are not inferior to the parent individualsx i' Is superior to the parent individual in at least one objectx i' Individual offspringx i' *Dominant parent individualsx i' ;
S25, offspring individualsx i' *Substitute for father individualsx i' ;
S26, if the offspring individualsx i' *And father individualsx i' Mutually non-dominant, executeStep S27, otherwise, executing step S28; wherein non-dominant finger: if there is no offspring individualx i' *Dominant parent individualsx i' And offspring individualsx i' *On at least one target than parent individualsx i' Inferior and father individualsx i' Comparing offspring individuals on at least one targetx i' *Inferior, the offspring individuals are calledx i' *And father individualsx i' Non-dominant relationship;
s27, ifDom(x i' *) Less thanDom(x i' ) Step S25 is executed, otherwise, step S29 is executed; wherein the method comprises the steps ofDom(x i' *) AndDom(x i' ) Respectively represent the individuals capable of being dominated by the current optimized task populationx i' *And individualsx i' Is the number of individuals;
s28, discarding offspringx i' *This variation was not accepted;
S29, ifDom(x i' *) AndDom(x i' ) Equal and individualx i' *Is greater than the diversity of individualsx i' Step S25 is performed, otherwise step S28 is performed;
s210, adding 1 to the individual number;
s211, if the individual numberi' >The scale of the optimized task population indicates that all individuals in the optimized task population have been traversed, step S212 is executed, otherwise step S23 is executed;
s212, evolving generation numbereAdding 1;
s213, if the optimized task population is the migration task population, if the current evolution generation numbereGreater than the maximum number of evolutionary generationsEStep S214 is executed, otherwise step S22 is executed; if the optimized task population is the target task populatione-1Is thate 0 Step S214 is performed, otherwise step S22 is performed;
and S214, outputting the optimized task population as a final optimization result.
Preferably, the evaluation index obtained by evaluating all individuals in the population by using the objective function comprises a reverse generation distance index IGD or an over-volume index HV; the minimum value of IGD is the optimal value and the maximum value of HV is the optimal value.
Further, an application of the method described above in accelerating convergence of solutions for K tasks includes: and encoding the solutions of the K tasks into a unified decision space before the generation number e output in the step S8, simultaneously solving a plurality of tasks and multiplexing knowledge in each task for accelerating convergence of the solutions of the K tasks.
As described above, the present invention first uses a single-task multi-objective evolutionary algorithm to individually optimize objective tasks and migration tasks, and stores the decision variables of individuals in the objective population at certain algebraic intervals. And then, taking the final optimized population with good convergence and diversity of the migration task as a source of constant migration information, and hybridizing the final optimized population with the target task with the population stored at regular evolutionary algebra. After information migration, the generated child individuals are evaluated by performing on the target task. When the population quality is optimal, the corresponding evolution generation is the optimal migration generation, and the generation mark is output. The method has effectiveness and reliability, can generate more accurate prediction of the optimal migration occurrence time, and effectively improves the efficiency of multi-task and multi-objective optimization.
Drawings
FIG. 1 is a flow chart of an algorithm of the present invention;
FIG. 2 is a flow chart of a single-task multi-objective evolutionary algorithm;
FIG. 3 shows the best migration opportunities among different multitasking optimization tasks predicted by the algorithm of the present invention.
Detailed Description
In order that the invention may be more readily understood, specific embodiments thereof will be described further below.
A method for predicting the best migration opportunity in a multi-task multi-objective optimization problem, the algorithm flow chart of which is shown in fig. 1, comprising the following steps:
s1, in a multi-task cloud optimization environment, the method is provided withKThe tasks are optimized simultaneously, and the final purpose is to find the optimal solution or optimal solution set of all the tasks. Multitasking optimization is intended to improve overall optimization efficiency by sharing useful information in simultaneous optimization tasks. Traversing all tasks, and setting the task currently being optimized as a taskk,k∈{1,2,3…,K}Then the task currently being optimizedkIs a target task. The task selection method is characterized in that a migration task is allocated to the target task to assist the evolution of the target task, and various task selection methods can be adopted, wherein a migration task is allocated from non-target tasks in a random allocation mode. Migration task sequence numberqThe generation mode of (2) is shown in the formula (1). Wherein,,randomas a function of the random number(s),qin the case of the number [1 ],K]random integers in the range.
When a taskkAfter the optimization is completed, executek=k+1 operations, i.e. tasks in cloud environmentkIs considered as the target task.
Set the repeated sampling test times of the migration task population asTMaximum number of evolutionary generationsEMigrating task populationsQScale ofN Q The dimension number of the migration task decision variable is set to be D Q The repeated sampling test times of the target task population are as followsHThe generation number of the sampling interval of the target task ise 0 Target task populationPScale ofN P The dimension number of the target task decision variable is set to beD P The initialization is performed in the decision space using a uniform sampling approach. In general, the number of the devices used in the system,Tis set to be 30 degrees (half a meter),Eis set to be 1000 degrees per square (1000 a),N Q set to be 100 a and,D Q setting according to the objective optimization problem being processed by the server,His set to be 30 degrees (half a meter),e 0 is set to be 50 degrees (half a meter),N P set to be 100 a and,D P setting according to the migration optimization problem selected randomly.
S2, independently optimizing the migration task population and reserving the final population by using a single-task multi-objective evolutionary algorithm MaOES, wherein the single-task multi-objective evolutionary algorithm is shown in FIG. 2.
Zhang Kai, xu Zhiwei, xie Shengli, et al Evolution strategy-based many-objective evolutionary algorithm through vector equilibrium [ J ]. IEEE Transactions on Cybernetics, 2021, 51 (11): 5455-5467 (Zhang Kai, xu Zhiwei, xie Shengli, et al. Vector-balanced multi-objective evolutionary algorithm based on evolutionary strategies [ J ]. IEEE control theory, J.2021, 51 (11): 5455-5467.) describes a single-task multi-objective evolutionary algorithm MaOES.
The step S2 specifically comprises the following steps:
s21, initializing the generation number of evolution e1.
S22, initializing individual numbers in the optimized task populationi ' 1, represents traversing from the first individual.
S23, mutating the first task population in the current optimized task populationi ' individualsx i' Variant generation offspring is marked asx i' *。
S24, if offspring individualsx i' *Can dominate the parent individualsx i' Step S25 is performed, otherwise step S26 is performed, wherein the dominant finger: if the offspring is individualx i' *All target solutions are not inferior to the parent individualsx i' Is superior to the parent individual in at least one objectx i' Individual offspringx i' *Dominant parent individualsx i' 。
S25, offspring individualsx i' *Substitute for father individualsx i' 。
S26, if the offspring individualsx i' *And father individualsx i' Mutually non-dominant, go to step S27, noThen, step S28 is performed; wherein non-dominant finger: if there is no offspring individualx i' *Dominant parent individualsx i' And offspring individualsx i' *On at least one target than parent individualsx i' Inferior and father individualsx i' Comparing offspring individuals on at least one targetx i' *Inferior, the offspring individuals are calledx i' *And father individualsx i' Non-dominant relationship.
S27, ifDom(x i' *) Less thanDom(x i' ) Step S25 is executed, otherwise, step S29 is executed; wherein the method comprises the steps ofDom(x i' *) AndDom(x i' ) Respectively represent the individuals capable of being dominated by the current optimized task population x i' *And individualsx i' Is a number of individuals.
S28, discarding offspringx i' *This variation was not accepted.
S29, ifDom(x i' *) AndDom(x i' ) Equal and individualx i' *Is greater than the diversity of individualsx i' Step S25 is performed, otherwise step S28 is performed. The maximum extension distance is used here to measure the diversity of individuals. The maximum extension distance is the product of the sum of the manhattan distances between the current individual and other individuals in the target space and the minimum manhattan distance between the current individual and other individuals. The larger the maximum extension distance is, the better the individual diversity is, and the smaller the maximum extension distance is, the worse the individual diversity is.
S210, adding 1 to the individual number.
S211, if the individual numberi' >And (3) the size of the optimized task population indicates that all individuals in the optimized task population have been traversed, executing step S212, otherwise executing step S23.
S212, evolving generation numbere1 is added.
S213, if the optimized task population is the migration task population, if the current evolution generation numbereGreater than the maximum number of evolutionary generationsEStep S214 is executed, otherwise step S22 is executed; if the optimized task population is the target task populatione-1Is thate 0 Step S214 is performed, otherwise step S22 is performed.
And S214, outputting the optimized task population as a final optimization result.
When the optimized task is a migration task, the whole migration task population parameter is stored offline for mating and analysis, and the process is repeatedTRecord the first timetThe final migration task population of the multiple iterations is saved asQ t ,。
S3, independently optimizing migration task populations by using single-task multi-objective evolutionary algorithmTSecondary final migration task populationQ t Averaging according to decision variable bits in the migration task population to generate an average final migration task population, which is recorded as,/>The j-th decision variable of the i-th individual +.>The calculation formula of (2) is shown in the formula;
wherein the method comprises the steps ofRepresent the firsttFinal migration task population for multiple iterations->Middle (f)iIndividual firstjThe bit decision variable is used to determine,representation ofTSecond->Average value of (2);
the decision variable dimension is the number of parameters to be optimized in the target task or the migration task. In a single-task multi-objective evolutionary algorithm, these decision variables need to be searched and optimized to find the optimal solution. For multiple target tasks, each task has a set of decision variables, which may differ in dimension. In order to compare and uniformly process the decision variables with different dimensions, the solutions searched and optimized according to the dimensions of the decision variables in each task can be averaged, so that the solutions corresponding to the different decision variables of different targets are subjected to cross operation to obtain an equalized population.
S4, independently optimizing target task populations by using a single-task multi-target evolution algorithm, wherein each evolution of the target task populations is performede 0 The intermediate population is saved after generation, and the optimization process is repeatedHRecord the first timehSecond repeat optimizationeThe generation-saved population isWhereine 0 Parameters set manually for saving the intermediate evolution results of the target population,eto preserve the number of evolutionary passages in the middle of the target population,/->;
S5, toHThe first to be savedeGeneration populationAveraging according to decision variable bits of the target task population to generate an averageeThe generation target task population is marked as +.>,/>The j-th decision variable of the i-th individual +.>The calculation formula of (2) is shown as formula (3); />
Wherein the method comprises the steps ofRepresent the firsthSubsampled firsteGeneration target task populationi*Individual firstj*Bit decision variable +_>Representation ofHSecond->Average value of (2);
evaluating all individuals in the population using the objective function and calculating the populationEvaluation index O (>)。
The population evaluation index herein may use a reverse generation distance (Inverted Generational Distance, IGD) or a Hyper Volume index (HV), etc., wherein a smaller IGD value or a larger HV value indicates a better convergence and diversity of tasks.
S6, optimizing the target task independently and storing the average value of the final population after every certain algebraAnd mean value of final population of migration tasks +.>Using SBX crossover operator for information migration and generating offspring populations +.>As shown in formula (4), where β represents the distribution index in the SBX operator, here set to 20. Then use the objective function to group +.>All individuals in the population are evaluated and the evaluation index O (/ -for the population is calculated>). The population evaluation index may be IGD, HV, or the like.
S7, comparing O%) If the population evaluation index can use IGD, when O (++>) And taking the minimum value, namely the offspring population obtained by information migration at the moment performs optimally. I.e. indicating information migration generation fetcheAnd the best performance can be achieved through information migration. If the population evaluation index can use HV, when O (++)>) And when the maximum value is taken, namely the offspring population obtained by information migration at the moment performs optimally. Thus, recordeAnd the value of (2) is the best time for information migration at this time, as shown in the formula (5).
S8, outputting the generation numbere。
Comparing corresponding generation target population and migrationPopulation of offspring after transferEvaluation index O (+)>) And O ()>) And the size of the (c) can be used for judging whether the positive migration or the negative migration occurs. If the offspring population evaluation index value O (++) after migration >) Evaluation index value O of specific target population (+)>) More preferably, the migration is effective or forward migration. If the offspring population evaluation index value O (++) after migration>) Evaluation index value O of specific target population (+)>) Worse, failure migration or negative migration.
As described above, the present invention first uses a single-task multi-objective evolutionary algorithm to individually optimize objective tasks and migration tasks, and stores the decision variables of individuals in the objective population at certain algebraic intervals. And then, taking the final optimized population with good convergence and diversity of the migration task as a source of constant migration information, and hybridizing the final optimized population with the target task with the population stored at regular evolutionary algebra. After information migration, the generated child individuals are evaluated by performing on the target task. When the population quality is optimal, the corresponding evolution generation is the optimal migration generation, and the generation mark is output. The method has effectiveness and reliability, can generate more accurate prediction of the optimal migration occurrence time, and effectively improves the efficiency of multi-task and multi-objective optimization.
Experiments were performed herein on a standard multitasking multi-objective test problem set. The standard test set is commonly issued by expert scholars from university of southern kenyaku, chongqing university, university of Royal melbourne in Australia, university of hong Kong City, university of national university of Singapore, university of Sullima, university of Santa Clay in England, university of Osaka, japan. A detailed description of this can be found in the articles Yuan Y, ong Y-S, feng L, qin A K, gupta A, da B, zhang Q, tan K C, jin Y, ishibuchi H. Evolutionary Multitasking for Multiobjective Continuous Optimization: benchmark Problems, performance Metrics and Baseline Results [ J ]. ArXiv:1706.02766 [ cs ], 2017. (Yuan Y, ong Y-S, feng L, qin A K, gupta A, da B, zhang Q, tan K C, jin Y, ishibuchi H. Multi-objective continuous optimization' S evolutionary multitasking: benchmark problem, performance index and baseline results [ J ]. ArXiv:1706.02766 [ cs ], 2017 ]). The standard test problem set can measure the performance of the evolutionary algorithm in solving the multi-task multi-objective optimization problem, and has the important significance of authoritative value and milestones. It is believed that the similarity of fitness landscape and the degree of intersection of optimal solutions to optimization problems are the two most important factors affecting the effectiveness of migration of genetic information between tasks. If the values of the corresponding dimensions of the optimal solutions of different tasks are closer, the genetic information among the tasks is more beneficial to migration. Similarly, the more similar the fitness landscape of the optimization functions of different tasks, the more helpful an individual learns from one task to indirectly optimize other tasks. Thus, the benchmark problem can be categorized into three categories, namely Complete Intersection (CI), partial Intersection (PI) and complete disjoint (NI), according to the degree of intersection that is globally optimal. The design benchmark questions can be categorized into three categories, namely, high Similarity (HS), medium Similarity (MS) and Low Similarity (LS), based on similarity of fitness landscapes.
As shown in fig. 3 (a), on the dual-task multi-objective test problem PILS with low similarity of the global optimum portion intersection, PILS1 is taken as a migration task, PILS2 is taken as an objective task, and PILS1 and PILS2 are optimized at the same time. The PILS1 problem is constructed by classical test functions Ackley, which inevitably sink into traps of locally optimal solutions in the process of finding globally optimal solutions, and thus are widely used for testing of optimization algorithms to verify optimalityThe ability of the chemosynthesis algorithm to find globally optimal solutions. The PILS2 problem is constructed by a classical Weierstrass function, is one of the most important functions in the field of statistics mathematics, is widely applied to the disciplines such as geometry, mathematic physics and complex transformation theory, and has quite important application value in optimizing physical properties of steel parts such as automobiles and bridges subjected to thermal action and real problems such as complex interest calculation in the financial field. In the experiment, when the information migration generation is 350 generations, the minimum IGD value 6.7122E-1 is obtained, and the optimal migration time is 350 generations. Wherein, the PILS1 and PILS2 problems are two double-target problems, the target function expressions are respectively shown in the formulas (6) and (7), the decision variable number n is 50, Representing a 49-dimensional offset vector.
The PILS2 problem constructed by the classical Weierstrass function is used in the engineering field to optimize physical property calculation of steel parts such as automobiles, bridges and the like subjected to thermal action. The following problems are as follows:
the combustion chamber design of an automotive engine is optimized to improve combustion efficiency and reduce emissions production.
The design of the bridge structure is optimized to improve the heating performance and prolong the service life.
The manufacturing process of the steel parts is optimized to improve the physical properties and reduce the production cost.
The heat treatment process of the steel is optimized to improve the physical properties such as strength, hardness and the like.
The corrosion resistance of the steel is optimized to improve its service life and reduce maintenance costs.
The thermal expansion coefficient of the steel is optimized to improve the stability and reliability of the steel in a high-temperature environment.
The physical properties such as the heat conductivity and the heat capacity of the steel are optimized so as to improve the performance of the steel in heat conduction and heat storage.
The thermal stability of the steel is optimized to improve its stability and reliability in high temperature environments.
The application of thermotechnical [ J ].2013 ] in optimizing the combustion chamber design of an automotive engine, using the PILS2 problem optimization algorithm, optimizes five tasks while achieving multiple objectives among the tasks:
Minimizing the volume of the combustion chamber: by optimizing the shape and size of the combustion chamber, the volume of the combustion chamber can be reduced, thereby improving the power density and fuel efficiency of the engine.
Maximizing combustion efficiency: by optimizing the shape and size of the combustion chamber, the mixing effect of fuel and air can be improved, and the combustion efficiency can be improved, thereby reducing the generation of emissions.
Minimizing the temperature gradient of the combustion chamber: by optimizing the shape and size of the combustion chamber, the temperature gradient inside the combustion chamber can be reduced, thereby reducing the thermal stress of the combustion chamber and prolonging the service life of the engine.
Minimizing noise and vibration of the combustion chamber: by optimizing the shape and size of the combustion chamber, noise and vibration inside the combustion chamber can be reduced, and the comfort and reliability of the engine can be improved.
Minimizing the manufacturing cost of the combustion chamber: by optimizing the shape and size of the combustion chamber, the manufacturing cost of the combustion chamber can be reduced, and the economy and competitiveness of the engine can be improved.
Therefore, after the algorithm of the invention finds out the optimal information migration generation of the PILS2 problem optimization algorithm, when the solutions of a plurality of tasks of the PILS2 problem optimization algorithm are encoded into a unified decision space before the optimal information migration generation, the knowledge in the plurality of tasks and multiplexing related tasks can be solved simultaneously without negative migration, so that the calculation resource can be saved, the convergence can be accelerated, and the overall optimization efficiency can be improved.
As shown in (b) of fig. 3, on the dual-task multi-objective test problem CIMS of similarity in global optimum full intersection, CIMS1 is taken as a migration task, CIMS2 is taken as a objective task, and CIMS1 and CIMS2 are simultaneously optimized. The CIMS1 test function is also constructed by a well-known Ackley function, and can evaluate the ability of an optimization algorithm to find global optima. CIMS2 test functions are constructed from well-known Rastrigin test functions. The Rastrigin function is a non-convex, high-dimensional function with multiple local minima and a global minimum, and its complexity and non-convex nature make it difficult for the optimization algorithm to find its globally optimal solution. The Rastrigin function can simulate non-convex high-dimensional optimization problems such as neural network parameter optimization, blind source separation in signal processing, design optimization in the aerospace field and the like. In the experiment, when the information migration generation is 150 generations, the minimum IGD value 7.869E-2 is obtained, and the optimal migration time is output for 150 generations. Wherein, the CIMS1 and CIMS2 problems are two double-target problems, the target function expressions are respectively shown in the formulas (8) and (9), the decision variable number n is 10,a rotation matrix of 9*9 is shown,representing a 9-dimensional offset vector.
CIMS problems constructed from classical Rastrigin functions are used in the engineering field to optimize design optimization in the aerospace field, solving the following problems:
and (3) aircraft design optimization: CIMS problems can be used to optimize the design of aircraft, including the design of wings, fuselage, engines, and the like. By optimizing the shape, size, and materials of these components, aircraft performance and efficiency may be improved, reducing fuel consumption and emissions.
Spacecraft design optimization: CIMS problems can be used to optimize the design of spacecraft, including the design of orbit, propulsion systems, control systems, and the like. By optimizing the parameters of these components, the performance and efficiency of the spacecraft can be improved, and the energy consumption and cost can be reduced.
And (3) optimizing the engine design: CIMS problems may be used to optimize engine design, including combustor, nozzle, turbine, etc. designs. By optimizing the shape, size, and materials of these components, the efficiency and performance of the engine can be improved, reducing fuel consumption and emissions.
Flight control optimization: CIMS problems can be used to optimize the design of flight control systems, including the design of autopilot, navigation, attitude control, and the like. By optimizing the parameters of these components, the performance and efficiency of the flight control system can be improved, reducing the incidence of flight accidents.
And (3) designing and optimizing an aviation material: CIMS problems can be used to optimize the design of aerospace materials, including those of metals, composites, and the like. By optimizing the structure and performance of these materials, the performance and efficiency of the aircraft can be improved, reducing energy consumption and cost.
In the design optimization of the aviation material, the following six tasks are optimized by using a CIMS problem optimization algorithm, and a plurality of targets in each task are simultaneously achieved:
minimizing the weight of the material: the weight of an aircraft is an important design criterion because it directly affects the flight performance and fuel consumption. By optimizing the density and shape of the material, the weight of the material can be minimized.
Maximizing the strength of the material: aircraft are required to have sufficient strength to withstand various loads and environmental conditions. By optimizing the composition and structure of the material, the strength of the material can be maximized. Minimizing the cost of materials: the manufacturing cost of an aircraft is an important consideration. By optimizing the choice and use of materials, the cost of the materials can be minimized.
Minimizing material loss: during use of the aircraft, the material may be subject to wear, corrosion, etc., resulting in loss of material. By optimizing the choice and use of materials, material loss can be minimized.
Maximizing the reliability of the material: aircraft are required to have sufficient reliability to ensure safety and sustainability. By optimizing the choice and use of materials, the reliability of the materials can be maximized.
Minimizing the environmental impact of the material: the manufacture and use of aircraft has a certain impact on the environment. By optimizing the choice and use of materials, the environmental impact of the materials can be minimized.
Therefore, after the algorithm of the invention finds out the optimal information migration generation of the CIMS problem optimization algorithm, when the solutions of a plurality of tasks of the CIMS problem optimization algorithm are encoded into a unified decision space before the optimal information migration generation, the knowledge in the plurality of tasks and multiplexing related tasks can be solved simultaneously without negative migration, so that the calculation resources can be saved, the convergence is accelerated, and the overall optimization efficiency is improved.
As shown in fig. 3 (c), on the dual-task multi-objective test problem PIMS of similarity in the global optimum part intersection, PIMS2 is taken as a migration task, PIMS1 is taken as a objective task, and PIMS1 and PIMS2 are optimized at the same time. The PIMS1 test function is constructed from a well-known Ackley test function that is characterized by being non-convex, multimodal and highly nonlinear, making it one of the standard test functions for optimization algorithm evaluation. By optimizing the Ackley function, indexes such as convergence, robustness, global optimization capacity and the like of an optimization algorithm can be tested, so that the performance of the algorithm is evaluated. The Ackley function may represent a complex periodic variation that may simulate, for example, weather changes, economic changes, etc. The PIMS2 test function is constructed from the well-known rosenblock test function. The Rosenblock function is characterized by complex valley, plateau and gradient direction changes, which makes it one of the standard test functions for optimization algorithm evaluation. The rosenblock function may represent a complex nonlinear relationship that may simulate real-world ecosystem optimization problems and economic system optimization problems. In the experiment, when the information migration generation is 50 generations, the minimum IGD value 5.403E-3 is obtained, and the optimal migration time is output for 50 generations. Wherein, PIMS1 and PIMS2 problems are two double-target problems, and the objective function is expressed The formula is shown as the formula (10) and the formula (11), the decision variable number is 50,represents a rotation matrix of 49 x 49, < >>Represents a rotation matrix of 49 x 49, < >>Representing a 49-dimensional offset vector.
The PIMS2 problem constructed by rosenblock functions is used in engineering to simulate real world ecosystem optimization problems, solving the following problems:
species diversity maintenance of the ecosystem: by optimizing the number and distribution of the various species in the ecosystem, species diversity in the ecosystem is maintained and improved.
Energy flow optimization of ecosystem: by optimizing the energy flow between the various species in the ecosystem, the efficiency of energy utilization in the ecosystem is improved.
Maintenance of the stability of the ecosystem: by optimizing the interaction relationship among the species in the ecological system, the stability of the ecological system is maintained and improved.
Resource utilization optimization of an ecological system: the resource utilization in the ecosystem is maximized by optimizing the utilization efficiency of the resources by each species in the ecosystem.
Environmental adaptability optimization of the ecosystem: the environmental adaptability in the ecological system is improved by optimizing the adaptability of each species in the ecological system to the environment.
The PIMS2 problem constructed by rosenblock functions uses a multi-objective optimization approach to solve the multitasking problem when modeling energy flow in an ecosystem. The following five tasks are optimized while achieving multiple objectives among the tasks:
maximizing the overall productivity of the ecosystem, i.e., maximizing the growth rate and reproductive rate of all organisms in the ecosystem. Competition and predation relationships among organisms in the ecosystem are minimized to ensure stability and sustainability of the ecosystem.
The diversity and richness of species in the ecosystem are maximized to enhance the anti-interference capability and adaptability of the ecosystem.
Mortality and loss rates of organisms in the ecosystem are minimized to ensure health and stability of the ecosystem.
The energy utilization efficiency and the conversion efficiency in the ecological system are maximized, so that the energy utilization rate and the production efficiency of the ecological system are improved.
Therefore, after the algorithm of the invention finds out the optimal information migration generation of the PIMS2 problem optimization algorithm, when the solutions of a plurality of tasks of the PIMS2 problem optimization algorithm are encoded into a unified decision space before the optimal information migration generation, the knowledge in the plurality of tasks and multiplexing related tasks is solved simultaneously without negative migration, so that the calculation resource can be saved, the convergence is accelerated, and the overall optimization efficiency is improved.
As shown in fig. 3 (d), on the globally optimal fully disjoint low-similarity dual-task multi-objective test problem NILS, NILS1 is taken as the migration task, NILS2 is taken as the objective task, and NILS1 and NILS2 are simultaneously optimized. The NILS1 test function is constructed from a well-known rastigin test function, which is a high-dimensional, non-convex, multimodal and global optimization problem that contains many local minima and a global minimum that are difficult to solve by conventional optimization methods. The NILS2 test function is constructed from the well-known Schwefel test function. The Schwefel function is a high-dimensional, non-convex, multimodal and global optimization problem that contains many local minima and a global minimum that are difficult to solve by conventional optimization methods. The Schwefel function can be used for simulating non-convex high-dimensional optimization problems such as signal processing optimization problems, machine learning model optimization problems, energy scheduling and the like. In the experiment, when the information migration generation is 200 generations, the minimum IGD value 6.782E-1 is obtained, and the optimal migration time 2 is outputGeneration 00. Wherein, NILS1 is a three-objective problem, NILS2 is a two-objective problem, and the objective function expressions are shown in formulas (12) and (13), respectively. For NILS1, the decision variable number is 25, for NILS2 n50.Representing a 24-dimensional offset vector.
The NILS2 problem constructed by Schwefel functions, when used for energy scheduling in the engineering field, solves the following problems:
scheduling a power system: in an electrical power system, the output of the generator needs to be scheduled to meet load demands and ensure system stability. The NILS2 problem may be used to optimize generator output of the electrical power system to minimize cost and carbon emissions.
Energy supply chain optimization: in the energy supply chain, there is a need to optimize the production, transportation and storage of energy to ensure reliable supply of energy and to minimize costs. The NILS2 problem can be used to optimize various links in the energy supply chain to maximize efficiency and profits.
Energy market trading: in the energy market, there is a need to predict and optimize the price and supply and demand of energy to maximize revenue and meet consumer demand. NILS2 questions can be used to optimize trading strategies and price prediction models in the energy market to maximize revenue and reduce risk.
And (3) energy consumption management: in energy consumption management, there is a need to optimize the use of energy to minimize cost and carbon emissions. The NILS2 problem can be used to optimize various links in energy consumption management, including purchasing, use, and recycling of energy, to maximize efficiency and reduce environmental impact.
S Dhanalakshm, S Kannan, S Baskar, K Mahadevan, multi-objective Generation Scheduling Using Modified Non-dominated Sorting Genetic Algorithm-II, international conference on swarm, evolutionary, and memetic computing [ J ].2015.456-470 (S Dhanalakshm, S Kannan, S Baskar, K Mahadevan, multi-objective Generation schedule based on improved non-dominant ordering genetic algorithm II, group, evolution and model cause computation International conference [ J ]. 2015.456-470.)
The NILS2 problem constructed by Schwefel functions is optimizing generator output of an electric power system, and adopts a multi-objective optimization method to solve the multi-task problem. The following five tasks are optimized while achieving multiple objectives among the tasks:
determining the output power of the generator; meanwhile, the power generation cost is minimized, the pollution emission is minimized, and the reliability and stability of the power system are maximized;
determining the starting and stopping time of the generator; meanwhile, the power generation cost is minimized, the pollution emission is minimized, and the reliability and stability of the power system are maximized;
determining a fuel type and a fuel consumption rate of the generator; meanwhile, the power generation cost is minimized, the pollution emission is minimized, and the reliability and stability of the power system are maximized;
Determining a maintenance plan for the generator; meanwhile, the power generation cost is minimized, the pollution emission is minimized, and the reliability and stability of the power system are maximized;
determining load demand and supply capacity of the power system; meanwhile, the power generation cost is minimized, the pollution emission is minimized, and the reliability and stability of the power system are maximized;
therefore, after the algorithm of the invention finds out the optimal information migration generation of the NILS2 problem optimization algorithm, when the solutions of a plurality of tasks of the NILS2 problem optimization algorithm are encoded into a unified decision space before the optimal information migration generation, the knowledge in the plurality of tasks and multiplexing related tasks can be solved simultaneously without negative migration, so that the calculation resource can be saved, the convergence can be accelerated, and the overall optimization efficiency can be improved.
Finally, it should be noted that the above embodiments are only for illustrating the technical solution of the present invention and not for limiting the scope of the present invention, and although the present invention has been described in detail with reference to the preferred embodiments, it should be understood by those skilled in the art that the technical solution of the present invention may be modified or substituted equally without departing from the spirit and scope of the technical solution of the present invention.
Claims (4)
1. A method for predicting an optimal migration opportunity in a multitasking, multitasking optimization problem, comprising the steps of:
S1,KOptimizing each task simultaneously, traversing all tasks, wherein the task currently being solved is a target task, randomly assigning one task from other tasks as a migration task to assist in optimizing the target task, wherein the population corresponding to the target task is a target population, and the population corresponding to the migration task is a migration population;
set up migration task populationQScale ofN Q The dimension number of the migration task decision variable is set to beD Q Target task populationPScale ofN P The dimension number of the target task decision variable is set to beD P The maximum evolution generation numbers of the target task and the migration task areE;
S2, independently optimizing the assigned migration task populations by using a single-task multi-objective evolutionary algorithm and reserving the final populations for mating and analysis, wherein each evolution of the migration task populationsEThe final population is saved after generation, and the optimization process is repeatedTRecord the first timetThe final population of the multiple iterations is saved asQ t ,t∈{1,2,3…,T};
S3, independently optimizing migration task populations by using single-task multi-objective evolutionary algorithmTSecondary final migration task populationQ t Averaging according to decision variable bits in the migration task population to generate an average final migration task population, which is recorded as,/>The j-th decision variable of the i-th individual +.>The calculation formula of (2) is shown in the formula;
Wherein the method comprises the steps ofRepresent the firsttFinal migration task population for multiple iterations->Middle (f)iIndividual firstjBit decision variable +_>Representation ofTSecond->Average value of (2);
s4, independently optimizing the current target task population by using a single-task multi-target evolution algorithm, wherein each evolution of the target task populatione 0 The intermediate population is saved after generation, and the optimization process is repeatedHRecord the first timehSecond repeat optimizationeThe generation-saved population isWhereine 0 Parameters set manually for saving the intermediate evolution results of the target population,eto preserve the number of evolutionary passages in the middle of the target population,/->;
S5, toHThe first to be savedeGeneration populationAveraging according to decision variable bits of the target task population to generate an averageeGeneration target task population recordIs->,/>The j-th decision variable of the i-th individual +.>The calculation formula of (2) is shown as formula (3);
wherein the method comprises the steps ofRepresent the firsthSubsampled firsteGeneration target task populationi*Individual firstj*The bit decision variable is used to determine,representation ofHSecond->Average value of (2);
s6, willAnd->Using SBX crossover operator for information migration and generating offspring populations +.>Wherein β represents a distribution index in the SBX operator as shown in formula (4); then use the objective function to group +. >All individuals in (1) are evaluated and the population +.>Evaluation index O (>);
S7, comparing O%) When O (+)>) When the optimal value is taken, the information migration generation is indicatedeWhen information migration is performed, the best performance can be achieved, and records are recordedeObtaining the optimal time for information migration;
s8, outputting the generation numbere。
2. The method of claim 1, wherein the step of individually optimizing the optimized tasks by the single-task multi-objective evolutionary algorithm comprises:
s21, initializing the generation number of evolutione1 is shown in the specification;
s22, initializing individual numbers in the optimized task populationi ' 1, indicating traversal from the first individual;
s23, mutating the first task population in the current optimized task populationi ' individualsx i' Variant generation offspring is marked asx i' *;
S24, if offspring individualsx i' *Can dominate the parent individualsx i' Step S25 is performed, otherwise step S26 is performed, wherein the dominant finger: if the offspring is individualx i' *All target solutions are not inferior to the parent individualsx i' And at least one ofTarget is superior to parent individualsx i' Individual offspringx i' *Dominant parent individualsx i' ;
S25, offspring individualsx i' *Substitute for father individualsx i' ;
S26, if the offspring individualsx i' *And father individualsx i' Mutually non-dominant, executing step S27, otherwise, executing step S28; wherein non-dominant finger: if there is no offspring individual x i' *Dominant parent individualsx i' And offspring individualsx i' *On at least one target than parent individualsx i' Inferior and father individualsx i' Comparing offspring individuals on at least one targetx i' *Inferior, the offspring individuals are calledx i' *And father individualsx i' Non-dominant relationship;
s27, ifDom(x i' *) Less thanDom(x i' ) Step S25 is executed, otherwise, step S29 is executed; wherein the method comprises the steps ofDom(x i' *) AndDom(x i' ) Respectively represent the individuals capable of being dominated by the current optimized task populationx i' *And individualsx i' Is the number of individuals;
s28, discarding offspringx i' *This variation was not accepted;
s29, ifDom(x i' *) AndDom(x i' ) Equal and individualx i' *Is greater than the diversity of individualsx i' Step S25 is performed, otherwise step S28 is performed;
s210, adding 1 to the individual number;
s211, if the individual numberi' >Optimized task speciesThe group scale indicates that all individuals in the optimized task population have been traversed, step S212 is executed, otherwise step S23 is executed;
s212, evolving generation numbereAdding 1;
s213, if the optimized task population is the migration task population, if the current evolution generation numbereGreater than the maximum number of evolutionary generationsEStep S214 is executed, otherwise step S22 is executed; if the optimized task population is the target task populatione-1Is thate 0 Step S214 is performed, otherwise step S22 is performed;
And S214, outputting the optimized task population as a final optimization result.
3. The method according to claim 1, wherein the evaluation index obtained by evaluating all individuals in the population using the objective function comprises a reverse generation distance index IGD or an over-volume index HV; the minimum value of IGD is the optimal value and the maximum value of HV is the optimal value.
4. Use of the method according to claim 1 for accelerating the convergence of the solutions of K tasks, wherein the solutions of K tasks are encoded into a unified decision space before the generation number e output in step S8, while solving a plurality of tasks and multiplexing the knowledge in each task.
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