Fruit Fly Optimization Algorithm For Constrained Optimization Problems

There are many constrained optimization problems generally in scientific research and engineering applications.How to solve the constrained optimization problem has very important theoretical significance and practical application value.The optimization of constrained optimization problem must consider both constraints and objectives.However,traditional optimization methods balance objective function and constraints based on gradient information.Therefore,these methods often depend on the mathematical properties of the problem and are difficult to solve complex constrained optimization problems effectively.In recent years,many evolutionary algorithms to solve constrained optimization problems have emerged.These methods make full use of the advantage of the group search mechanism of evolutionary algorithms,and have achieved good research results.However,they still face many challenges,mainly including the treatment of equation constraint,discrete constraint optimization,the imbalance between constraints and optimization objectives,the treatment of infeasible solutions,the lack of universal constraint and adaptive constraint processing methods.As a new swarm intelligence evolutionary optimization algorithm,fruit fly optimization algorithm(FOA)has the advantages of simple algorithm framework,less control parameters and strong local search ability.And it is easy to solve complex constrained optimization problems by embedding specific search methods according to the characteristics of problem,which can better balance the global search ability and local search ability of the algorithm.Therefore,this paper will carry out the research on using FOA to solve discrete and continuous optimization problems with constraints.The main work is as follows:(1)For the discrete multidimensional knapsack problem(MKP),aiming at the challenges of low quality of solution and slow convergence rate in solving large-scale MKP,a binary multi-swam fruit fly optimization algorithm(b MFOA)based on frequency tree mining is proposed.The b MFOA designs a new search strategy and heuristic operator to guide the direction of population evolution and improve the global search ability by constructing the item frequency tree.A multi-swarm cooperative strategy is designed to enhance population diversity,and a local escape strategy is proposed to avoid falling into local optimum.Finally,five classical representative algorithms for solving MKPs,including b FOA,TR-BDS,TE-BDS,HPSOGO and HBDE,are selected as the compared algorithms.Comparative experiments are carried out based on 58 standard test benchmarks.The experimental results show that b MFOA has good performance in solving MKP problems with different scales.(2)For the problem of continuous constrained uniform experimental design,aiming at the problems of poor population distribution diversity and weak local search ability in the existing two-stage uniform experimental design methods,a new two-stage fruit fly optimization algorithm(To PFOA)is proposed.In the first stage,To PFOA adopts the global search strategy by combining difference operator,and updates the center of cluster by k-means clustering and external document to dynamically improve the diversity of population distribution.In the second stage,a new operator is defined to improve the local search ability.Finally,two representative two-stage optimization algorithms,To PDEEDA and To PDE,are selected as compared algorithms.The comparative experiments are carried out based on 5 benchmarks and 1 industrial problem.The experimental results show that To PFOA is superior to To PDEEDA and To PDE in terms of solution quality and stability.(3)For the problem of continuous constrained uniform experimental design,most of the existing algorithms are based on two-stage optimization framework,which still has the disadvantages of high complexity of algorithm structure and insufficient use of valuable infeasible solutions.A heuristic fruit fly optimization algorithm based on greedy strategy(GSFOA)is proposed.GSFOA generates new individual by greedy strategy to improve the distribution uniformity of the population in the constrained area.An adaptive repair strategy is designed based on TMSC criterion to utilize valuable infeasible individuals,which can help enhancing the local search ability of the algorithm and further improve the performance of the algorithm.Finally,To PFOA,To PDEEDA and To PDE are selected as the compared algorithms,and comparative experiments are carried out based on 5 benchmarks and 1 industrial case.The results show that GSFOA is better than the compared algorithms in terms of solution quality,and behavior excellent in average running time.