Multi-objective Optimization Solution Set Distribution Of Mimicry Physics Research

Multi-objective optimization problems have drawn widely attention on bothengineering application and scientific research. How to find an efficientalgorithm for achieving the compromise between several targets to get a groupof optimal solutions is a key point for MOPs research. The multi-objectiveartificial physics optimization algorithm (MOAPO) is a stochastic optimizationalgorithm that is recently proposed. It has been successfully used for solvingglobal optimization problems. This paper mainly concentrates on distribution ofthe solution set of MOAPO by combing MOPs with MOAPO. The maincontents are as follows:1) According to uniform distribution of the solution set of MOPs, methodsfor maintaining distribution of the solution set in current MOAPO aresummarized. This paper combines characteristics of MOAPO withnon-dominated sorting and crowding distance and improves mass function instandard MOAPO. The crowding distance is reflected in the mass function of theMOAPO algorithm. MOAPO based on non-dominated sorting is relatively efficient through simulation testing.2) According to characteristics of the un-uniform distribution of the solutionset of MOPs, the MOPs with the un-uniform distribution of the solution set aredefined. And introduce some testing function for it. This paper combines theparticularity of the un-uniform distribution problems and idea of MOAPO andintroduces MOAPO based on max-min distance. Especially in the process ofeliminating the individual, choose individuals that are nearest to the one that hasthe max-min distance density to eliminate for maintaining the true distributionof the solution set. And using the basic knowledge of probability theory, theconvergence of this algorithm is proved. In the test process of this algorithm,choosing the degree of exposure to the algorithm, extensive and convergence ofdistribution of test, compared with the classical algorithm. The testing resultsshow this algorithm is effective for solving the un-uniform distribution of thesolution set in multi-objective optimization problem.