Using SP-MEC For Multiobjective Optimization Problems

There are many multi-objective optimization problems in the real world. The multi-objective optimization is a rising subject in the recent years.Evolutionary Algorithms (EA) have some advantages in the complex multi-objective optimization problems. Schaffer firstly used VEGA to optimize multi-objective problems in the mid -1980s. Most of the approaches can be put into three categories: (1) Aggregating approaches: this approach combines objectives into a single function to optimize. (2) Population-based non-Pareto approaches, e.g. Vector Evaluated Genetic Algorithms (VEGA): this approach performs the proportional selection according to each objective function. Although it modifies the selection mechanism of the GA, this approach behaves as an aggregating approach. (3) Pareto-based approaches, e.g. Strength Pareto Evolutionary Algorithm (SPEA): this approach is outstanding in the approaches to evolutionary multi-objective optimization.To overcome the problems of GA, Mind Evolutionary Computation (MEC) was proposed, which imitates two phenomena of human society - similartaxis and dissimilation. After several years' studies on its theory and experiment, MEC has been made great progress. So far, a preliminary system has already been established for MEC.This paper proposes a kind of multi-objective optimization algorithm, called Scored Pareto Mind Evolutionary Computation (SP-MEC). It uses Pareto theory and a mechanism of score in MEC to solve the multi-objective optimization problems.The principles of SP-MEC are: (1) A number of individuals are scattered in the whole solution space, and then some better individuals of them are selected as the initial centers for every group according to their scores. (2) Each group only searches a local area and gradually shifts from its initial center to the Pareto front. (3) During the process of shift to this front, this algorithm would bound the searching region of the group and control the shifting direction of the group. Both of above function (1) and function (3) are called as dissimilation, and function (2) is called as similartaxis.SP-MEC is compared with the reference algorithms of VEGA, NSGA, SPEA and Pareto-MEC. The test functions used in the experiment are a suit of four different test problems: convexity, non-convexity, discreteness and non-uniformity. On all test problems, SP-MEC outperforms VEGA, NSGA and SPEA. On the last test problem, SP-MEC is as good as Pareto-MEC; on other test problems, SP-MEC is better than Pareto-MEC.Two evaluative methods: Cover and Spacing are used as the quantificational criterion for SP-MEC on the test functions: non-convexity and non-uniformity. SPEA and Pareto-MEC with the superior performance are used the reference algorithms, where Pareto-MEC was proposed by us. The experiment shows the performance of SP-MEC from the angle of arith. With Spacing in non-uniformity test function, SPEA is better than SP-MEC, andPareto-MEC is almost as good as SP-MEC. With Spacing in non-convexity test function, SP-MEC is better than not only SPEA but also Pareto-MEC. With Cover in two test functions, SP-MEC is better than not only SPEA but also Pareto-MEC.Different from the reference algorithms that use the pre-specified generation number as their terminations, SP-MEC and Pareto-MEC have an objective termination criterion that can ensure the quality of solutions and the computational efficiency.