Expressing And Obtaining Pareto Solutions In Multi-Objective Optimization Problem

The relative high volume of research conducted on many methods solving multi-objective optimization problems (MOP) in the last few years. The methods mainly are divided into two kinds: conventional mathematical methods and methods based on artificial intelligence.Firstly, the paper provides an overview of MOP for its mathematical model, history and research direction.Secondly, the paper discusses conventional mathematical methods (direct and indirect) of MOP. This paper first reveals graphically the law of the location of the Pareto optimal frontier of the linear MOP that has convex Pareto optimal frontier. Then, the paper elaborates basic ideas of many kinds of conventional mathematical direct methods of MOP, and describes their defects. Besides, the paper discusses in detail many kinds of methods based on artificial intelligence (GA, ASO, PSO, and so on).Third, this paper proposes a novel multi-objective genetic algorithm (MOGA) which obtains efficiently distributed uniformly Pareto non-dominated solutions. This algorithm is mainly criticized for a new fitness function that uses the minimum distance between an individual and optimal non-dominated solutions to compute the individual fitness in a population.Finally, the paper uses testing functions and performance metrics (convergence and diversity) to evaluate experimentally the algorithm above, and compares it with other MOGAs. It can be seen from the experimental results that the algorithm can be applied to convex or non-convex, uniform or non-uniform, and continuous or non-continuous MOPs, and it has more excellent convergence comparing with other MOGAs.