Abstract
When faced with complex optimization problems with multiple objectives and multiple variables, many multiobjective particle swarm algorithms are prone to premature convergence. To enhance the convergence and diversity of the multiobjective particle swarm algorithm, a multiobjective particle swarm optimization algorithm based on the grid technique and multistrategy (GTMSMOPSO) is proposed. The algorithm randomly uses one of two different evaluation index strategies (convergence evaluation index and distribution evaluation index) combined with the grid technique to enhance the diversity and convergence of the population and improve the probability of particles flying to the real Pareto front. A combination of grid technology and a mixed evaluation index strategy is used to maintain the external archive to avoid removing particles with better convergence based only on particle density, which leads to population degradation and affects the particle exploitation ability. At the same time, a variation operation is proposed to avoid rapid degradation of the population, which enhances the particle search capability. The simulation results show that the proposed algorithm has better convergence and distribution than CMOPSO, NSGAII, MOEAD, MOPSOCD, and NMPSO.
Highlights
Most of today’s scientific and engineering problems are characterized by the fact that they usually have multiple conflicting objectives [1], and decision makers need to simultaneously optimize multiple objectives as best as possible within a given range, namely, multiobjective optimization problems (MOPs). e optimization result of such problems is not single, and there exists a Pareto optimal solution set consisting of a set of compromise solutions [2]. e goal of solving such problems is to obtain well-distributed Pareto fronts in the objective space [3,4,5,6]
E mean (Mean) and standard deviation (Std.) of the inverse generation distance (IGD) metrics and HV metrics for GTMSMOPSO and the five multiobjective intelligence algorithms on the 14 tested functions are given in Tables 1 and 2, respectively. e bolded data in the table represent the best values
We propose a multiobjective particle swarm algorithm based on grid technology and multistrategy. e algorithm is improved by the maintenance of external archives and the selection of global optimal samples, and the variational operation of positions is proposed
Summary
Most of today’s scientific and engineering problems are characterized by the fact that they usually have multiple conflicting objectives [1], and decision makers need to simultaneously optimize multiple objectives as best as possible within a given range, namely, multiobjective optimization problems (MOPs). e optimization result of such problems is not single, and there exists a Pareto optimal solution set consisting of a set of compromise solutions [2]. e goal of solving such problems is to obtain well-distributed Pareto fronts in the objective space [3,4,5,6].With the expansion of human existence and the widening of the scope of understanding and transforming the world, the complex optimization problems encountered in reality are characterized by complex, multipolar, nonlinear, strongly constrained, and difficult modeling, which cannot be solved in polynomial time by classical algorithms, such as simplex algorithm and conjugate gradient method, or even cannot be solved effectively with the model. With the development of information technology, swarm intelligence algorithms are widely used, and such algorithms simulate the centralized learning process of a group composed of individuals. Such algorithms can effectively overcome the models that cannot be solved by classical algorithms. E definition of the general multiobjective optimization problem is described as follows: min F(x) f1(x), f2(x), . E set PF of all objective function values with the Pareto optimal solution set as the feasible region is called the Pareto frontier and is defined as PF y f1(x), f2(x), . Definition 4 (Pareto frontier). e set PF of all objective function values with the Pareto optimal solution set as the feasible region is called the Pareto frontier and is defined as PF y f1(x), f2(x), . . . , fk(x)|x ∈ S. (5)
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