Metaheuristic

Algorithm

Optimization algorithm

Multi-swarm optimization

Variable (mathematics)

Particle swarm optimization

Computer science

Mathematical optimization

Mathematics

Mathematical analysis

Derivative-free optimization

Swarm and Evolutionary Computation

Many optimization problems in reality involve both continuous and discrete decision variables, and these problems are called mixed-variable optimization problems (MVOPs). The mixed decision variables of MVOPs increase the complexity of search space and make them difficult to be solved. The Particle Swarm Optimization (PSO) algorithm is easy to implement due to its simple framework and high speed of convergence, and has been successfully applied to many difficult optimization problems. Many existing PSO variants have been proposed to solve continuous or discrete optimization problems, which make it feasible and promising for solving MVOPs. In this paper, a new PSO algorithm for solving MVOPs is proposed, namely null null null null P null S null null O null null m null v null null null , null null null null which can deal with both continuous and discrete decision variables simultaneously. To efficiently handle mixed variables, the null null null null P null S null null O null null m null v null null null null null null employs a mixed-variable encoding scheme. Based on the mixed-variable encoding scheme, two reproduction methods respectively for continuous variables and discrete variables are proposed. Furthermore, an adaptive parameter tuning strategy is employed and a constraints handling method is utilized to improve the overall efficiency of the null null null null P null S null null O null null m null v null null null null null .The experimental results on 28 artificial MVOPs and two practical MVOPs demonstrate that the proposed null null null null P null S null null O null null m null v null null null null null null is a competitive algorithm for MVOPs.

A particle swarm optimization algorithm for mixed-variable optimization problems