Particle Swarm Optimization Algorithm For Nonlinear Mixed Discrete Optimization Problem

Nonlinear mixed discrete optimization problem exists widely in engineering design, resource dispatching and management design-making. It is important to study how to solve this problem. Particle swarm optimization (PSO) is a new swarm algorithm. Because of simpleness, less parameter, no grads information and fast convergence, PSO has a great ability to solve engineering problem and has been successfully applied in many areas. PSO is mainly a method to find a global optimal solution for a nonlinear continuous optimization problem, and there have been few studies into optimization problems with discrete decision variables.By handling the discrete design variables as penalty function, the augmented objective function is constructed. As a result, all design variables can be treated as the continuous design variables. The augmented objective function and the primary objective function have same value at the discrete points. That is, finding optimum of discrete design variables is transformed into finding global optimum of this augmented objective function. Standard PSO algorithm will likely fall into local optimal solution and exist premature convergence. A hybrid tabu search (TS) and particle swarm optimization (TSPSO) algorithm is proposed, which has memory ability and efficient hill-climbing capability. Simulation results on the Rosenbrock's function and the pressure vessel problem show that the disadvantage of getting in the local best point of standard PSO is overcome effectively and the ability of global optimality is toned up.Particle swarm optimization is a very simple and effective method for continuous optimization. It is easy to design neighborhood structure for discrete variables so as to use neighborhood search algorithm to calculate optimization points. A hybrid simulated annealing (SA) and particle swarm optimization (SAPSO) algorithm is proposed, in which SA is used to deal with discrete variables and PSO is used to deal with continuous ones. Simulation results on ring design show that SAPSO has a good ability to find the global optimization.Finally, research conclusions and future directions of using particle swarm optimization to solve nonlinear mixed discrete optimization problem are summarized.