A Hybrid Particle Swarm with Velocity Mutation for Constraint Optimization Problems

Two approaches for solving numerical continuous domain constrained optimization problems are proposed and experimented with. The first approach is based on particle swarm optimization algorithm with a new mutation operator in its velocity updating rule. Also, a gradient mutation is proposed and incorporated into the algorithm. This algorithm uses epsilon-level constraint handling method. The second approach is based on covariance matrix adaptation evolutionary strategy with the same method for handling constraints. It is experimentally shown that the first approach needs less number of function evaluations than the second one to find a feasible solution while the second approach is more effective in optimizing the objective value. Thus, a hybrid approach is proposed (third approach) which uses the first approach for locating potentially different feasible solutions and the second approach for further improving the solutions found so far. Also, a multi-swarm mechanism is used in which several instances of the first approach are run to locate potentially different feasible solutions. The proposed hybrid approach is applied to 18 standard constrained optimization benchmarks with up to 30 dimensions. Comparisons with two other state-of-the-art approaches show that the hybrid approach performs better in terms of finding feasible solutions and minimizing the objective function.