A hybrid Particle Swarm Evolutionary Algorithm for Constrained Multi-Objective Optimization

In this paper, a hybrid particle swarm evolutionary algorithm is proposed for solving constrained multi-objective optimization. Firstly, in order to keep some particles with smaller constraint violations, a threshold value is designed, the updating strategy of particles is revised based on the threshold value; then in order to keep some particles with smaller rank values, an infeasible elitist preservation strategy is proposed in order to make the infeasible elitists act as bridges connecting disconnected feasible regions. Secondly, in order to find a set of diverse and well-distributed Pareto-optimal solutions, a new crowding distance function is designed for bi-objective optimization problems. It can assign larger crowding distance function values not only for the particles located in the sparse region but also for the particles located near to the boundary of the Pareto front. In this step, the reference points are given, and the particles which are near to the reference points are kept no matter how crowded these points are. Thirdly, a new mutation operator with two phases is proposed. In the first phase, the total force is computed first, then it is used as a mutation direction, searching along this direction, better particles will be found. The comparative study shows the proposed algorithm can generate widely spread and uniformly distributed solutions on the entire Pareto front