Electromagnetism-like Method for Constrained Optimization Problems

Electromagnetism-like method (EM) has proved to be a very robust algorithm for solving non-differentiable and non-convex unconstrained optimization problems. In this paper, we extend EM to solve constrained optimization problems. Firstly, a new constraint handling approach is introduced which transforms constrained optimization problem into a bi-objective optimization problem, and a preference selection strategy is proposed in order to find the global optimality for the original constrained problem. Secondly, new formula for computing charges is designed for the bi-objective optimization problem. It can assign larger charges to the feasible particles while smaller ones to unfeasible particles. Thirdly, a particular formula for computing the force between two particles is proposed that encourage the particles to move towards the attractive valleys, and discourage further away from steeper hills. Finally, an adaptive movement is presented to create new particle. Simulation results on benchmark test functions indicate the potential of this new approach.