Two Novel Evolutionary Algorithms For Constrained Optimization Problems

Constrained optimization problems have a wide range of applications in many fields. When problems are non-differentiable, it is difficult to solve them with traditional methods. Evolutionary algorithms provide a new idea for these problems. In order to solve constrained optimization problems efficiently. Two new Evolutionary algorithms are proposed in this paper.In the first algorithm, the constrained optimization problem is first transformed into a two objective optimization problem with preference, where one objective function is the original objective function; the other is generated from the constraints. Then a new evolutionary algorithm for this two objective optimization problem is proposed. This algorithm is different from the common one. In the initial stage of the evolution, it prefers the solutions optimizing the second objective, i.e., it will evolve the solutions to satisfy the constraints; while in the later stage, it prefers the solutions optimizing the first objective, i.e., it will evolve the solutions to get better and better original objective function values. To realize this idea, a new fitness function with dynamic weights is presented to guide the search. Furthermore, the global convergence of the proposed algorithm is proved, and the simulations on ten standard benchmark problems are made. The results indicate the proposed algorithm is effective.In the second algorithm, a new fitness function is constructed firstly. It has the following properties: in the feasible region, it is a monotone function of the objective function, and maps the feasible region into interval [-1, 1]. In the infeasible region, it is a monotone function of the penalty function, and maps the infeasible region into interval [1, 2]. The fitness function constructed in this way not only can directly judge any feasible solution is better than any infeasible solution, but also can directly distinguish the quality of any two feasible solutions and the quality of any two infeasible solutions. Based on this, a new evolutionary algorithm without penalty parameter is presented. It simultaneously searches the feasible and the infeasible regions, and forces the search gradually into the feasible region, and finally finds the global optimal solution. The simulation results on ten standard benchmark problems indicate the proposed algorithm is efficient.