New Simulated Annealing Algorithms For Constrained Optimization

We propose a Population based dual-sequence Non-Penalty Annealing algorithm (PNPA) for solving the general nonlinear constrained optimization problem. The PNPA maintains a population of solutions that are intermixed by crossover to supply a new starting solution for simulated annealing throughout the search. Every time the search gets stuck at a local optimum, this crossover procedure is triggered and simulated annealing search re-starts from a new subspace. In both the crossover and simulated annealing procedures, the objective function value and the total solution infeasibility degrees are treated as separate performance criteria. Feasible solutions are assessed according to their objective function values and infeasible solutions are assessed with regard to their absolute degree of constraint infeasibility. In other words, in the proposed approach, there exist two sequences of solutions: the feasible sequence and the infeasible sequence. We compare the population based dual sequence PNPA with the standard single sequence Penalty Annealing (the PA), and with the random seed dual sequence Non-Penalty Annealing (NPA). Numerical experiments show that PNPA is more effective than its counterparts.