A deterministic constrained global optimization algorithm without penalty function

Penalty function approach is a commonly used method for constrained optimization in engineering design. However, the optimization results are quite sensitive to the value of penalty factor, and many trials are generally required to identify a suitable penalty factor for a special problem. To avoid the repeated parameter selection process, the filter-based constraint handling mechanism and a deterministic global optimization algorithm (i. e., DIRECT) are integrated for solving constrained optimization problems, notated as filtered-DIRECT. The filter approach is based on the domination concept in multi-objective optimizations and a filter is constructed in terms of the objective value and constraint violations, in which all the points are mutually non-dominated. Consequently, the constraint could be considered without using penalty function. In the optimization process of filtered-DIRECT, the hyper-rectangles chosen from the filter are divided to sample the design space, and the new sampling points are generated to update the filter for improving the feasibility and optimality until convergence. Filtered-DIRECT independent of using penalty function is believed to possess appealing performance, since no tuning process of penalty factor is required. Finally, the proposed filtered-DIRECT is compared with the penalty-based DIRECT, penalty-based PSO, and penalty-based GA on two engineering benchmark problems. The comparison results show that filtered-DIRECT outperforms the other competitive algorithms in terms of efficiency, robustness and the quality of optimal solutions. Hence, the proposed filtered-DIRECT is an effective method for constrained engineering optimizations.