Summary: This paper describes a multi-start with clustering strategy for use on constrained optimization problems. It is based on the characteristics of nonlinear constrained global optimization problems and extends a strategy previously tested on unconstrained problems. Earlier studies of multi-start with clustering found in the literature have focused on unconstrained problems with little attention to nonlinear constrained problems.
In this study, variations of multi-start with clustering are considered including a simulated annealing or random search procedure for sampling the design domain and a quadratic programming (QP) subproblem used in cluster formation. The strategies are evaluated by solving 18 nonlinear mathematical problems and six engineering design problems.
Numerical results show that the solution of a one-step QP subproblem helps predict possible regions of attraction of local minima and can enhance robustness and effectiveness in identifying local minima without sacrificing efficiency. In comparison to other multi-start techniques found in the literature, the strategies of this study can be attractive in terms of the number of local searches performed, the number of minima found, whether the global minimum is located, and the number of the function evaluations required.