Abstract
Heuristic methods, such as tabu search, are efficient for global optimizations. Most studies, however, have focused on constraintβfree optimizations. Penalty functions are commonly used to deal with constraints for global optimization algorithms in dealing with constraints. This is sometimes inefficient, especially for equality constraints, as it is difficult to keep the global search within the feasible region by purely adding a penalty to the objective function. A combined global and local search method is proposed in this paper to deal with constrained optimizations. It is demonstrated by combining continuous tabu search (CTS) and sequential quadratic programming (SQP) methods. First, a nested innerβ and outerβloop method is presented to lead the search within the feasible region. SQP, a typical local search method, is used to quickly solve a nonβlinear programming purely for constraints in the inner loop and provides feasible neighbors for the outer loop. CTS, in the outer loop, is used to seek for the global optimal. Finally, another local search using SQP is conducted with the results of CTS as initials to refine the global search results. Efficiency is demonstrated by a number of benchmark problems. Copyright Β© 2008 John Wiley & Sons, Ltd.