Hybrid extreme point tabu search

We develop a new hybrid tabu search method for optimizing a continuous diieren-tiable function over the extreme points of a polyhedron. The method combines extreme point tabu search with traditional descent algorithms based on linear programming. The tabu search algorithm utilizes both recency-based and frequency-based memory and oscillates between local improvement and diversiication phases. The hybrid algorithm iterates between using the descent algorithm to nd a local minimum and using tabu search to improve locally and then move to a new area of the search space. This algorithm can be used on many important classes of problems in global optimization including bilinear programming, multilinear programming, multiplicative programming, concave minimization, and complementarity problems. The algorithm is applied to two practical problems: the quasistatic multi-rigid-body contact problem in robotics and the global tree optimization problem in machine learning. Computational results show that the hybrid algorithm outperforms the descent and tabu search algorithms used alone. The authors wish to thank Fred Glover for suggesting the use of tabu search for the global tree optimization problem.