An attractor-based trajectory search method for solving local minima problems

A new deterministic method for solving local minima problems is proposed. The proposed method consists of three phases. The first phase is a gradient-based local searches to locate a local minimum by building a generalized-gradient system. The second phase employs a terminal repeller strategy to escape from this local minimum. The third phase is a attractor-based trajectory searches to locate new lower local minimum by building a quotient gradient system. Several analytical results for generalized gradient systems and a quotient gradient systems are developed and are applied to derive the convergence properties of this method. Benchmark results show that the proposed method is competitive with the best previously reported global optimization techniques