Global optimization by Darwin and Boltzmann mixed strategy

Abstract

This paper presents a Darwin and Boltzmann mixed strategy to solve the global optimization problems. The algorithm is based on the integration of the Darwin strategy and the Boltzmann annealing strategy, it is a hybrid of the Stochastic Evolution (SE) and the Simulated Annealing (SA). The proposed algorithm is proved to converge asymptotically to the global optimal solutions and its approximation implementation has shown to be polynomial in complexity. Experimental results show that the proposed algorithm is more efficient than the SA algorithm and is comparable to other methods on six well-known test problems. Scope and purpose Global optimization concerns with the computation and characterization of global optimums of nonlinear functions. They are widely used in the areas of engineering, operations research, statistics, computer science, and molecular biology. Extensive efforts have been made to address the issue and many global optimization methods have been developed. Global optimization methods are different from local optimization methods in the sense that they are to find the overall optimal solution or global optimum over a bounded set. Depending on whether or not they incorporate any stochastic elements, global optimization methods are classified into deterministic and stochastic ones. Current research in stochastic methods for global optimization focuses on new methods to improve efficiency and to establish trade-offs between accuracy, reliability and computational burden. This paper aims at proposing a new stochastic algorithm for global optimization. The proposed algorithm is analysed and compared with several existing methods on six well-known test problems and the experimental results are given.