Global optimization by successive local optimization and escape

Abstract

Many engineering problems are formulated as general nonlinear optimization problems which are generally nonconvex and may have multiple local optima. In this thesis, a new global optimization algorithm is proposed for unconstrained problems which uses a local optimization algorithm and escaping sequence iteratively. Robust algorithms for local optimization are well-developed and readily available for use. But using local optimization algorithm itself, we may be trapped in a local optimum solution. So we need an escape phase from local optimum point. The proposed algorithm is composed of two phases: local optimization phase (LOP) and escape phase (EP). The LOP finds a local optimum, and the EP escapes from that local optimum and finds a new starting point using cutting plane method and global line search. The interaction between LOP and EP continues until termination criterion is satisfied. The proposed algorithm is successfully applied to a number of general nonlinear unconstrained optimization problems and shows excellent performance in terms of number of function calls compared to the interval branch and bound method. Also it is expected that the proposed algorithm shows much smaller number of function evaluations than stochastic methods, such as, random search, simulated annealing, and genetic algorithm.