Multi-start Space Reduction (MSSR) surrogate-based global optimization method

Abstract

In this work, a new Multi-start Space Reduction (MSSR) and surrogate-based search algorithm is introduced for solving global optimization problems with computationally expensive black-box objective and/or expensive black-box constraint functions. In this new algorithm, the design space is classified into: the original design space or global space (GS), the reduced medium space (MS) that contains the promising region, and the local space (LS) that is a local area surrounding the present best solution in the search. During the search, a kriging-based multi-start optimization process is used for local optimization, sample selection and exploration. In this process, Latin hypercube sampling is used to acquire the starting points and sequential quadratic programming (SQP) is used for the local optimization. Based upon a newly introduced selection strategy, better sample points are obtained to supplement the kriging model, and the estimated mean square error of kriging is used to guide the search of the unknown areas. The multi-start search process is carried out alternately in GS, MS and LS until the global optimum is identified. The newly introduced MSSR algorithm was tested using various optimization benchmark problems, including fifteen bound constrained examples, two nonlinear constrained optimization problems, and four nonlinear constrained engineering applications. The test results revealed noticeable advantages of the new algorithm in dealing with computationally expensive black-box problems. In comparison with two nature-inspired algorithms, three space exploration methods, and two recently introduced surrogate-based global optimization algorithms, MSSR showed improved search efficiency and robustness.