SOMS: SurrOgate MultiStart algorithm for use with nonlinear programming for global optimization

Abstract

SOMS is a general surrogate-based multistart algorithm, which is used in combination with any local optimizer to find global optima for computationally expensive functions with multiple local minima. SOMS differs from previous multistart methods in that a surrogate approximation is used by the multistart algorithm to help reduce the number of function evaluations necessary to identify the most promising points from which to start each nonlinear programming local search. SOMS's numerical results are compared with four well-known methods, namely, Multi-Level Single Linkage (MLSL), MATLAB's MultiStart, MATLAB's GlobalSearch, and GLOBAL. In addition, we propose a class of wavy test functions that mimic the wavy nature of objective functions arising in many black-box simulations. Extensive comparisons of algorithms on the wavy test functions and on earlier standard global-optimization test functions are done for a total of 19 different test problems. The numerical results indicate that SOMS performs favorably in comparison to alternative methods and does especially well on wavy functions when the number of function evaluations allowed is limited.

Multistart with early termination of descents

“…The clustering aided implementation of this idea was started by A.Törn; for the early investigations see [10], and for the later results and references see [11]. Recent discussions on the use of multistart are included in [3] and [6]. In this paper, we further develop this idea and demonstrate that some local descents can be stopped very early, well before they get close to a local minimizer.…”

Methods for anaerobic digestion model fitting—comparison between heuristic and automatic approach

“…It can potentially save calculation time, which is very important for a rather complicated and demanding biological system. However, it needs to be noticed that the GlobalSearch algorithm uses a scatter-search mechanism [32], which is more complicated than in the case of the MultiStart [33] and cannot run parallel on multiple CPU cores, which can affect performance in some cases. As a result, the GlobalSearch returns a vector of solutions, which are a representation of points assume as the global minimum for the optimization problem.…”