Unified approach for solving box-constrained models with continuous or discrete variables by non monotone direct search methods
- 64 Downloads
This paper is an outgrowth of previous works devoted to the application of non monotone direct search methods (DSMs) to locate the global minimum of an objective function subjected to bounds on its variables defined in the Euclidean space. This paper proves that DSMs can be easily adapted for solving models with discrete variables, as long as these variables are regularly spaced along each coordinate. Convergence is established without imposing additional conditions on the objective function, but the construction of the search directions plays a fundamental role. Moreover, function evaluations are carried out only on discrete feasible points, avoiding spurious computations on non feasible points. The paper describes a pseudo code and a preliminary code written in C, which is applied to solve a discretized version of a continuous problem with encouraging results.
KeywordsDirect search methods Discrete variable Non monotone
Authors’ research is being partly funded by Grants TEC2016-76465-C2-2-R (Mineco, Spain) and GRC2014/046 (Xunta de Galicia, Spain).
- 4.Custodio, A.L., Scheinberg, K., Nunes Vicente, L.: Methodologies and software for derivative-free optimization. Internal Report (2017). http://www.mat.uc.pt/~lnv/papers/dfo-survey.pdf
- 11.(2017). https://www.inverseproblem.co.nz/OPTI/index.php/Main/HomePage. Accessed 21 Oct 2017
- 15.Newby, E.: General solution methods for mixed integer quadratic programming and derivative free mixed integer non-linear programming problems. Dissertation Thesis, University of the Witwatersrand (2013)Google Scholar
- 17.Ng, K.-M.: A continuation approach for solving nonlinear optimization problems with discrete variables. Dissertation Thesis, Stanford University (2002)Google Scholar
- 19.Powell, M.J.D.: The BOBYQA algorithm for bound constrained optimization without derivatives. Cambridge Report NA2009/06, University of Cambridge (2009)Google Scholar
- 21.Rodríguez-Hernández, P.S.: (2016). http://webs.uvigo.es/pedro.rodriguez/pub/DFO_GGR. Accessed 5 July 2016
- 23.Torczon, V.J.: Multi-directional search: a direct search algorithm for parallel machines. PhD Thesis, Rice University, Houston, TX (1989)Google Scholar