MinFinder v2.0: An improved version of MinFinder

Abstract

A new version of the “MinFinder” program is presented that offers an augmented linking procedure for Fortran-77 subprograms, two additional stopping rules and a new start-point rejection mechanism that saves a significant portion of gradient and function evaluations. The method is applied on a set of standard test functions and the results are reported. New version program summary Program title: MinFinder v2.0 Catalogue identifier: ADWU_v2_0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/ADWU_v2_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC Licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 14 150 No. of bytes in distributed program, including test data, etc.: 218 144 Distribution format: tar.gz Programming language used: GNU C++, GNU FORTRAN, GNU C Computer: The program is designed to be portable in all systems running the GNU C++ compiler Operating system: Linux, Solaris, FreeBSD RAM: 200 000 bytes Classification: 4.9 Catalogue identifier of previous version: ADWU_v1_0 Journal reference of previous version: Computer Physics Communications 174 (2006) 166–179 Does the new version supersede the previous version?: Yes Nature of problem: A multitude of problems in science and engineering are often reduced to minimizing a function of many variables. There are instances that a local optimum does not correspond to the desired physical solution and hence the search for a better solution is required. Local optimization techniques can be trapped in any local minimum. Global optimization is then the appropriate tool. For example, solving a non-linear system of equations via optimization, one may encounter many local minima that do not correspond to solutions, i.e. they are far from zero. Solution method: Using a uniform pdf, points are sampled from a rectangular domain. A clustering technique, based on a typical distance and a gradient criterion, is used to decide from which points a local search should be started. Further searching is terminated when all the local minima inside the search domain are thought to be found. This is accomplished via three stopping rules: the “double-box” stopping rule, the “observables” stopping rule and the “expected minimizers” stopping rule. Reasons for the new version: The link procedure for source code in Fortran 77 is enhanced, two additional stopping rules are implemented and a new criterion for accepting-start points, that economizes on function and gradient calls, is introduced. Summary of revisions: 1. Addition of command line parameters to the utility program make_program. 2. Augmentation of the link process for Fortran 77 subprograms, by linking the final executable with the g2c library. 3. Addition of two probabilistic stopping rules. 4. Introduction of a rejection mechanism to the Checking step of the original method, that reduces the number of gradient evaluations. Additional comments: A technical report describing the revisions, experiments and test runs is packaged with the source code. Running time: Depending on the objective function.