Algorithms for multi-extremal mathematical programming problems employing the set of joint space-filling curves

Abstract

Some powerful algorithms for multi-extremal non-convex-constrained optimization problems are based on reducing these multi-dimensional problems to those of one dimension by applying Peano-type space-filling curves mapping a unit interval on the real axis onto a multi-dimensional hypercube. Here is presented and substantiated a new scheme simultaneously employing several joint Peano-type scannings which conducts the property of nearness of points in many dimensions to a property of nearness of pre-images of these points in one dimension significantly better than in the case of a scheme with a single space-filling curve. Sufficient conditions of global convergence for the new scheme are investigated.

Search Optimization Opportunities of Modified Self-Organizing Migrating Algorithm in Multi-Extremal Tasks Environment

“…Such situation requires decisions, which take into consideration several identical or close extremes, and the best choice in-between them has to be made. The classical theory of scheduling gives examples, where several identical op-timums and identical sub-optimums, close to them exist [1], [3], [4] and [5]. The majority of discrete, integer and combinatory programming problems diers in such property [24], [22], [23], [24] and [25], in particular, when nding solution for graphs [26], [27], [28] and [29].…”

“…For solving real optimization problems, it has been common to apply methods called heuristic. These methods are the most perspective to obtain solutions for the ME problems [4] and [5]. The bright representative this type of methods is VOLUME: 1 | ISSUE: 2 | 2017 | November Self-Organizing Migrating Algorithm (SOMA) [6], [7] and [8].…”

Index information algorithm with local tuning for solving multidimensional global optimization problems with multiextremal constraints

“…It has been shown in [5,38,40] (see also [42]) that the multi-dimensional problem ϕ * = ϕ(y * ) = min{ϕ(y) : y ∈ D},…”

“…Problem 2. In this problem (see [40]) the same function as in the first experiment, over the same domain D, is minimized subject to the constraints…”

Symposium on Applied Mathematical Programming and Modeling (APMOD93) Held in Budapest, Hungary on January 6-8, 1993. Volume of Extended Abstracts

“…Such a restriction is, from the theoretical point of view, admissible in view of the fact that multidimensional global optimization problems can be transformed into one-dimensional ones e.g. by means of Peano-mappings (Strongin, 1992). The authors are obviously aware of the computathonal difficulties inherent to such transformation; however the analysis of one-dimensional global optimization problems is already sufficiently complex to be worthwhile, and, in the authors' opinion, it can shed light into the challenging problem ( 1).…”