A new “Optimization‐Preserving‐Operator” applied to global optimization

Abstract

Purpose

To introduce Optimization‐Preserving‐Operators (O‐P‐Os), which are operators that are defined on classes of real functions that depend on a single variable, and allow us to eliminate local optima and to preserve global optima.

Design/methodology/approach

Outline a new method to build O‐P‐Os. These are introduced as O‐P‐O* and lead to a new approach for solving global optimization problems.

Findings

It was found that classical discretization methods for obtaining optimum of one variable function was too time‐consuming. The simple method introduced provided solutions to the test functions chosen as examples. The solutions were provided in a short time.

Research limitations/implications

Provides new tools for mathematical programming and in particular the global optimization problems. The O‐P‐O* introduced innovative technique for solving such problems.

Practical implications

O‐P‐O* produces solutions to global optimization problems in a much improved time. The algorithm derived, and the steps for its operation proved on implementation, the efficiency of the new method. This was demonstrated by numerical results for selected functions obtained using microcomputer systems.

Originality/value

Provides new way of solving global optimization problems.

Citation

Konfe, B.O., Cherruault, Y., Some, B. and Benneouala, T. (2005), "A new “Optimization‐Preserving‐Operator” applied to global optimization", Kybernetes, Vol. 34 No. 7/8, pp. 1112-1124. https://doi.org/10.1108/03684920510605920