Balira O. Konfe, Yves Cherruault, Blaise Some and Titem Benneouala
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…
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.
Details
Keywords
Balira O. Konfe, Yves Cherruault, Blaise Some and Titem Benneouala
This paper presents an efficient algorithm for solving general constrained optimization problems that arise in operational research (OR).
Abstract
Purpose
This paper presents an efficient algorithm for solving general constrained optimization problems that arise in operational research (OR).
Design/methodology/approach
An unified approach is accomplished by converting the constrained optimization problem into an unconstrained one and by using Alienor method coupled to the new optimization preserving operator* (OPO*) technique for the resolution.
Findings
A new algorithm for solving general constrained optimization problems with continuous objective function contributes to research in this area and in particular, to applications to OR.
Research limitations/implications
Some improvements could probably be obtained at calculation time. We will in future work, develop an adaption of these methods and techniques to optimization problems with mixed variables or with integer and Boolean variables.
Practical implications
The new algorithm can be advantageously compared with other methods such as generalized reduced gradient. Small‐sized numerical examples are given.
Originality/value
A new algorithm is given which guarantees a global optimal solution is easily obtained in all cases.
Details
Keywords
Mahamat Maimos, Yves Cherruault, Balira O. Konfe and Ange‐gar S. Nkokolo Massamba
The purpose of this paper is to present an efficient algorithm to solve multi‐objective linear programming (MOLP) problem.
Abstract
Purpose
The purpose of this paper is to present an efficient algorithm to solve multi‐objective linear programming (MOLP) problem.
Design/methodology/approach
This new approach consists to convert the constrained multicriteria problem into an unconstrained global optimization problem. Then, the Alienor method coupled to the optimization preserving operators* (OPO*) technique is used to solve the transformed problem.
Findings
A determinist algorithm for solving general MOLP problem contributes to research in the decision‐makers area.
Research limitations/implications
Some improvements could probably be obtained. In future work, other scalarized functions will be used and this algorithm's complexity will be studied.
Practical implications
The new algorithm can be advantageously compared with other methods To illustrate this new approach, an example is studied.
Originality/value
A new algorithm is given which guarantees all efficient solutions are easily obtained in most cases.
Details
Keywords
Balira O. Konfe, Yves Cherruault and Blaise Some
To propose a new method for solving constrained global optimization problems using a method that consists of transforming a constrained global optimization problem into an…
Abstract
Purpose
To propose a new method for solving constrained global optimization problems using a method that consists of transforming a constrained global optimization problem into an unconstrained one without using any penalty coefficients.
Design/methodology/approach
Use of an unconstrained global optimization method such as the Alienor method which has been adapted for several variables.
Findings
Use of the adapted Alienor method allowed the solution of the transformed problem with little difficulty.
Research limitations/implications
Transforms the original objective function into a new one involves the introduction of some extra parameters. Cannot guarantee the convergence to a global solution of the original problem. The simple described approach, provides new possibilities.
Practical implications
No further parameters introduced in this new approach, and no conditions or hypotheses are imposed on the objective function or on the constraints.
Originality/value
New method of transforming a constrained problem into an unconstrained one, with use of proven Alienor method adapted to several variables.
Details
Keywords
Balira O. Konfé, Yves Cherruault and Titem Benneouala
To use α‐dense curves to allow the transform of a multiple function into a single variable function in order to solve global optimization problems.
Abstract
Purpose
To use α‐dense curves to allow the transform of a multiple function into a single variable function in order to solve global optimization problems.
Design/methodology/approach
Use is made of the established Alienor method which has already been applied to biological and industrial processes. The problems tackled have a number of variables and the chosen optimization method is a variant of the Alienor method.
Findings
A new method for solving global optimization problem, called the Alienor method is now the subject of many variants. In this paper, it was found that a new reducing transformation α‐dense in Rn was successful in solving this type of problem when associated to a functional depending on a large number of variables. The reducing transformation is very efficient and accurate.
Research limitations/implications
This is a variant of the proven Alienor Method which has improved the resolution of global optimization problems. It showed that the reducing transformation has the advantage that a small calculation time is obtained even when the relevant series are slowly increasing. Further development of the method is anticipated.
Practical implications
Proved very effective for obtaining the global optimum with good precision and very short calculation time for large numbers of variables. Can be performed on micro‐calculators.
Originality/value
New variant of proven method. Of interest in solution of concrete problems in biology and industry.