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Selforganizology, 2024, 11(3-4): 54-75
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Article

An interactive interior point method for mathematical multi-objective linear optimization problems based on approximate gradients

M. Tlas
Scientific Services Department, Atomic Energy Commission, P. O. Box 6091, Damascus, Syria

Received 15 January 2024;Accepted 20 February 2024;Published online 10 March 2024;Published 1 December 2024
IAEES

Abstract
An interactive interior point method for solving multiple-objective linear programming problems has been proposed. The method uses a single-objective linear variant in order to generate, at each iterate, interior search directions. New feasible points are found along these directions which will be later used for deriving bestapproximation to the gradient of the implicitly-known utility function at the current iterate. Using this approximate gradient, a single feasible interior direction for the implicitly-utility function could be generated by projecting this approximate gradient onto the null space of the feasible region. An interior step can be taken from the current iterate to the next one along this feasible direction. During the execution of the algorithm, a sequence of interior points will be generated. It has been proved that this sequence converges to an ŠĆ - optimal solution, where ŠĆ is a predetermined error tolerance known a priori. A numerical multi-objective example is illustrated using this algorithm.

Keywords multi-objective mathematical programming;multi-criteria decision making;multi-criteria optimization;interactive methods;interior point methods.


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