eng
International Academy of Ecology and Environmental Sciences
Selforganizology
2410-0080
2024-12-1
11
3-4
54
75
2
article
An interactive interior point method for mathematical multi-objective
linear optimization problems based on approximate gradients
M. Tlas
1
2
Scientific Services Department, Atomic Energy Commission, P. O. Box 6091, Damascus, Syria
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 e - optimal solution, where e is a predetermined error tolerance known a priori. A numerical multi-objective example is illustrated using this algorithm.
http://www.iaees.org/publications/journals/selforganizology/articles/2024-11(3-4)/interactive-interior-point-method.pdf
multi-objective mathematical programming
multi-criteria decision making
multi-criteria
optimization
interactive methods
interior point methods