Pareto-critical equilibrium condition for non-linear multiobjective optimization problems with applications

• Published in: Heliyon Vol. 10; no. 21; p. e39498
• Main Authors: Muhammad, Shakoor, Rehman, Abdul, Iqbal, Amjad, Ali, Taimur, Khan, Faisal
• Format: Journal Article
• Language: English
• Published: England Elsevier Ltd 15.11.2024; Elsevier
• Subjects: Downlink transmit beamforming; Multi-agent system; Multiobjective optimization; objectives; Pareto-critical equilibrium condition; solutions; system optimization; Pareto-critical equilibrium condition; Multi-agent system; Multiobjective optimization; Downlink transmit beamforming
• ISSN: 2405-8440; 2405-8440
• DOI: 10.1016/j.heliyon.2024.e39498

The new (necessary) Pareto-critical equilibrium condition (PCEC) discussed in this study is based on the Pareto-critical condition for non-linear optimization problems. The proposed condition is evaluated by defining a multiobjective optimization problems (MOOPs) subject to a set of constraints. Then this MOOPs is converted to a single objective optimization problem by using the available optimization techniques, for instance, the weighted sum method, and solved by the non-linear Nelder-Mead simplex method. The obtained solution points satisfy the proposed PCEC of an unconstrained multiobjective optimization problem (MOOPs) under the convexity assumption. This PCEC is evaluated in a search that either results in a point inside the feasible region or a point for which the PCEC holds. The resulting Pareto-critical equilibrium condition is globally valid for convex problems. Numerical experiments are carried out in order to clarify the proposed condition's validity. Moreover, the proposed PCEC is used to place a downlink transmit beamforming system base station in an ideal position as a first application and is also employed in situations where there are multiple agents working towards a common goal as a second application.