New Heuristic Method Based on Evolution of Random Points to the Pareto Frontier for Bi-objective Optimization Problems.

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Bibliographic Details
Title:	New Heuristic Method Based on Evolution of Random Points to the Pareto Frontier for Bi-objective Optimization Problems.
Authors:	Martinez, André Luís Machado¹ martinez@utfpr.edu.br, Martinez, Cristiane Aparecida Pendeza² crismartinez@utfpr.edu.br, Castelani, Emerson Vitor³ evcastelani@uem.br
Source:	IAENG International Journal of Applied Mathematics. Apr2025, Vol. 55 Issue 4, p711-719. 9p.
Subjects:	Code division multiple access, Particle swarm optimization, Telecommunication systems, Energy consumption, Point set theory
Abstract:	We introduce a Pareto dominance-based heuristic designed to address bi-objective optimization problems by tracing the evolution from a random point to the Pareto frontier. The heuristic consists of three main steps. First, a feasible random approximation for the bi-objective problem is established. Next, this point evolves towards the optimal objectives and the Pareto frontier, leveraging trust regions around each approximation. Additionally, at specific iteration intervals, the current approximations optimizing the objectives are integrated as new approximations to the Pareto frontier, enriching the set of points along the frontier. This process iterates until convergence is reached. We would also like to propose an enhanced version of this method, which includes multiple initial points while maintaining the original method's structure. In this work, we compare the performance of the classic Weighted Sum (WS) method with both the EORP and the improved EMRP methods for solving the energy efficiency (EE) and spectral efficiency (SE) trade-off in optical code division multiple access (OCDMA) communication systems. The WS method is examined in two variants: one combined with the Hill Climbing heuristic (WS-HC) and the other with the Particle Swarm Optimization heuristic (WS-PSO). [ABSTRACT FROM AUTHOR]
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Database:	Engineering Source

Description
Abstract:	We introduce a Pareto dominance-based heuristic designed to address bi-objective optimization problems by tracing the evolution from a random point to the Pareto frontier. The heuristic consists of three main steps. First, a feasible random approximation for the bi-objective problem is established. Next, this point evolves towards the optimal objectives and the Pareto frontier, leveraging trust regions around each approximation. Additionally, at specific iteration intervals, the current approximations optimizing the objectives are integrated as new approximations to the Pareto frontier, enriching the set of points along the frontier. This process iterates until convergence is reached. We would also like to propose an enhanced version of this method, which includes multiple initial points while maintaining the original method's structure. In this work, we compare the performance of the classic Weighted Sum (WS) method with both the EORP and the improved EMRP methods for solving the energy efficiency (EE) and spectral efficiency (SE) trade-off in optical code division multiple access (OCDMA) communication systems. The WS method is examined in two variants: one combined with the Hill Climbing heuristic (WS-HC) and the other with the Particle Swarm Optimization heuristic (WS-PSO). [ABSTRACT FROM AUTHOR]
ISSN:	19929978