Binary Particle Swarm Optimization in Banach Spaces via Mixed Greedy and Dual Approaches
Ywo Josue BAZIE *
Departement de Mathematiques, Universite Joseph KI-ZERBO, 03 BP 7021, Ouagadougou, Burkina Faso.
Raogo Frank Emile 1er Jumeau KABORE
Departement de Mathematiques, Universite Joseph KI-ZERBO, 03 BP 7021, Ouagadougou, Burkina Faso.
Abel ZONGO
Departement de Mathematiques, Universite Joseph KI-ZERBO, 03 BP 7021, Ouagadougou, Burkina Faso.
Pierre Clovis NITIEMA
Departement de Mathematiques de Decision, Universite Thomas Sankara, 12 BP 417, Ouagadougou, Burkina Faso.
*Author to whom correspondence should be addressed.
Abstract
This paper explores theoretical and practical extensions of Binary Particle Swarm Optimization (BPSO) to infinite-dimensional Banach spaces, introducing a novel framework that integrates Mixed Greedy and Dual Binary strategies. While BPSO has shown success in discrete optimization within finite-dimensional settings, its adaptation to Banach spaces poses significant challenges. The proposed operators for the Mixed Greedy and Dual Binary approaches are analyzed in depth, particularly regarding their convergence properties under various conditions. Key results demonstrate improved performance over traditional methods, including faster functional convergence rates, strong convergence in norm, and convergence in expectation. These methods prove effective for solving complex optimization problems such as Neural Machine Translation (NMT). Numerical experiments on benchmark functions validate the applicability and efficiency of the proposed framework.
Keywords: Approximation, stochastic modelling, greedy, dual binary, particle swarm optimization