Huynh Thi Thanh Binh

Minh Hieu Ha, Hung Phan, Tung Duy Doan et al.

Multi-objective combinatorial optimization problems (MOCOP) frequently arise in practical applications that require the simultaneous optimization of conflicting objectives. Although traditional evolutionary algorithms can be effective, they typically depend on domain knowledge and repeated parameter tuning, limiting flexibility when applied to unseen MOCOP instances. Recently, integration of Large Language Models (LLMs) into evolutionary computation has opened new avenues for automatic heuristic generation, using their advanced language understanding and code synthesis capabilities. Nevertheless, most existing approaches predominantly focus on single-objective tasks, often neglecting key considerations such as runtime efficiency and heuristic diversity in multi-objective settings. To bridge this gap, we introduce Multi-heuristics for MOCOP via Pareto-Grid-guided Evolution of LLMs (MPaGE), a novel enhancement of the Simple Evolutionary Multiobjective Optimization (SEMO) framework that leverages LLMs and Pareto Front Grid (PFG) technique. By partitioning the objective space into grids and retaining top-performing candidates to guide heuristic generation, MPaGE utilizes LLMs to prioritize heuristics with semantically distinct logical structures during variation, thus promoting diversity and mitigating redundancy within the population. Through extensive evaluations, MPaGE demonstrates superior performance over existing LLM-based frameworks, and achieves competitive results to traditional Multi-objective evolutionary algorithms (MOEAs), with significantly faster runtime. Our code is available at: https://github.com/langkhachhoha/MPaGE.

Pham Vu Tuan Dat, Long Doan, Huynh Thi Thanh Binh

Automatic Heuristic Design (AHD) is an active research area due to its utility in solving complex search and NP-hard combinatorial optimization problems in the real world. The recent advancements in Large Language Models (LLMs) introduce new possibilities by coupling LLMs with evolutionary computation to automatically generate heuristics, known as LLM-based Evolutionary Program Search (LLM-EPS). While previous LLM-EPS studies obtained great performance on various tasks, there is still a gap in understanding the properties of heuristic search spaces and achieving a balance between exploration and exploitation, which is a critical factor in large heuristic search spaces. In this study, we address this gap by proposing two diversity measurement metrics and perform an analysis on previous LLM-EPS approaches, including FunSearch, EoH, and ReEvo. Results on black-box AHD problems reveal that while EoH demonstrates higher diversity than FunSearch and ReEvo, its objective score is unstable. Conversely, ReEvo's reflection mechanism yields good objective scores but fails to optimize diversity effectively. With this finding in mind, we introduce HSEvo, an adaptive LLM-EPS framework that maintains a balance between diversity and convergence with a harmony search algorithm. Through experimentation, we find that HSEvo achieved high diversity indices and good objective scores while remaining cost-effective. These results underscore the importance of balancing exploration and exploitation and understanding heuristic search spaces in designing frameworks in LLM-EPS.

Huynh Thi Thanh Binh, Le Van Cuong, Dang Hai Dang et al.

Recently, Wireless Rechargeable Sensor Networks (WRSNs) that leveraged the advantage of wireless energy transfer technology have opened a promising opportunity in solving the limited energy issue. However, an ineffective charging strategy may reduce the charging performance. Although many practical charging algorithms have been introduced, these studies mainly focus on optimizing the charging path with a fully charging approach. This approach may lead to the death of a series of sensors due to their extended charging latency. This paper introduces a novel partial charging approach that follows a bi-level optimized scheme to minimize energy depletion in WRSNs. We aim at optimizing simultaneously two factors: the charging path and time. To accomplish this, we first formulate a mathematical model of the investigated problem. We then propose two approximate algorithms in which the optimization of the charging path and the charging time are considered as the upper and lower level, respectively. The first algorithm combines a Multi-start Local Search method and a Genetic Algorithm to find a solution. The second algorithm adopts a nested approach that utilizes the advantages of the Multitasking and Covariance Matrix Adaptation Evolutionary Strategies. Experimental validations on various network scenarios demonstrate that our proposed algorithms outperform the existing works.