Self-adjusting optimization algorithm for solving the setunion knapsack problem

TL;DR

This paper introduces two self-adjusting optimization algorithms based on TLBO for solving the complex set-union knapsack problem, demonstrating superior performance over existing swarm intelligence methods on benchmark datasets.

Contribution

The paper proposes novel self-adjusting algorithms tailored for SUKP, incorporating dynamic repair and optimization operators, and enhances TLBO with elite opposite search and natural selection mechanisms.

Findings

I-DTLBO outperforms other swarm intelligence methods on SUKP.

I-DTLBO achieves new upper boundaries on 15 instances.

E-DTLBO performs well on small and medium datasets but not on large-scale instances.

Abstract

The set-union knapsack problem (SUKP) is a constrained composed optimization problem. It is more difficulty for solving because values and weights depend on items and elements respectively. In this paper, we present two self-adjusting optimization algorithms for approximating SUKP from items and elements perspective respectively. By analyzing the dynamic characters in the SUKP, we design two types of self-adjusting repair and optimization operators that are based on the different loading process. We use the novel teaching-learning-based optimization algorithm (TLBO) to design a general discrete framework (DTLBO) suitable for these two types of operators. In addition, we introduce elite opposite search and natural selection mechanism into DTLBO to furtherly improve the performance of the algorithm from the perspective of population. Finally, we performed experimental comparisons on benchmark sets to verify the effectiveness of the proposed algorithm. The experimental results show that the item-based self-adjusting optimization algorithm I-DTLBO is outstanding, and the algorithm is superior to the other swarm intelligence methods for solving SUKP. IDTLBO algorithm reaches the upper boundary of the current swarm intelligence algorithms for solving SUKP in 10 instances, and gotten new upper boundary in 15 instances. The algorithm E-DTLBO based on element loading only perform slightly better on small and middle data sets, but worse on large-scale instances. It shows that element-based design is not suitable for solving SUKP.