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.

The Set-union Knapsack Problem (SUKP) is a generalization of the popular 0-1 knapsack problem. Given a set of weighted elements and a set of items with profits where each item is composed of a subset of elements, the SUKP involves packing a subset of items in a capacity-constrained knapsack such that the total profit of the selected items is maximized while their weights do not exceed the knapsack capacity. In this work, we present an effective iterated two-phase local search algorithm for this NP-hard combinatorial optimization problem. The proposed algorithm iterates through two search phases: a local optima exploration phase that alternates between a variable neighborhood descent search and a tabu search to explore local optimal solutions, and a local optima escaping phase to drive the search to unexplored regions. We show the competitiveness of the algorithm compared to the state-of-the-art methods in the literature. Specifically, the algorithm discovers 18 improved best results (new lower bounds) for the 30 benchmark instances and matches the best-known results for the 12 remaining instances. We also report the first computational results with the general CPLEX solver, including 6 proven optimal solutions. Finally, we investigate the effectiveness of the key ingredients of the algorithm on its performance.