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The minimum weighted vertex cover (MWVC) problem, an extension of the classical minimum vertex cover (MVC) problem, is an important NP-complete combinatorial optimization problem with a wide range of applications. The objective of this paper is to design an efficient local search algorithm to solve the MWVC problem. First, the weighted edge strategy is proposed to define the dynamic scoring strategy so that our algorithm can find different possible optimal solutions. Second, the weighted configuration checking (WCC) strategy is proposed to overcome the cycling problem in local search. By combining the WCC strategy with the scoring strategy, we design the vertex selection strategy to determine the vertex to be selected as a candidate solution component. Based on these strategies, a novel local search framework, namely diversion local search based on weighted configuration checking (DLSWCC), is presented. DLSWCC is evaluated against several state-of-the-art algorithms on various benchmark instances. Experimental results show that DLSWCC outperforms its competitors in terms of both solution quality and computational efficiency in most classical instances. Specifically, DLSWCC can obtain 22 new upper bounds of 71 moderate-scale problem instances, 5 new upper bounds of 15 large-scale problem instances, and 56 new upper bounds of 56 massive graph instances. [ABSTRACT FROM AUTHOR]

Abstract: Assume that there exists a collection C of subsets of a finite set S, and a positive integer K ⩽∣S∣, and we need to know whether there is a subset S′⊆ S with ∣S′∣⩽ K such that S′ contains at least one element of each subset in C. In other words, S′ is the subset that intersects every subset in C and is called the hitting-set. In this paper, a DNA-based algorithm is proposed to solve the small hitting-set problem. A small hitting-set is a hitting-set with the smallest K value, i.e., the hitting-set with the smallest number of elements. Furthermore, another algorithm is introduced to find the number of ones from 2 n combinations and minimum numbers of ones represents the small hitting-set since K is expected to be as small as possible. The complexity of the proposed DNA-based algorithm is discussed, in terms of time complexity, volume complexity, numbers of test tube used and the longest library strand in solution space. Finally, the simulated experiment is applied to verify the correctness of our proposed DNA-based algorithm, in order to solve the well-known hitting-set problem. [Copyright &y& Elsevier]