For many real-world problems, users are often interested not only in finding a single solution but in obtaining a sufficiently diverse collection of solutions. In this work, we consider the Diverse SAT problem, aiming to find a set of diverse satisfying assignments for a given propositional formula. We propose a novel and effective local search algorithm, DiverSAT, to solve the problem. To cope with diversity, we introduce three heuristics and a perturbation strategy based on some relevant information. We conduct extensive experiments on a large number of public benchmarks, collected from semiformal hardware verification, logistics planning, and other domains. The results show that DiverSAT outperforms the existing algorithms on most of these benchmarks.

The Diversified Top-k MaxSAT (DTKMS) problem is an extension of MaxSAT. The objective of DTKMS is to find k feasible assignments of a given formula, such that each assignment satisfies all hard clauses and the k assignments together satisfy the maximum number of soft clauses. This paper presents a local search algorithm, DTKMS-DIA, which incorporates a new approach to generating initial assignments. Experimental results indicate that DTKMS-DIA can achieve attractive performance on 826 instances compared with state-of-the-art solvers.

All Solution SAT (AllSAT) is a variant of Propositional Satisfiability, which aims to find all satisfying assignments for a given formula. AllSAT has significant applications in different domains, such as software testing, data mining, and network verification. In this paper, observing that the lack of component analysis may result in more work for algorithms with non-chronological backtracking, we propose a DPLL-based algorithm for solving AllSAT problem, named AllSATCC, which takes advantage of component analysis to reduce work repetition caused by non-chronological backtracking. The experimental results show that our algorithm outperforms the state-of-the-art algorithms on most instances.

In this paper, we investigate the hybrid tractability of binary Quantified Constraint Satisfaction Problems (QCSPs). First, a basic tractable class of binary QCSPs is identified by using the broken-triangle property. In this class, the variable ordering for the broken-triangle property must be same as that in the prefix of the QCSP. Second, we break this restriction to allow that existentially quantified variables can be shifted within or out of their blocks, and thus identify some novel tractable classes by introducing the broken-angle property. Finally, we identify a more generalized tractable class, i.e., the min-of-max extendable class for QCSPs.

The rigorous theoretical analyses of algorithms for #SAT have been proposed in the literature. As we know, previous algorithms for solving #SAT have been analyzed only regarding the number of variables as the parameter. However, the time complexity for solving #SAT instances depends not only on the number of variables, but also on the number of clauses. Therefore, it is significant to exploit the time complexity from the other point of view, i.e. the number of clauses. In this paper, we present algorithms for solving #2-SAT and #3-SAT with rigorous complexity analyses using the number of clauses as the parameter. By analyzing the algorithms, we obtain the new worst-case upper bounds O(1.1892m) for #2-SAT and O(1.4142m) for #3-SAT, where m is the number of clauses.

The permutation flow shop problem (PFSSP) is a well-known difficult combinatorial optimization problem. In this paper, we present a new hybrid optimization algorithm named SIGSA to solve the PFSSP. This algorithm is composed by the LRV rule, SA-based local search and IIS-based local search. First, to make GSA suitable for PFSSP, a new LRV rule based on random key is introduced to convert the continuous position in GSA to the discrete job permutation. Second, to enhance the searching capability, the SA-based local search is designed to help the algorithm to escape from local minimum. Then, the IIS-based local search is used for enhancing the individuals in GSA with a certain probability. Additionally, Comparison with other results in the literature shows that the SIGSA is an efficient and effective approach for the PFSSP.