Chu Min Li

New inference rules for Max-SAT

Exact Max-SAT solvers, compared with SAT solvers, apply little inference at each node of the proof tree. Commonly used SAT inference rules like unit propagation produce a simplified formula that preserves satisfiability but, unfortunately, solving the Max-SAT problem for the simplified formula is not equivalent to solving it for the original formula. In this paper, we define a number of original inference rules that, besides being applied efficiently, transform Max-SAT instances into equivalent Max-SAT instances which are easier to solve. The soundness of the rules, that can be seen as refinements of unit resolution adapted to Max-SAT, are proved in a novel and simple way via an integer programming transformation. With the aim of finding out how powerful the inference rules are in practice, we have developed a new Max-SAT solver, called MaxSatz, which incorporates those rules, and performed an experimental investigation. The results provide empirical evidence that MaxSatz is very competitive, at least, on random Max-2SAT, random Max-3SAT, Max-Cut, and Graph 3-coloring instances, as well as on the benchmarks from the Max-SAT Evaluation 2006.

Diversification and determinism in local search for satisfiability

The choice of the variable to flip in the Walksat family procedures is always random in that it is selected from a randomly chosen unsatisfied clause c. This choice in Novelty or R-Novelty heuristics also contains some determinism in that the variable to flip is always limited to the two best variables in c. In this paper, we first propose a diversification parameter for Novelty (or R-Novelty) heuristic to break the determinism in Novelty and show its performance compared with the random walk parameter in Novelty+. Then we exploit promising decreasing paths in a deterministic fashion in local search using a gradient-based approach. In other words, when promising decreasing paths exist, the variable to flip is no longer selected from a randomly chosen unsatisfied clause but in a deterministic fashion to surely decrease the number of unsatisfied clauses. Experimental results show that the proposed diversification and the determinism allow to significantly improve Novelty (and Walksat).

Greedy algorithms for packing unequal circles into a rectangular container

In this paper, we study the problem of packing unequal circles into a two-dimensional rectangular container. We solve this problem by proposing two greedy algorithms. The first algorithm, denoted by B1.0, selects the next circle to place according to the maximum-hole degree rule, that is inspired from human activity in packing. The second algorithm, denoted by B1.5, improves B1.0 with a self-look-ahead search strategy. The comparisons with the published methods on several instances taken from the literature show the good performance of our approach.

Combining adaptive noise and look-ahead in local search for SAT

The adaptive noise mechanism was introduced in Novelty+ to automatically adapt noise settings during the search [4]. The local search algorithm G2WSAT deterministically exploits promising decreasing variables to reduce randomness and consequently the dependence on noise parameters. In this paper, we first integrate the adaptive noise mechanism in G2WSAT to obtain an algorithm adaptG2WSAT, whose performance suggests that the deterministic exploitation of promising decreasing variables cooperates well with this mechanism. Then, we propose an approach that uses look-ahead for promising decreasing variables to further reinforce this cooperation. We implement this approach in adaptG2WSAT, resulting in a new local search algorithm called adaptG2WSATP. Without any manual noise or other parameter tuning, adaptG2WSATP shows generally good performance, compared with G2WSAT with approximately optimal static noise settings, or is sometimes even better than G2WSAT. In addition, adaptG2WSATP is favorably compared with state-of-the-art local search algorithms such as R+adaptNovelty+ and VW.

New heuristics for packing unequal circles into a circular container

We propose two new heuristics to pack unequal circles into a two-dimensional circular container. The first one, denoted by A1.0, is a basic heuristic which selects the next circle to place according to the maximal hole degree rule. The second one, denoted by A1.5, uses a self look-ahead strategy to improve A1.0. We evaluate A1.0 and A1.5 on a series of instances up to 100 circles from the literature and compare them with existing approaches. We also study the behaviour of our approach for packing equal circles comparing with a specified approach in the literature. Experimental results show that our approach has a good performance in terms of solution quality and computational time for packing unequal circles.

Exploiting unit propagation to compute lower bounds in branch and bound Max-SAT solvers

One of the main differences between complete SAT solvers and exact Max-SAT solvers is that the former make an intensive use of unit propagation at each node of the proof tree while the latter, in order to ensure optimality, can only apply unit propagation to a restricted number of nodes. In this paper, we describe a branch and bound Max-SAT solver that applies unit propagation at each node of the proof tree to compute the lower bound instead of applying unit propagation to simplify the formula. The new lower bound captures the lower bound based on inconsistency counts that apply most of the state-of-the-art Max-SAT solvers as well as other improvements, like the start rule, that have been defined to get a lower bound of better quality. Moreover, our solver incorporates the Jeroslow-Wang variable selection heuristic, the pure literal and dominating unit clause rules, and novel preprocessing techniques. The experimental investigation we conducted to compare our solver with the most modern Max-SAT solvers provides experimental evidence that our solver is very competitive. Research partially supported by projects TIN2004-07933-C03-03 and TIC2003-00950 funded by the Ministerio de Educacion y Ciencia. The second author is supported by a grant Ramon y Cajal.

Exploiting Cycle Structures in Max-SAT

We investigate the role of cycles structures (i.e., subsets of clauses of the form

A Parallelization Scheme Based on Work Stealing for a Class of SAT Solvers

\bar{l}_{1}\vee l_{2}, \bar{l}_{1}\vee l_{3},\bar{l}_{2}\vee\bar{l}_{3}

A Hybrid Approach for SAT

) in the quality of the lower bound (LB) of modern MaxSAT solvers. Given a cycle structure, we have two options: (i) use the cycle structure just to detect inconsistent subformulas in the underestimation component, and (ii) replace the cycle structure with

Parallelizing Satz Using Dynamic Workload Balancing

\bar{l}_{1},l_{1}\vee\bar{l}_{2}\vee\bar{l}_{3},\bar{l}_{1}\vee l_{2}\vee l_{3}