The survey propagation (SP) algorithm has been shown to work well on large instances of the random 3-SAT problem near its phase transition. It was shown that SP estimates marginals over covers that represent clusters of solutions. The SP-y algorithm generalizes SP to work on the maximum satisfiability (Max-SAT) problem, but the cover interpretation of SP does not generalize to SP-y. In this paper, we formulate the relaxed survey propagation (RSP) algorithm, which extends the SP algorithm to apply to the weighted Max-SAT problem. We show that RSP has an interpretation of estimating marginals over covers violating a set of clauses with minimal weight. This naturally generalizes the cover interpretation of SP. Empirically, we show that RSP outperforms SP-y and other state-of-the-art Max-SAT solvers on random Max-SAT instances. RSP also outperforms state-of-the-art weighted Max-SAT solvers on random weighted Max-SAT instances.

The identification of performance-optimizing parameter settings is an important part of the development and application of algorithms. We describe an automatic framework for this algorithm configuration problem. More formally, we provide methods for optimizing a target algorithms performance on a given class of problem instances by varying a set of ordinal and/or categorical parameters. We review a family of local-search-based algorithm configuration procedures and present novel techniques for accelerating them by adaptively limiting the time spent for evaluating individual configurations. We describe the results of a comprehensive experimental evaluation of our methods, based on the configuration of prominent complete and incomplete algorithms for SAT. We also present what is, to our knowledge, the first published work on automatically configuring the CPLEX mixed integer programming solver. All the algorithms we considered had default parameter settings that were manually identified with considerable effort. Nevertheless, using our automated algorithm configuration procedures, we achieved substantial and consistent performance improvements.

Ant colony optimization (ACO) has been applied to the field of combinatorial optimization widely. But the study of convergence theory of ACO is rare under general condition. In this paper, the authors try to find the evidence to prove that entropy is related to the convergence of ACO, especially to the estimation of the minimum iteration number of convergence. Entropy is a new view point possibly to studying the ACO convergence under general condition.

Nurse rostering is a complex scheduling problem that affects hospital personnel on a daily basis all over the world. This paper presents a new component-based approach with evolutionary eliminations, for a nurse scheduling problem arising at a major UK hospital. The main idea behind this technique is to decompose a schedule into its components (i.e. the allocated shift pattern of each nurse), and then to implement two evolutionary elimination strategies mimicking natural selection and natural mutation process on these components respectively to iteratively deliver better schedules. The worthiness of all components in the schedule has to be continuously demonstrated in order for them to remain there. This demonstration employs an evaluation function which evaluates how well each component contributes towards the final objective. Two elimination steps are then applied: the first elimination eliminates a number of components that are deemed not worthy to stay in the current schedule; the second elimination may also throw out, with a low level of probability, some worthy components. The eliminated components are replenished with new ones using a set of constructive heuristics using local optimality criteria. Computational results using 52 data instances demonstrate the applicability of the proposed approach in solving real-world problems.

LSCS is a satellite workshop of the international conference on principles and practice of Constraint Programming (CP), since 2004. It is devoted to local search techniques in constraint satisfaction, and focuses on all aspects of local search techniques, including: design and implementation of new algorithms, hybrid stochastic-systematic search, reactive search optimization, adaptive search, modeling for local-search, global constraints, flexibility and robustness, learning methods, and specific applications.

Constrained Optimum Path (COP) problems appear in many real-life applications, especially on communication networks. Some of these problems have been considered and solved by specific techniques which are usually difficult to extend. In this paper, we introduce a novel local search modeling for solving some COPs by local search. The modeling features the compositionality, modularity, reuse and strengthens the benefits of Constrained-Based Local Search. We also apply the modeling to the edge-disjoint paths problem (EDP). We show that side constraints can easily be added in the model. Computational results show the significance of the approach.

Using constraint-based local search, we effectively model and efficiently solve the problem of balancing the traffic demands on portions of the European airspace while ensuring that their capacity constraints are satisfied. The traffic demand of a portion of airspace is the hourly number of flights planned to enter it, and its capacity is the upper bound on this number under which air-traffic controllers can work. Currently, the only form of demand-capacity balancing we allow is ground holding, that is the changing of the take-off times of not yet airborne flights. Experiments with projected European flight plans of the year 2030 show that already this first form of demand-capacity balancing is feasible without incurring too much total delay and that it can lead to a significantly better demand-capacity balance.

We explore the use of the Cell Broadband Engine (Cell/BE for short) for combinatorial optimization applications: we present a parallel version of a constraint-based local search algorithm that has been implemented on a multiprocessor BladeCenter machine with twin Cell/BE processors (total of 16 SPUs per blade). This algorithm was chosen because it fits very well the Cell/BE architecture and requires neither shared memory nor communication between processors, while retaining a compact memory footprint. We study the performance on several large optimization benchmarks and show that this achieves mostly linear time speedups, even sometimes super-linear. This is possible because the parallel implementation might explore simultaneously different parts of the search space and therefore converge faster towards the best sub-space and thus towards a solution. Besides getting speedups, the resulting times exhibit a much smaller variance, which benefits applications where a timely reply is critical.

Stochastic local search (SLS) has been an active field of research in the last few years, with new techniques and procedures being developed at an astonishing rate. SLS has been traditionally associated with satisfiability solving, that is, finding a solution for a given problem instance, as its intrinsic nature does not address unsatisfiable problems. Unsatisfiable instances were therefore commonly solved using backtrack search solvers. For this reason, in the late 90s Selman, Kautz and McAllester proposed a challenge to use local search instead to prove unsatisfiability. More recently, two SLS solvers - Ranger and Gunsat - have been developed, which are able to prove unsatisfiability albeit being SLS solvers. In this paper, we first compare Ranger with Gunsat and then propose to improve Ranger performance using some of Gunsat's techniques, namely unit propagation look-ahead and extended resolution.

When a high-level constraint programming (CP) language lacks a (possibly global) constraint that would allow the formulation of a particular model of a combinatorial problem, then the modeller traditionally has the choice of (1) switching to another CP language that has all the required constraints, (2) formulating a different model that does not require the lacking constraints, or (3) implementing the lacking constraint in the low-level implementation language of the chosen CP language. This paper addresses the core question of facilitating the third option, and as a side effect often makes the first two options unnecessary. The user-level extensibility of CP languages has been an important goal for over a decade. In the traditional global search approach to CP (namely heuristic-based tree search interleaved with propagation), higher-level abstractions for describing new constraints include indexicals [17]; (possibly enriched) deterministic finite automata (DFAs) via the automaton [2] and regular [11] generic constraints; and multivalued decision diagrams (MDDs) via the mdd [5] generic constraint. Usually, a generic but efficient propagation algorithm achieves a suitable level of local consistency by processing the higher-level description of the new constraint.