The maximum density still life problem (MDSLP) is a hard constraint optimization problem based on Conway's game of life. It is a prime example of weighted constrained optimization problem that has been recently tackled in the constraint-programming community. Bucket elimination (BE) is a complete technique commonly used to solve this kind of constraint satisfaction problem. When the memory required to apply BE is too high, a heuristic method based on it (denominated mini-buckets) can be used to calculate bounds for the optimal solution. Nevertheless, the curse of dimensionality makes these techniques unpractical for large size problems. In response to this situation, we present a memetic algorithm for the MDSLP in which BE is used as a mechanism for recombining solutions, providing the best possible child from the parental set. Subsequently, a multi-level model in which this exact/metaheuristic hybrid is further hybridized with branch-and-bound techniques and mini-buckets is studied. Extensive experimental results analyze the performance of these models and multi-parent recombination. The resulting algorithm consistently finds optimal patterns for up to date solved instances in less time than current approaches. Moreover, it is shown that this proposal provides new best known solutions for very large instances.

Backtracking is a basic strategy to solve constraint satisfaction problems (CSPs). A satisfiable CSP instance is backtrack-free if a solution can be found without encountering any dead-end during a backtracking search, implying that the instance is easy to solve. We prove an exact phase transition of backtrack-free search in some random CSPs, namely in Model RB and in Model RD. This is the first time an exact phase transition of backtrack-free search can be identified on some random CSPs. Our technical results also have interesting implications on the power of greedy algorithms, on the width of random hypergraphs and on the exact satisfiability threshold of random CSPs.

It has previously been an open problem whether all Boolean submodular functions can be decomposed into a sum of binary submodular functions over a possibly larger set of variables. This problem has been considered within several different contexts in computer science, including computer vision, artificial intelligence, and pseudo-Boolean optimisation. Using a connection between the expressive power of valued constraints and certain algebraic properties of functions, we answer this question negatively. Our results have several corollaries. First, we characterise precisely which submodular functions of arity 4 can be expressed by binary submodular functions. Next, we identify a novel class of submodular functions of arbitrary arities which can be expressed by binary submodular functions, and therefore minimised efficiently using a so-called expressibility reduction to the Min-Cut problem. More importantly, our results imply limitations on this kind of reduction and establish for the first time that it cannot be used in general to minimise arbitrary submodular functions. Finally, we refute a conjecture of Promislow and Young on the structure of the extreme rays of the cone of Boolean submodular functions.

Airport gate assignment is of great importance in airport operations. In this paper, we study the Airport Gate Assignment Problem (AGAP), propose a new model and implement the model with Optimization Programming language (OPL). With the objective to minimize the number of conflicts of any two adjacent aircrafts assigned to the same gate, we build a mathematical model with logical constraints and the binary constraints, which can provide an efficient evaluation criterion for the Airlines to estimate the current gate assignment. To illustrate the feasibility of the model we construct experiments with the data obtained from Continental Airlines, Houston Gorge Bush Intercontinental Airport IAH, which indicate that our model is both energetic and effective. Moreover, we interpret experimental results, which further demonstrate that our proposed model can provide a powerful tool for airline companies to estimate the efficiency of their current work of gate assignment.

Solving Multiagent Networks Using Distributed Constraint Optimization

In many cooperative multiagent domains, the effect of local interactions between agents can be compactly represented as a network structure. Given that agents are spread across such a network, agents directly interact only with a small group of neighbors. A distributed constraint optimization problem (DCOP) is a useful framework to reason about such networks of agents. Given agents’ inability to communicate and collaborate in large groups in such networks, we focus on an approach called k-optimality for solving DCOPs. In this approach, agents form groups of one or more agents until no group of k or fewer agents can possibly improve the DCOP solution; we define this type of local optimum, and any algorithm guaranteed to reach such a local optimum, as k-optimal. The article provides an overview of three key results related to koptimality. The first set of results gives worst-case guarantees on the solution quality of k-optima in a DCOP. These guarantees can help determine an appropriate k-optimal algorithm, or possibly an appropriate constraint graph structure, for agents to use in situations where the cost of coordination between agents must be weighed against the quality of the solution reached. The second set of results gives upper bounds on the number of k-optima that can exist in a DCOP. These results are useful in domains where a DCOP must generate a set of solutions rather than a single solution. Finally, we sketch algorithms for k-optimality and provide some experimental results for 1-, 2- and 3-optimal algorithms for several types of DCOPs.

This report describes experimental results for a set of benchmarks on program verification. It compares the capabilities of CPBVP "Constraint Programming framework for Bounded Program Verification" [4] with the following frameworks: ESC/Java, CBMC, Blast, EUREKA and Why.

This paper studies how to verify the conformity of a program with its specification and proposes a novel constraint-programming framework for bounded program verification (CPBPV). The CPBPV framework uses constraint stores to represent the specification and the program and explores execution paths nondeterministically. The input program is partially correct if each constraint store so produced implies the post-condition. CPBPV does not explore spurious execution paths as it incrementally prunes execution paths early by detecting that the constraint store is not consistent. CPBPV uses the rich language of constraint programming to express the constraint store. Finally, CPBPV is parametrized with a list of solvers which are tried in sequence, starting with the least expensive and less general. Experimental results often produce orders of magnitude improvements over earlier approaches, running times being often independent of the variable domains. Moreover, CPBPV was able to detect subtle errors in some programs while other frameworks based on model checking have failed.

We describe decomposition during search (DDS), an integration of And/Or tree search into propagation-based constraint solvers. The presented search algorithm dynamically decomposes sub-problems of a constraint satisfaction problem into independent partial problems, avoiding redundant work. The paper discusses how DDS interacts with key features that make propagation-based solvers successful: constraint propagation, especially for global constraints, and dynamic search heuristics. We have implemented DDS for the Gecode constraint programming library. Two applications, solution counting in graph coloring and protein structure prediction, exemplify the benefits of DDS in practice.

When implementing a propagator for a constraint, one must decide about variants: When implementing min, should one also implement max? Should one implement linear equations both with and without coefficients? Constraint variants are ubiquitous: implementing them requires considerable (if not prohibitive) effort and decreases maintainability, but will deliver better performance. This paper shows how to use variable views, previously introduced for an implementation architecture, to derive perfect propagator variants. A model for views and derived propagators is introduced. Derived propagators are proved to be indeed perfect in that they inherit essential properties such as correctness and domain and bounds consistency. Techniques for systematically deriving propagators such as transformation, generalization, specialization, and channeling are developed for several variable domains. We evaluate the massive impact of derived propagators. Without derived propagators, Gecode would require 140000 rather than 40000 lines of code for propagators.