Given a graph G, the minimum Connected-k-Subgraph Cover problem (MinCkSC) is to find a minimum vertex subset C of G such that every connected subgraph of G on k vertices has at least one vertex in C. If furthermore the subgraph of G induced by C is connected, then the problem is denoted as MinCkSC$_{con}$. In this paper, we first present a PTAS for MinCkSC on an H-minor-free graph, where H is a graph with a constant number of vertices. Then, we design an $O((\omega+1)(2(k-1)(\omega+2))^{3\omega+3})|V|$-time FPT algorithm for MinCkSC$_{con}$ on a graph with treewidth $\omega$, based on which we further design an $O(2^{O(\sqrt{t}\log t)}|V|^{O(1)})$ time subexponential FPT algorithm for MinCkSC$_{con}$ on an H-minor-free graph, where t is an upper bound of solution size.

This paper presents a detailed analysis of the scalability and parallelization of local search algorithms for the Satisfiability problem. We propose a framework to estimate the parallel performance of a given algorithm by analyzing the runtime behavior of its sequential version. Indeed, by approximating the runtime distribution of the sequential process with statistical methods, the runtime behavior of the parallel process can be predicted by a model based on order statistics. We apply this approach to study the parallel performance of two SAT local search solvers, namely Sparrow and CCASAT, and compare the predicted performances to the results of an actual experimentation on parallel hardware up to 384 cores. We show that the model is accurate and predicts performance close to the empirical data. Moreover, as we study different types of instances (random and crafted), we observe that the local search solvers exhibit different behaviors and that their runtime distributions can be approximated by two types of distributions: exponential (shifted and non-shifted) and lognormal.

This paper presents a heuristic approach combining constraint satisfaction, local searchand a constructive optimization algorithm for a large-scale energy management andmaintenance scheduling problem. The methodology shows how to successfully combine andorchestrate different types of algorithms and to produce competitive results. We alsopropose an efficient way to scale the method for huge instances. A large part of thepresented work was done to compete in the ROADEF/EURO Challenge 2010, organized jointly bythe ROADEF, EURO and Électricité de France. The numerical results obtained on officialcompetition instances testify about the quality of the approach. The method achieves 3 outof 15 possible best results.

The tool switching problem (ToSP) is well known in the domain of flexible manufacturing systems. Given a reconfigurable machine, the ToSP amounts to scheduling a collection of jobs on this machine (each of them requiring a different set of tools to be completed), as well as the tools to be loaded/unloaded at each step to process these jobs, such that the total number of tool switches is minimized. Different exact and heuristic methods have been defined to deal with this problem. In this work, we focus on memetic approaches to this problem. To this end, we have considered a number of variants of three different local search techniques (hill climbing, tabu search, and simulated annealing), and embedded them in a permutational evolutionary algorithm. It is shown that the memetic algorithm endowed with steepest ascent hill climbing search yields the best results, performing synergistically better than its stand-alone constituents, and providing better results than the rest of the algorithms (including those returned by an effective ad hoc beam search heuristic defined in the literature for this problem).

In this paper we deal with the preemptive asymmetric stacker crane problem in a heuristic way. We first present some theoretical results which allow us to turn this problem into a specific tree design problem. We next derive from this new representation an integer linear programming model together with simple and efficient greedy and local search heuristics. We conclude by presenting experimental results which aim at both testing the efficiency of our heuristic and evaluating the impact of the preemption hypothesis.

The goal of this paper is to provide a strong integration between constraint modelling and relational DBMSs. To this end we propose extensions of standard query languages such as relational algebra and SQL, by adding constraint modelling capabilities to them. In particular, we propose non-deterministic extensions of both languages, which are specially suited for combinatorial problems. Non-determinism is introduced by means of a guessing operator, which declares a set of relations to have an arbitrary extension. This new operator results in languages with higher expressive power, able to express all problems in the complexity class NP. Some syntactical restrictions which make data complexity polynomial are shown. The effectiveness of both extensions is demonstrated by means of several examples. The current implementation, written in Java using local search techniques, is described.

The decision repair algorithm (Jussien and Lhomme, Artificial Intelligence139 (2002) 21–45),which has been designed to solve constraint satisfaction problems (CSP), canbe seen, either (i) as an extension of the classical depth first treesearch algorithm with the introduction of a free choice of the variable towhich to backtrack in case of inconsistency, or (ii) as a localsearch algorithm in the space of the partial consistent variableassignments. or (iii) as a hybridisation between local searchand constraint propagation. Experiments reported in Pralet and Verfailllie (2004) show that some heuristics for the choice of thevariable to which to backtrack behave well on consistent instances andthat other heuristics behave well on inconsistent ones. They show alsothat, despite its a priori incompleteness, decision repair,equipped with some specific heuristics, can solve within a limited timealmost all the consistent and inconsistent randomly generatedinstances over the whole constrainedness spectrum. In this paper, wediscuss the heuristics that could be used by decisionrepair to solve consistent instances, on the one hand, andinconsistent ones, on the other hand. Moreover, we establish thatsome specific heuristics make decision repair complete.

As models for molecular evolution, immune response, and local search algorithms, various authors have used a stochastic process called the evolutionary walk, which goes as follows. Assign a random number to each vertex of the infinite N-ary tree, and start with a particle on the root. A step of the process consists of searching for a child with a higher number and moving the particle there; if no such child exists, the process stops. The average number of steps in this process is asymptotic, as N → ∞, to log N, a result first proved by Macken and Perelson. This paper relates the evolutionary walk to a process called random bisection, familiar from combinatorics and number theory, which can be thought of as a transformed Poisson process. We first give a thorough treatment of the exact walk length, computing its distribution, moments and moment generating function. Next we show that the walk length is asymptotically normally distributed. We also treat it as a mixture of Poisson random variables and compute the asymptotic distribution of the Poisson parameter. Finally, we show that in an evolutionary walk with uniform vertex numbers, the ‘jumps’, ordered by size, have the same asymptotic distribution as the normalized cycle lengths in a random permutation.