Christine Solnon

Ants can solve constraint satisfaction problems

We describe a novel incomplete approach for solving constraint satisfaction problems (CSPs) based on the ant colony optimization (ACO) metaheuristic. The idea is to use artificial ants to keep track of promising areas of the search space by laying trails of pheromone. This pheromone information is used to guide the search, as a heuristic for choosing values to be assigned to variables. We first describe the basic ACO algorithm for solving CSPs and we show how it can be improved by combining it with local search techniques. Then, we introduce a preprocessing step, the goal of which is to favor a larger exploration of the search space at a lower cost, and we show that it allows ants to find better solutions faster. Finally, we evaluate our approach on random binary problems.

Ant Colony Optimization for Multi-Objective Optimization Problems

We propose in this paper a generic algorithm based on ant colony optimization to solve multi-objective optimization problems. The proposed algorithm is parameterized by the number of ant colonies and the number of pheromone trails. We compare different variants of this algorithm on the multi-objective knapsack problem. We compare also the obtained results with other evolutionary algorithms from the literature.

Measuring the similarity of labeled graphs

This paper proposes a similarity measure to compare cases represented by labeled graphs. We first define an expressive model of directed labeled graph, allowing multiple labels on vertices and edges. Then we define the similarity problem as the search of a best mapping, where a mapping is a correspondence between vertices of the graphs. A key point of our approach is that this mapping does not have to be univalent, so that a vertex in a graph may be associated with several vertices of the other graph. Another key point is that the quality of the mapping is determined by generic functions, which can be tuned in order to implement domain-dependant knowledge. We discuss some computational issues related to this problem, and we describe a greedy algorithm for it. Finally, we show that our approach provides not only a quantitative measure of the similarity, but also qualitative information which can prove valuable in the adaptation phase of CBR.

A study of greedy, local search, and ant colony optimization approaches for car sequencing problems

This paper describes and compares several heuristic approaches for the car sequencing problem. We first study greedy heuristics, and show that dynamic ones clearly outperform their static counterparts. We then describe local search and ant colony optimization (ACO) approaches, that both integrate greedy heuristics, and experimentally compare them on benchmark instances. ACO yields the best solution quality for smaller time limits, and it is comparable to local search for larger limits. Our best algorithms proved one instance being feasible, for which it was formerly unknown whether it is satisfiable or not.

Reactive tabu search for measuring graph similarity

Graph matching is often used for image recognition. Different kinds of graph matchings have been proposed such as (sub)graph isomorphism or error-tolerant graph matching, giving rise to different graph similarity measures. A first goal of this paper is to show that these different measures can be viewed as special cases of a generic similarity measure introduced in [8]. This generic similarity measure is based on a non-bijective graph matching (like [4] and [2]) so that it is well suited to image recognition. In particular, over/under-segmentation problems can be handled by linking one vertex to a set of vertices. In a second part, we address the problem of computing this measure and we describe two algorithms: a greedy algorithm, that quickly computes sub-optimal solutions, and a reactive Tabu search algorithm, that may improve these solutions. Some experimental results are given.

A study of ACO capabilities for solving the maximum clique problem

This paper investigates the capabilities of the Ant Colony Optimization (ACO) meta-heuristic for solving the maximum clique problem, the goal of which is to find a largest set of pairwise adjacent vertices in a graph. We propose and compare two different instantiations of a generic ACO algorithm for this problem. Basically, the generic ACO algorithm successively generates maximal cliques through the repeated addition of vertices into partial cliques, and uses “pheromone trails” as a greedy heuristic to choose, at each step, the next vertex to enter the clique. The two instantiations differ in the way pheromone trails are laid and exploited, i.e., on edges or on vertices of the graph.We illustrate the behavior of the two ACO instantiations on a representative benchmark instance and we study the impact of pheromone on the solution process. We consider two measures—the re-sampling and the dispersion ratio—for providing an insight into the performance at run time. We also study the benefit of integrating a local search procedure within the proposed ACO algorithm, and we show that this improves the solution process. Finally, we compare ACO performance with that of three other representative heuristic approaches, showing that the former obtains competitive results.

AllDifferent-based filtering for subgraph isomorphism

The subgraph isomorphism problem involves deciding if there exists a copy of a pattern graph in a target graph. This problem may be solved by a complete tree search combined with filtering techniques that aim at pruning branches that do not contain solutions. We introduce a new filtering algorithm based on local all different constraints. We show that this filtering is stronger than other existing filterings - i.e., it prunes more branches - and that it is also more efficient - i.e., it allows one to solve more instances quicker.

Searching for maximum cliques with ant colony optimization

In this paper, we investigate the capabilities of Ant Colony Optimization (ACO) for solving the maximum clique problem. We describe Ant-Clique, an algorithm that successively generates maximal cliques through the repeated addition of vertices into partial cliques. ACO is used to choose, at each step, the vertex to add. We illustrate the behaviour of this algorithm on two representative benchmark instances and we study the impact of pheromone on the solution process. We also experimentally compare Ant-Clique with GLS, a Genetic Local Search approach, and we show that Ant-Clique finds larger cliques, on average, on a majority of DIMACS benchmark instances, even though it does not reach the best known results on some instances.

Solving subgraph isomorphism problems with constraint programming

The subgraph isomorphism problem consists in deciding if there exists a copy of a pattern graph in a target graph. We introduce in this paper a global constraint and an associated filtering algorithm to solve this problem within the context of constraint programming. The main idea of the filtering algorithm is to label every node with respect to its relationships with other nodes of the graph, and to define a partial order on these labels in order to express compatibility of labels for subgraph isomorphism. This partial order over labels is used to filter domains. Labelings can also be strengthened by adding information from the labels of neighbors. Such a strengthening can be applied iteratively until a fixpoint is reached. Practical experiments illustrate that our new filtering approach is more effective on difficult instances of scale free graphs than state-of-the-art algorithms and other constraint programming approaches.

Integration of ACO in a Constraint Programming Language

We propose to integrate ACO in a Constraint Programming (CP) language. Basically, we use the CP language to describe the problem to solve by means of constraints and we use the CP propagation engine to reduce the search space and check constraint satisfaction; however, the classical backtrack search of CP is replaced by an ACO search. We report first experimental results on the car sequencing problem and compare different pheromone strategies for this problem.