Marie-José Huguet

YIELDS: A Yet Improved Limited Discrepancy Search for CSPs

In this paper, we introduce a Yet ImprovEd Limited Discrepancy Search (YIELDS), a complete algorithm for solving Constraint Satisfaction Problems. As indicated in its name, YIELDS is an improved version of Limited Discrepancy Search (LDS). It integrates constraint propagation and variable order learning. The learning scheme, which is the main contribution of this paper, takes benefit from failures encountered during search in order to enhance the efficiency of variable ordering heuristic. As a result, we obtain a search which needs less discrepancies than LDS to find a solution or to state a problem is intractable. This method is then less redundant than LDS. n nThe efficiency of YIELDS is experimentally validated, comparing it with several solving algorithms: Depth-bounded Discrepancy Search, Forward Checking, and Maintaining Arc-Consistency. Experiments carried out on randomly generated binary CSPs and real problems clearly indicate that YIELDS often outperforms the algorithms with which it is compared, especially for tractable problems.

A study of constraint programming heuristics for the car-sequencing problem

In the car-sequencing problem, a number of cars has to be sequenced on an assembly line respecting several constraints. This problem was addressed by both Operations Research (OR) and Constraint Programming (CP) com-munities, either as a decision problem or as an optimization problem. In this paper, we consider the decision variant of the car sequencing problem and we propose a systematic way to classify heuristics for solving it. This classification is based on a set of four criteria, and we consider all relevant combinations for these criteria. Some combinations correspond to common heuristics used in the past, whereas many others are novel. Not surprisingly, our empirical evaluation confirms earlier findings that specific heuristics are very important for efficiently solving the car-sequencing problem (see for in-stance [17]), in fact, often as important or more than the propagation method. Moreover, through a criteria analysis, we are able to get several new insights into what makes a good heuristic for this problem. In particular, we show that the criterion used to select the most constrained option is critical, and the best choice is fairly reliably the load of an option. Similarly, branching on the type of vehicle is more efficient than branching on the use of an option. Overall, we can therefore indicate with a relatively high confidence which is the most robust strategy, or at least outline a small set of potentially best strategies. Last, following a remark in [14] stating that the notion of slack used in heuristics induces a pruning rule, we propose an algorithm for this method and experimentally evaluate it, showing that, although computationally cheap and easy to implement, this is in practice a very efficient way to solve car-sequencing benchmarks.

Dedicated constraint propagation for Job-Shop problem with generic time-lags

This paper addresses the Job-Shop scheduling problem with generic time-lags (JSPGTL). This problem is a generalization of the Job-Shop scheduling problem where extra (minimum and maximum) delays can be introduced between any operations. First a state of the art on the job-shop scheduling with time-lags is provided and we outline that the determination of a feasible solution for the JSPGTL is clearly a difficult problem as contrary to more basic time-lags problems. Secondly we propose some dedicated constraint propagation rules wich aim to detect some inconsistancies for the JSPGTL. The efficiency of these rules is illustrated on a small example. These propagation rules can be included in a heuristic method for the acceleration of the search for feasible solution thanks to early detection of certain inconsistancies. This work is the first step of a collaboration which aims to propose a new feature for the resolution of JSPGTL.

Online virtual links resource allocation in Software-Defined Networks

Network virtualization is seen as a key networking paradigm for building diverse network services and architectures over a shared network infrastructure. Assigning network resources to virtual links and, more generally to virtual network topologies, efficiently and on-demand is one of the most challenging components of any network virtualization solution. This paper addresses the problem of on-line resource allocation of multiple virtual links on a Software Defined Network (SDN) infrastructure. The application context that is targeted is primarily the online provisioning of virtual overlay networks even if it can be broadened to address more general virtual networks. Considering an SDN physical infrastructure allows a complete freedom in choosing the optimal physical paths and the associated resources that support the virtual links with no interference from any other network function (such as routing). However, for the time being, forwarding in an SDN network is resource consuming with a noticeable impact on the size of the flow tables. Hence, forwarding (i.e. switching) resources should be carefully considered by the network resource allocation algorithm. This paper proposes a novel Integer-Linear formulation of the above cited problem by taking into account: (1) point-to-point as well as point-to-multipoint virtual links, each with an associated bandwidth requirement and a maximum transfer delay requirement, (2) two types of network resources, namely network links bandwidth and nodes switching resources, and (3) optionally, path splitting which allows a virtual link to be established on multiple physical paths. We report preliminary experimental results on a real network topology in an overloaded scenario (bandwidth requests largely exceed network capacity); they show that our algorithm outperforms shortest path heuristics with a gain on the admission rate (of virtual links requests) that ranges from 5 to 15% (compared to the most efficient heuristic) and with a computation time less than a few seconds.

Adaptations of k-shortest path algorithms for transportation networks

The computation of the k-shortest paths, should they be elementary or not, has been extensively investigated in the literature, yielding to extremely performant algorithms. For elementary paths, the best known algorithm to this day is the algorithm of Yen enhanced by the extension of Lawler, while for the search of non-elementary paths, the algorithm with the best complexity is due to Eppstein but is outperformed in practice by the Recursive Enumeration Algorithm. In the context of transportation networks, graphs are time dependent, meaning that the cost of an edge depends on the time at which it is crossed. If for each edge one cannot arrive later if he departs earlier, the network is said to respect the FIFO property. Under this hypothesis, the usual Dijkstra shortest path algorithm is still polynomial. Additionally, since each edge is associated to a transportation type, one may want to restrict a path to be in a regular language. To find a shortest path under this constraint a polynomial algorithm, called DRegLC, works on the product of the network and the graph representing an automaton accepting the regular language. In this paper, some k-shortest paths algorithms are adapted to be used on such transportation networks with a regular language constraint. Also, the computation of the k-shortest elementary paths is considered using k-shortest non elementary paths algorithms, deleting loops while searching if possible. To address this approach, a new algorithm is presented to speed-up the search of elementary paths while scanning as few paths containing loops as possible.

Finding stable flows in multi-agent networks under an equal-sharing policy☆

A Multi-Agent network flow problem is addressed in this paper where a set of transportation-agents can control the capacities of a set of routes. Each agent incurs a cost proportional to the chosen capacity. A third-party agent, a customer, is interesting in maximizing the product flow transshipped from a source to a sink node through the network. He offers a reward proportional to the flow value, which is shared equally among the transportation-agents. We address the problem of finding a stable strategy (i.e., a Nash Equilibrium) which maximizes the network flow. We show that this problem, already proved to be NP-hard, can be modeled and solved using mixed integer linear programming (MILP).

Climbing discrepancy search for flowshop and jobshop scheduling with time lags

This paper addresses the jobshop and the flowshop scheduling problems with minimum and maximum time lags. To solve this kind of problems, we propose adaptations of Climbing Discrepancy Search (CDS). We study various parameter settings. Computational experiments are provided to evaluate the propositions.

Stability requirement in a weekly waste collection problem

Based on a practical study in a local authority, this paper deals with a study on a new criterion for a weekly waste collection problem to consider the stability of proposed routes. In the problem under consideration, some parts of the network must be collected once a week (at the beginning of the week) and some parts twice a week (at the beginning and at the end of the week); for a week there are then two waste collection problems to solve. Each of them is modeled as a VRP with Time Windows. To solve this weekly waste collection problem, we propose several two-steps heuristic methods: first one computes one set of routes with usual criteria (cost) and secondly one computes the other set of routes by adding a new criteria for taking into account the stability between the two sets of routes. Then, we provide an experimental comparison of the proposed methods on VRPTW instances.