Search

Local branching is a general purpose heuristic search method successfully used in Mixed Integer Programming (MIP). We propose its integration and extension in Constraint Programming (CP). [ABSTRACT FROM AUTHOR]

This paper describes a complete and efficient solution to the scheduling of conditional task graphs whose nodes are activities and whose arcs can be labelled with a probability distribution. Tasks are executed if a set of conditions hold at scheduling execution time. The model is therefore stochastic. The minimization of the expected makespan implies an exponential-sized description of the objective function. We propose an analytic formulation of the stochastic objective function based on the task graph analysis, and a conditional constraint that handles it efficiently. Experimental results show the effectiveness of our approach in comparison with (1) an approach using a deterministic objective function and (2) scenario based constraint programming taking into account all scenarios or only a part of them. [ABSTRACT FROM AUTHOR]

We propose two algorithms achieving generalized arc consistency for the soft global cardinality constraint with variable-based violation and with value-based violation. They are based on graph theory and their complexity is $O(\sqrt{n}m)$ where n is the number of variables and m is the sum of the cardinalities of the domains. They improve previous algorithms that ran respectively in O(n(m+nlog n)) and O((n+k)(m+nlog n)) where k is the cardinality of the union of the domains. [ABSTRACT FROM AUTHOR]

In this paper we introduce a complex allocation and scheduling problem for variable voltage Multi-Processor System-on-Chip (MPSoC) platforms. We propose a methodology to formulate and solve to optimality the allocation, scheduling and discrete voltage selection problem, minimizing the system energy dissipation and the overhead for frequency switching. Our approach is based on the Logic Benders decomposition technique where the allocation is solved through an Integer Programming solver, and the scheduling through a Constraint Programming solver. The two solvers are interleaved and their interaction regulated by cutting plane generation. The objective function depends on both master and sub-problem variables. We demonstrate the efficiency of our approach on a set of realistic instances. [ABSTRACT FROM AUTHOR]

This paper describes a complete and efficient solution to the stochastic allocation and scheduling for Multi-Processor System-on-Chip (MPSoC). Given a conditional task graph characterizing a target application and a target architecture with alternative memory and computation resources, we compute an allocation and schedule minimizing the expected value of communication cost, being the communication resources one of the major bottlenecks in modern MPSoCs. Our approach is based on the Logic Based Benders decomposition where the stochastic allocation is solved through an Integer Programming solver, while the scheduling problem with conditional activities is faced with Constraint Programming. The two solvers interact through no-goods. The original contributions of the approach appear both in the allocation and in the scheduling part. For the first, we propose an exact analytic formulation of the stochastic objective function based on the task graph analysis, while for the scheduling part we extend the timetable constraint for conditional activities. Experimental results show the effectiveness of the approach. [ABSTRACT FROM AUTHOR]

Hybrid algorithms combining local and systematic search often use nondeterminism in fundamentally different ways. They may differ in the strategy to explore the search tree and/or in how computation states are represented. This paper presents nondeterministic control structures to express a variety of hybrid search algorithms concisely and elegantly. These nondeterministic abstractions describe the search tree and are compiled in terms of first-class continuations. They are also parameterized by search controllers that are under user control and specify the state representation and the exploration strategy. The resulting search language is thus high-level, flexible, and directly extensible. The abstractions are illustrated on a jobshop scheduling algorithm that combines tabu search and a limited form of backtracking. Preliminary experimental results indicate that the control structures induce small, often negligible, overheads. [ABSTRACT FROM AUTHOR]

Integration of explanations into a CSP solver is a technique addressing difficult question "why my problem has no solution". Moreover, explanations together with advanced search methods like directed backjumping can effectively cut off parts of the search tree and thus speed up the search. In order to use explanations, propagation algorithms must provide some sort of reasons (justifications) for their actions. For binary constraints it is mostly easy. In the case of global constraints computation of factual justifications can be tricky and/or computationally expensive. This paper shows how to effectively compute explanations for the unary resource constraint. The explanations are computed in a lazy way. The technique is experimentally demonstrated on job-shop benchmark problems. The following propagation algorithms are considered: edge-finding, not-first/not-last and detectable precedences. Speed of these filtering algorithms and speed of the explanation computation is the main interest. [ABSTRACT FROM AUTHOR]

Creating good integer programming formulations had, as a basic axiom, the rule "Find formulations with tighter linear relaxations". This rule, while useful when using unsophisticated branch-and-bound codes,is insufficient when using state-of-the-art codes that understand and embed many of the obvious formulation improvements. As these optimization codes become more sophisticated it is important to have finer control over their operation. Modelers need to be even more creative in reformulating their integer programs in order to improve on the automatic reformulations of the optimization codes. [ABSTRACT FROM AUTHOR]

An optimization problem arising in the design of optical fibre networks is discussed. A network contains client nodes, each installed on one or more SONET rings. A constraint programming model of the problem is described and compared with a mixed integer programming formulation. In the CP model the search is decomposed into two stages; first partially solving the problem by deciding how many rings each node should be on, and then making specific assignments of nodes to rings. The model includes implied constraints derived by considering optimal solutions to subproblems. In both the MIP and CP models, it is important to deal with the symmetry of the problem. In the CP model, two sources of symmetry are separated; one is eliminated dynamically during search and the other by assigning ranges rather than explicit values to one set of decision variables. The resulting CP model allows optimal solutions to be found easily for benchmark problems. [ABSTRACT FROM AUTHOR]

We present the tree-of-BDDs approach, a decomposition scheme for compiling configuration problems. Methods for minimum explanations and full interchangeable value sets detection are also given. Experiments show that the techniques presented here can drastically reduce the time and space requirements for interactive configurators. [ABSTRACT FROM AUTHOR]

In this paper, we present a method for solving Mixed Logical/ Integer Linear Programming (MLILP) problems that integrates a polynomial-time ILP solver for the special class of Unit-Two-Variable-Per-Inequality (unit TVPI or UTVPI) constraints of the form ax + by ≤ d, where a, b ∈ {-1, 0, 1}, into generic Boolean SAT solvers. In our approach the linear constraints are viewed as special literals and replaced by binary "indicator" variables to generate a pure logical problem. The resulting problem is subsequently solved using a SAT search procedure which invokes the linear UTVPI solver to incrementally check the consistency of the UTVPI constraints whenever any of the indicator variables are assigned to true. The linear UTVPI solver, on the other hand, can possibly pass implications or no-good constraints to the Boolean SAT solver. Checking the consistency of the UTVPI constraints incrementally enables the UTVPI solver to efficiently interact with the different components of the SAT solver. Additionally, several heuristics and encoding methods are proposed to accommodate the special circumstances of activating UTVPI constraints by the SAT solver. Empirical evidence is presented that demonstrates the advantages of our combined method for large problems. [ABSTRACT FROM AUTHOR]

We identify a property of constraints called smoothness, and present an extremely simple randomized algorithm for solving smooth constraints. The complexity of the algorithm is much less than the lower bound for establishing path-consistency, and because smoothness is shown to be identical to connected row-convexity (CRC) for the case of binary constraints, the time and space complexity of solving CRC constraints is improved. Central to our algorithm is the relationship of smooth constraints to random walks on directed graphs. We also provide simple deterministic algorithms to test for the smoothness of a given CSP under given domain orderings of the variables. Finally, we show that some other known tractable constraint languages, like the set of implicational constraints, and the set of binary integer linear constraints, are special cases of smooth constraints, and can therefore be solved much more efficiently than the traditional time and space complexities attached with them. [ABSTRACT FROM AUTHOR]

A cardinality constraint imposes that each value of a set V must be taken a certain number of times by a set of variables X, whereas an among constraint imposes that a certain number of variables of a set X must take a value in the set V. This paper studies several combinations of among constraints and several conjunctions of among constraints and cardinality constraints. Some filtering algorithms are proposed and they are characterized when it is possible. Moreover, a weak form of Singleton arc consistency is considered. At last, it is shown how the global sequencing constraint and the global minimum distance constraint can be easily modeled by some conjunctions of cardinality and among constraints. Some results are also given for the global minimum distance constraint. They show that our study outperforms the existing constraint in ILOG Solver. [ABSTRACT FROM AUTHOR]

This paper presents a CSPs filtering method combining arc-consistency and dual Lagrangean relaxation techniques. First, we model the constraint satisfaction problem as a 0/1 linear integer program (IP); then, the consistency of a value is defined as an optimization problem on which a dual Lagrangean relaxation is defined. While solving the dual Lagrangean relaxation, values inconsistencies may be detected (dual Lagrangean inconsistent values); the constraint propagation of this inconsistency can be performed by arc-consistency. After having made the CSP arc-consistent, the process iteratively selects values of variables which may be dual Lagrangean inconsistent. Computational experiments performed over randomly generated problems show the advantages of the hybrid filtering technique combining arc-consistency and dual Lagrangean relaxation. Keywords: Arc-Consistency, Lagrangean Relaxation, Subgradient Algorithm. [ABSTRACT FROM AUTHOR]

The effects of combining search and modelling techniques can be complex and unpredictable, so guidelines are very important for the design and development of effective and robust solvers and models. A recently observed phenomenon is the negative effect of symmetry breaking constraints on local search performance. The reasons for this are poorly understood, and we attempt to shed light on the phenomenon by testing three conjectures: that the constraints create deep new local optima; that they can reduce the relative size of the basins of attraction of global optima; and that complex local search heuristics reduce their negative effects. [ABSTRACT FROM AUTHOR]

We present an algorithmic framework for integrating solution methods that is based on search, inference, and relaxation and their interactions. We show that the following are special cases: branch and cut, CP domain splitting with propagation, popular global optimization methods, DPL methods for SAT with conflict clauses, Benders decomposition and other nogood-based methods, partial-order dynamic backtracking, various local search metaheuristics, and GRASPs (greedy randomized adaptive search procedures). The framework allows elements of different solution methods to be combined at will, resulting in a variety of integrated methods. These include continuous relaxations for global constraints, the linking of integer and constraint programming via Benders decomposition, constraint propagation in global optimization, relaxation bounds in local search and GRASPs, and many others. [ABSTRACT FROM AUTHOR]

Producing work schedules for airline crew normally results in individually different schedules. Some airlines do however want to give the same schedule to groups of people. The construction of such groups must respect certain rules, provide a good matching of certain factors and fit well into the normal process of producing anonymous trips starting and ending at the home base and assigning these to the crew. In this paper we present an application, implemented and delivered to a large European airline, which addresses these needs. The problem is challenging to solve for certain cases. Hence two different approaches have been applied, one using constraint programming and the other using column generation. These two methods are described and compared - along with computational results. [ABSTRACT FROM AUTHOR]

Constraint programming (CP) based column generation uses CP to solve the pricing subproblem. We consider a set partitioning formulation with a huge number of variables, each of which can be generated by solving a CP subproblem. We propose two customized search strategies to solve the CP subproblem, which aim to improve the coordination between the master problem and the subproblem. Specifically, these two strategies attempt to generate more promising columns for the master problem in order to counter the effect of slow convergence and the difficulty of reaching integer solutions. The first strategy uses the dual variables to direct the search towards columns that drive the relaxed master problem faster to optimality. The second strategy exploits the structure of the constraints in the master problem to generate columns that help to reach integer solutions more quickly. We use a physician scheduling problem to test the strategies. [ABSTRACT FROM AUTHOR]

We describe the problem of scheduling astronomy observations for the Stratospheric Observatory for Infrared Astronomy, an airborne telescope. The problem requires maximizing the number of requested observations scheduled subject to a mixture of discrete and continuous constraints relating the feasibility of an astronomical observation to the position and time at which the observation begins, telescope elevation limits, Special Use Airspace limitations, and available fuel. Solving the problem requires making discrete choices (e.g. selection and sequencing of observations) and continuous ones (e.g. takeoff time and setup actions for observations by repositioning the aircraft). Previously, we developed an incomplete algorithm called ForwardPlanner using a combination of AI and OR techniques including progression planning, lookahead heuristics, stochastic sampling and numerical optimization, to solve a simplified version of this problem. While initial results were promising, ForwardPlanner fails to scale when accounting for all relevant constraints. We describe a novel combination of Squeaky Wheel Optimization (SWO), an incomplete algorithm designed to solve scheduling problems, with previously devised numerical optimization methods and stochastic sampling approaches, as well as heuristics based on reformulations of the SFPP to traditional OR scheduling problems. We show that this new algorithm finds as good or better flight plans as the previous approaches, often with less computation time. [ABSTRACT FROM AUTHOR]

Recently, new cost-based filtering algorithms for shorter-path constraints have been developed. However, so far only the theoretical properties of shorter-path constraint filtering have been studied. We provide the first extensive experimental evaluation of the new algorithms in the context of the resource constrained shortest path problem. We show how reasoning about path-substructures in combination with CP-based Lagrangian relaxation can help to improve significantly over previously developed problem-tailored filtering algorithms and investigate the impact of required-edge detection, undirected versus directed filtering, and the choice of the algorithm optimizing the Lagrangian dual. [ABSTRACT FROM AUTHOR]

We propose a natural generalization of arc-consistency, which we call multiconsistency: A value v in the domain of a variable x is k-multiconsistent with respect to a constraint C if there are at least k solutions to C in which x is assigned the value v. We present algorithms that determine which variable-value pairs are k-multiconsistent with respect to several well known global constraints. In addition, we show that finding super solutions is strictly harder than finding arbitrary solutions and suggest multiconsistency as an alternative way to search for robust solutions. [ABSTRACT FROM AUTHOR]

The Employee Timetabling Problem (ETP) is a general class of problems widely encountered in service organizations (such as call centers for instance). Given a set of activities, a set of demand curves (specifying the demand in terms of employees for each activity for each time period) the problem consists of constructing a set of work shifts such that each activity is at all time covered by a sufficient number of employees. Work shifts can cover many activities and must meet work regulations such as breaks, meals and maximum working time constraints. Furthermore, it is often desired to optimize a global objective function such as minimizing labor costs or maximizing a quality of service measure. This paper presents variants of this problem which are modeled with the Dantzig formulation. This approach consists of first generating all feasible work shifts and then selecting the optimal set. We propose to address the shift generation problem with constraint satisfaction techniques based on expressive and efficient global constraints such as gcc and regular. The selection problem, which is modeled with an integer linear program, is solved by a standard MIP solver for smaller instances and addressed by column generation for larger ones. Since a column generation procedure needs to generate only shifts of negative reduced cost, the optimization constraint cost-regular is introduced and described. Preliminary experimental results are given on a typical ETP. [ABSTRACT FROM AUTHOR]

The scheduling of social golfers has attracted significant attention in recent years because of its highly symmetrical and combinatorial nature. In particular, it has become one of the standard benchmarks for symmetry breaking in constraint programming. This paper presents a very effective, local search, algorithm for scheduling social golfers. The algorithm find the first known solutions to 11 instances and matches, or improves, state-of-the-art results from constraint programming on all but 3 instances. Moreover, most instances of the social golfers are solved within a couple of seconds. Interestingly, the algorithm does not incorporate any symmetry-breaking scheme and illustrates the nice complementarity between constraint programming and local search on this scheduling application. [ABSTRACT FROM AUTHOR]

The minimal Steiner tree problem is a classical NP-complete problem that has several applications in the communication and transportation sectors. It has recently emerged as a subproblem in decomposition techniques such as column generation and Lagrangian schemes. This has set new computational challenges to the state of the art solving approaches. Our goal is to improve on existing branch-and-cut algorithms so that our approach successfully serves as a fast subproblem solver in a decomposition context. Compared with existing literature, our technical contributions include 1) a new preflow-push cutting strategy, revisiting a little known graph algorithm, that halves the runtime of the separation step, and 2) a branching scheme that fairly balances the search tree and speeds up the search. An evaluation in a multicast design application shows that the algorithm enhances a column generation hybrid. Moreover, our approach offers a significant speedup factor on a publicly available set of challenging Steiner tree benchmarks. Keywords: networks, preflow-push algorithms, branch-and-cut, Steiner trees. [ABSTRACT FROM AUTHOR]

This paper presents a hybrid algorithm for a class of resource constrained scheduling problems based on decomposition. The general minimum completion time problem is considered, which has not been solved in a decomposed way by existing methods. The problem is first decomposed into an assignment master problem and a number of scheduling subproblems. The subproblem is formulated as both a constraint programming model and an integer programming model. The hybrid algorithm then combines constraint programming, integer programming and linear programming solvers in its three steps: the master problem solving, the subproblems solving and the cut generation. In particular, the cut generation method is based on the integer programming model, and in practice it is done by solving a linear program. Computational experiments have been carried out for the considered minimum completion time problems. The results show that the proposed algorithm could substantially reduce the solving time, compared with directly solving by mixed integer solvers. [ABSTRACT FROM AUTHOR]

Recent work have exhibited specific structure among combinatorial problem instances that could be used to speed up search or to help users understand the dynamic and static intimate structure of the problem being solved. Several Operations Research approaches apply decomposition or relaxation strategies upon such a structure identified within a given problem. The next step is to design algorithms that adaptatively integrate that kind of information during search. We claim in this paper, inspired by previous work on impact-based search strategies for constraint programming, that using an explanation-based constraint solver may lead to collect invaluable information on the intimate dynamic and static structure of a problem instance. We define several impact graphs to be used to design generic search guiding techniques and to identify hidden structures of instances. Finally, we discuss how dedicated OR solving strategies (such as Benders decomposition) could be adapted to constraint programming when specific relationships between variables are exhibited. [ABSTRACT FROM AUTHOR]

This article presents an arc-consistency algorithm for the tree constraint, which enforces the partitioning of a digraph into a set of vertex-disjoint anti-arborescences. It provides a necessary and sufficient condition for checking the tree constraint in time, as well as a complete filtering algorithm taking time. [ABSTRACT FROM AUTHOR]

The constraint NValue counts the number of different values assigned to a vector of variables. Propagating generalized arc consistency on this constraint is NP-hard. We show that computing even the lower bound on the number of values is NP-hard. We therefore study different approximation heuristics for this problem. We introduce three new methods for computing a lower bound on the number of values. The first two are based on the maximum independent set problem and are incomparable to a previous approach based on intervals. The last method is a linear relaxation of the problem. This gives a tighter lower bound than all other methods, but at a greater asymptotic cost. [ABSTRACT FROM AUTHOR]

In face of the unwieldiness of non-monotonic logic engines, or Prolog/CLP meta interpreters as they are commonly used for model based reasoning and diagnosis, this paper proposes a simple, but effective improvement for performing the complex diagnostic task. The chosen approach is twofold: firstly, the problem of contradicting first order system descriptions with a set of observations is reduced to propositional logic using the notion of symptoms, and secondly, the determination of conflict sets and minimal diagnoses is mapped to a problem whose technical solution has experienced a sheer boost over the past years, namely k-satisfiability using state-of-the-art SAT-solvers. Since the involved problems are (mostly) -complete, the ideas for additional improvements for a more diagnosis-specific SAT-solver are also sketched and their implementation by means of a non-destructive solver, LSAT, evaluated. Keywords: model based reasoning, model based diagnosis, SAT-solving, system monitoring, formal specification. [ABSTRACT FROM AUTHOR]

Many combinatorial (optimisation) problems have natural models based on, or including, set variables and set constraints. This was already known to the constraint programming community, and solvers based on constructive search for set variables have been around for a long time. In this paper, set variables and set constraints are put into a local-search framework, where concepts such as configurations, penalties, and neighbourhood functions are dealt with generically. This scheme is then used to define the penalty functions for five (global) set constraints, and to model and solve two well-known applications. [ABSTRACT FROM AUTHOR]

This paper introduces a problem called the temporal knapsack problem, presents several algorithms for solving it, and compares their performance. The temporal knapsack problem is a generalisation of the knapsack problem and specialisation of the multidimensional (or multiconstraint) knapsack problem. It arises naturally in applications such as allocating communication bandwidth or CPUs in a multiprocessor to bids for the resources. The algorithms considered use and combine techniques from constraint programming, artificial intelligence and operations research. [ABSTRACT FROM AUTHOR]

Plant PowerOps (PPO) [9] is a new ILOG product, based on business rules and optimization technology, dedicated to production planning and detailed scheduling for manufacturing. This paper describes how PPO integrates a rule based system with the optimization engines and the graphical user interface. The integration proposed is motivated by the need to allow business users to manage unexpected changes in their environment. It provides a flexible interface for configuring, maintaining and tuning the system and for managing optimization scenarios. The proposed approach is discussed via several use cases we encountered in practice in supply chain management. Nevertheless, we believe that most of the ideas described in this paper apply in almost any area of optimization application. [ABSTRACT FROM AUTHOR]

This paper describes an efficient, complete approach for solving a complex allocation and scheduling problem for Multi-Processor System-on-Chip (MPSoC). Given a throughput constraint for a target application characterized as a task graph annotated with computation, communication and storage requirements, we compute an allocation and schedule which minimizes communication cost first, and then the makespan given the minimal communication cost. Our approach is based on problem decomposition where the allocation is solved through an Integer Programming solver, while the scheduling through a Constraint Programming solver. The two solvers are interleaved and their interaction regulated by no-good generation. Experimental results show speedups of orders of magnitude w.r.t. pure IP and CP solution strategies. [ABSTRACT FROM AUTHOR]

We present the system LAP (Learning Abductive Programs) that is able to learn abductive logic programs from examples and from a background abductive theory. A new type of induction problem has been defined as an extension of the Inductive Logic Programming framework. In the new problem definition, both the background and the target theories are abductive logic programs and abductive derivability is used as the coverage relation. LAP is based on the basic top-down ILP algorithm that has been suitably extended. In particular, coverage of examples is tested by using the abductive proof procedure defined by Kakas and Mancarella [24]. Assumptions can be made in order to cover positive examples and to avoid the coverage of negative ones, and these assumptions can be used as new training data. LAP can be applied for learning in the presence of incomplete knowledge and for learning exceptions to classification rules. [ABSTRACT FROM AUTHOR]

The Travelling Salesman Problem is a classic problem of Combinatorial Optimisation and involves routing around a number of cities in order to cover the minimum total distance. It is notoriously difficult to solve practical sized instances optimally. The classical Integer Programming formulation involves an exponential number of constraints. [ABSTRACT FROM AUTHOR]

Embedded systems are everywhere: from alarm clocks to PDAs, from mobile phones to cars, almost all the devices we use are controlled by embedded systems. Over 99% of the microprocessors produced today are used in embedded systems, and recently the number of embedded systems in use has become larger than the number of humans on the planet. [ABSTRACT FROM AUTHOR]