Finding regions of local repair in hierarchical constraint satisfaction

Algorithms for solving constraint satisfaction problems (CSP) have been successfully applied to several fields including scheduling, design, and planning. Latest extensions of the standard CSP to constraint optimization problems (COP) additionally provided new opportunities for solving several problems of combinatorial optimization more efficiently. Basically, two classes of algorithms have been used for searching constraint satisfaction problems (CSP): local search methods and systematic tree search extended by the classical constraint-processing techniques like e.g. forward checking and backmarking. Both classes exhibit characteristic advantages and drawbacks. This report presents a novel approach for solving constraint optimization problems that combines the advantages of local search and tree search algorithms which have been extended by constraint-processing techniques. This method proved applicability in a commercial nurse scheduling system as well as on randomly generated problems

Dynamic agent prioritisation with penalties in distributed local search.

Distributed Constraint Satisfaction Problems (DisCSPs) solving techniques solve problems which are distributed over a number of agents.The distribution of the problem is required due to privacy, security or cost issues and, therefore centralised problem solving is inappropriate. Distributed local search is a framework that solves large combinatorial and optimization problems. For large problems it is often faster than distributed systematic search methods. However, local search techniques are unable to detect unsolvability and have the propensity of getting stuck at local optima. Several strategies such as weights on constraints, penalties on values and probability have been used to escape local optima. In this paper, we present an approach for escaping local optima called Dynamic Agent Prioritisation and Penalties (DynAPP) which combines penalties on variable values and dynamic variable prioritisation for the resolution of distributed constraint satisfaction problems. Empirical evaluation with instances of random, meeting scheduling and graph colouring problems have shown that this approach solved more problems in less time at the phase transition when compared with some state of the art algorithms. Further evaluation of the DynAPP approach on iteration-bounded optimisation problems showed that DynAPP is competitive

Parallel local search for solving Constraint Problems on the Cell Broadband Engine (Preliminary Results)

We explore the use of the Cell Broadband Engine (Cell/BE for short) for combinatorial optimization applications: we present a parallel version of a constraint-based local search algorithm that has been implemented on a multiprocessor BladeCenter machine with twin Cell/BE processors (total of 16 SPUs per blade). This algorithm was chosen because it fits very well the Cell/BE architecture and requires neither shared memory nor communication between processors, while retaining a compact memory footprint. We study the performance on several large optimization benchmarks and show that this achieves mostly linear time speedups, even sometimes super-linear. This is possible because the parallel implementation might explore simultaneously different parts of the search space and therefore converge faster towards the best sub-space and thus towards a solution. Besides getting speedups, the resulting times exhibit a much smaller variance, which benefits applications where a timely reply is critical

A reusable iterative optimization software library to solve combinatorial problems with approximate reasoning

Real world combinatorial optimization problems such as scheduling are typically too complex to solve with exact methods. Additionally, the problems often have to observe vaguely specified constraints of different importance, the available data may be uncertain, and compromises between antagonistic criteria may be necessary. We present a combination of approximate reasoning based constraints and iterative optimization based heuristics that help to model and solve such problems in a framework of C++ software libraries called StarFLIP++. While initially developed to schedule continuous caster units in steel plants, we present in this paper results from reusing the library components in a shift scheduling system for the workforce of an industrial production plant.Comment: 33 pages, 9 figures; for a project overview see http://www.dbai.tuwien.ac.at/proj/StarFLIP

Certified Algorithms: Worst-Case Analysis and Beyond

In this paper, we introduce the notion of a certified algorithm. Certified algorithms provide worst-case and beyond-worst-case performance guarantees. First, a ?-certified algorithm is also a ?-approximation algorithm - it finds a ?-approximation no matter what the input is. Second, it exactly solves ?-perturbation-resilient instances (?-perturbation-resilient instances model real-life instances). Additionally, certified algorithms have a number of other desirable properties: they solve both maximization and minimization versions of a problem (e.g. Max Cut and Min Uncut), solve weakly perturbation-resilient instances, and solve optimization problems with hard constraints. In the paper, we define certified algorithms, describe their properties, present a framework for designing certified algorithms, provide examples of certified algorithms for Max Cut/Min Uncut, Minimum Multiway Cut, k-medians and k-means. We also present some negative results

Generalizing backdoors

Abstract. A powerful intuition in the design of search methods is that one wants to proactively select variables that simplify the problem instance as much as possible when these variables are assigned values. The notion of “Backdoor ” variables follows this intuition. In this work we generalize Backdoors in such a way to allow more general classes of sub-solvers, both complete and heuristic. In order to do so, Pseudo-Backdoors and Heuristic-Backdoors are formally introduced and then applied firstly to a simple Multiple Knapsack Problem and secondly to a complex combinatorial optimization problem in the area of stochastic inventory control. Our preliminary computational experience shows the effectiveness of these approaches that are able to produce very low run times and — in the case of Heuristic-Backdoors — high quality solutions by employing very simple heuristic rules such as greedy local search strategies.