Symmetry is an important feature of many constraint programs. We show that any symmetry acting on a set of symmetry breaking constraints can be used to break symmetry. Different symmetries pick out different solutions in each symmetry class. We use these observations in two methods for eliminating symmetry from a problem. These methods are designed to have many of the advantages of symmetry breaking methods that post static symmetry breaking constraint without some of the disadvantages. In particular, the two methods prune the search space using fast and efficient propagation of posted constraints, whilst reducing the conflict between symmetry breaking and branching heuristics. Experimental results show that the two methods perform well on some standard benchmarks.

A problem that often arises in using abstraction is the generation of abstract states, called spurious states, that are—in the abstract space—reachable from some abstract image of a state s, but which have no corresponding state in the original space reachable from s. Spurious states can have a negative effect on pattern database sizes and heuristic quality. We formally define a property—the downward path preserving property (DPP)—that guarantees an abstraction has no spurious states. Analyzing the computational complexity of (i) testing the DPP property for a given state space and abstraction and of (ii) determining whether this property is achievable at all for a given state space, results in strong hardness theorems. On the positive side, we identify formal conditions under which finding DPP abstractions is tractable.

We study novel approaches for solving of hard combinatorial problems by translation to Boolean Satisfiability (SAT). Our focus is on combinatorial problems that can be represented as a permutation of n objects, subject to additional constraints. In the case of the Hamiltonian Cycle Problem (HCP), these constraints are that two adjacent nodes in a permutation should also be neighbors in the original graph for which we search for a Hamiltonian cycle. We use the absolute SAT encoding of permutations, where for each of the n objects and each of its pos- sible positions in a permutation, a predicate is defined to indicate whether the object is placed in that position. For implementation of this predicate, we compare the direct and logarithmic encodings that have been used previously, against 16 hierarchical parameterizable encodings of which we explore 416 instantiations. We propose the use of enumerative adjacency constraints—that enumerate the possible neighbors of a node in a permutation — instead of, or in addition to the exclusivity adjacency constraints — that exclude impossible neighbors, and that have been applied previously. We study 11 heuristics for efficiently choosing the first node in the Hamiltonian cycle, as well as 8 heuristics for static CNF variable ordering. We achieve at least 4 orders of magnitude average speedup on HCP benchmarks from the phase transition region, relative to the previously used encodings for solving of HCPs via SAT, such that the speedup is increasing with the size of the graphs.

Pattern Databases (PDBs) are the most common form of memory-based heuristics, and they have been widely used in a variety of permutation puzzles and other domains. We explore the true-distance heuristics (TDHs) (also appeared in  (Sturtevant et al. 2009)) which are a different form of memory-based heuristics, designed to work in problem states where there isn't a fixed goal state. Unlike PDBs, which build a heuristic based on distances in an abstract state space, TDHs store distances which are computed in the actual state space. We look in detail at how TDHs work, providing both theoretical and experimental motivation for their use.

The methods focus on the online behaviour of the backtracking solver, as well as the structure of the problem. Modern SAT solvers present several challenges to estimate search cost including coping with nonchronological backtracking, learning and restarts. Our first method adapt an existing algorithm for estimating the size of a search tree to deal with these challenges. We then suggest a second method that uses a linear model trained on data gathered online at the start of search. We compare the effectiveness of these two methods using random and structured problems. We also demonstrate that predictions made in early restarts can be used to improve later predictions. We conclude by showing that the cost of solving a set of problems can be reduced by selecting a solver from a portfolio based on such cost estimations.

The article presents a study of rather simple local search heuristics for the single machine total weighted tardiness problem (SMTWTP), namely hillclimbing and Variable Neighborhood Search. In particular, we revisit these approaches for the SMTWTP as there appears to be a lack of appropriate/challenging benchmark instances in this case. The obtained results are impressive indeed. Only few instances remain unsolved, and even those are approximated within 1% of the optimal/best known solutions. Our experiments support the claim that metaheuristics for the SMTWTP are very likely to lead to good results, and that, before refining search strategies, more work must be done with regard to the proposition of benchmark data. Some recommendations for the construction of such data sets are derived from our investigations.

The article describes the proposition and application of a local search metaheuristic for multi-objective optimization problems. It is based on two main principles of heuristic search, intensification through variable neighborhoods, and diversification through perturbations and successive iterations in favorable regions of the search space. The concept is successfully tested on permutation flow shop scheduling problems under multiple objectives and compared to other local search approaches. While the obtained results are encouraging in terms of their quality, another positive attribute of the approach is its simplicity as it does require the setting of only very few parameters.

We describe the implementation and deployment of a software decision support tool for themaintenance planning of gas turbines. The tool is used to plan the maintenance for turbines manufactured and maintained by Siemens Industrial Turbomachinery AB (SIT AB) with the goal to reduce the direct maintenance costs and the often very costly production losses during maintenance downtime. The optimization problem is formally defined, and we argue that feasibility in it is NP-complete. We outline a heuristic algorithm that can quickly solve the problem for practical purposes, and validate the approach on a real-world scenario based on an oil production facility. We also compare the performance of our algorithm with results from using mixed integer linear programming, and discuss the deployment of the application. The experimental results indicate that downtime reductions up to 65% can be achieved, compared to traditional preventive maintenance. In addition, using our tool is expected to improve availability with up to 1% and reduce the number of planned maintenance days with 12%. Compared to a mixed integer programming approach, our algorithm not optimal, but is orders of magnitude faster and produces results which are useful in practice. Our test results and SIT AB's estimates based on operational use both indicate that significant savings can be achieved by using our software tool, compared to maintenance plans with fixed intervals.

My thesis will demonstrate that distributed constraint optimization (DCOP) search algorithms can be scaled up (i.e.

A* is the optimal algorithm for finding optimal solutions to heuristic search problems. Given the same amount of information, no search can expand fewer nodes. Many applications of heuristic search only require that we find solutions of reasonable quality or in a reasonable amount of time, where reasonable is defined by the needs of a user. My doctoral work will address these problems by developing new bounded suboptimal algorithms which perform better than the previous approaches. I will show that anytime searches can incorporate these new algorithms to improve their own performance. I will demonstrate that anytime search is not the correct approach when a deadline is known at the beginning of the search, and introduce deadline-aware search algorithms that address this setting directly.