Alpha-Beta pruning is one of the most powerful and fundamental MiniMax search improvements. It was designed for sequential two-player zero-sum perfect information games. In this paper we introduce an Alpha-Beta-like sound pruning method for the more general class of “stacked matrix games” that allow for simultaneous moves by both players. This is accomplished by maintaining upper and lower bounds for achievable payoffs in states with simultaneous actions and dominated action pruning based on the feasibility of certain linear programs. Empirical data shows considerable savings in terms of expanded nodes compared to naive depth-first move computation without pruning.

We address the problem of making single-point decisions in large partially observable games, where players interleave observation, deliberation, and action.  We present information set generation as a key operation needed to reason about games in this way.  We show how this operation can be used to implement an existing decision-making algorithm.  We develop a constraint satisfaction algorithm for performing information set generation and show that it scales better than the existing depth-first search approach on multiple non-trivial games.

A key challenge in developing efficient local search solvers is to effectively minimise search stagnation (i.e. avoiding traps or local minima). A majority of the state-of-the-art local search solvers perform random and/or Novelty-based walks to overcome search stagnation. Although such strategies are effective in diversifying a search from its current local minimum, they do not actively prevent the search from visiting previously encountered local minima. In this paper, we propose a new preventative strategy to effectively minimise search stagnation using pseudo-conflict learning. We define a pseudo-conflict as a derived path from the search trajectory that leads to a local minimum. We then introduce a new variable selection scheme that penalises variables causing those pseudo-conflicts. Our experimental results show that the new preventative approach significantly improves the performance of local search solvers on a wide range of structured and random benchmarks.

Korf, Reid and Edelkamp initiated a line of research for developing methods (KRE and later CDP) that predict the number of nodes expanded by IDA* for a given start state and cost bound. Independent of that, Chen developed a method (SS) that can also be used to predict the number of nodes expanded by IDA*. In this paper we advance both of these prediction methods. First, we develop a variant of CDP that can be orders of magnitude faster than CDP while producing exactly the same predictions. Second, we show how ideas developed in the KRE line of research can be used to substantially improve the predictions produced by SS. Third, we make an empirical comparison between our new enhanced versions of CDP and SS. Our experimental results point out that CDP is suitable for applications that require less accurate but very fast predictions, while SS is suitable for applications that require more accurate predictions but allow more computation time.

In recent years, significant progress in the area of search, constraint satisfaction, and automated reasoning has been driven in part by the study of challenge problems from combinatorics and finite algebra. This work has led to the discovery of interesting discrete structures with intricate mathematical properties. While some of those results have resolved open questions and conjectures, a shortcoming is that they generally do not provide further mathematical insights, from which one could derive more general observations. We propose an approach that integrates specialized combinatorial search, using so-called streamlining, with a human computation component. We use this approach to discover efficient constructive procedures for generating certain classes of combinatorial objects of any size. More specifically, using our framework, we discovered two complementary efficient constructions for generating so-called Spatially Balanced Latin squares (SBLS) of any order N, such that 2N+1 is prime. Previously constructions for SBLSs were not known. Our approach also enabled us to derive a new lower bound for so-called weak Schur numbers, improving on a series of earlier results for Schur numbers.

Instead, we cluster Search is an integral part of solution approaches for NPhard training instances according to their features and determine combinatorial optimization and decision problems. Once the an assignment of branching heuristics to clusters that results ability to reason deterministically is exhausted, state-of-theart in the best performance when the branching heuristic is dynamically solvers try out different alternatives which may lead to chosen based on the current subproblem's nearest an improved (in case of optimization) or feasible (in case cluster. We test our approach on the MIP-solver Cplex that of satisfaction) solution. This consideration of alternatives we use to tackle set partitioning problems. Our experiments may take place highly opportunistically as in local search approaches, show that this approach can effectively boost search performance or systematically as in backtracking-based methods.

Local Search is one of the fundamental approaches to combinatorial optimization and it is used throughout AI. Several local search algorithms are based on searching the k -exchange neighborhood. This is the set of solutions that can be obtained from the current solution by exchanging at most k elements. As a rule of thumb, the larger k is, the better are the chances of finding an improved solution. However, for inputs of size n, a naive brute-force search of the k-exchange neighborhood requires n (O( k )) time, which is not practical even for very small values of k. Fellows et al. (IJCAI 2009) studied whether this brute-force search is avoidable and gave positive and negative answers for several combinatorial problems. They used the notion of local search in a strict sense. That is, an improved solution needs to be found in the k-exchange neighborhood even if a global optimum can be found efficiently. In this paper we consider a natural relaxation of local search, called permissive local search (Marx and Schlotter, IWPEC 2009) and investigate whether it enhances the domain of tractable inputs. We exemplify this approach on a fundamental combinatorial problem, Vertex Cover. More precisely, we show that for a class of inputs, finding an optimum is hard, strict local search is hard, but permissive local search is tractable. We carry out this investigation in the framework of parameterized complexity.

The increasing availability of “utility computing” resources such as clouds, grids, and massively parallel shared clusters can provide practically unlimited processing and memory capacity on demand, at some cost per unit of resource usage. This requires a new perspective in the design and evaluation of parallel search algorithms. Previous work in parallel search implicitly assumed ownership of a cluster with a static amount of CPU cores and RAM, and emphasized wallclock runtime. With utility computing resources, trade-offs between performance and monetary costs must be considered. This paper considers dynamically increasing the usage of utility computing resources until a problem is solved. Efficient resource allocation policies are analyzed in comparison with an optimal allocation strategy. We evaluate our iterative allocation strategy by applying it to the HDA* parallel search algorithm. The experimental results validate our theoretical predictions. They show that, in practice, the costs incurred by iterative allocation are reasonably close to an optimal (but a priori unknown) policy, and are significantly better than the worst-case analytical bounds.

A* is often described as being `optimal', in that it expands the minimum number of unique nodes. But, A* may generate many extra nodes which are never expanded. This is a performance loss, especially when the branching factor is large. Partial Expansion A* addresses this problem when expanding a node, n, by generating all the children of n but only storing children with the same f-cost as n. n is re-inserted into the OPEN list, but with the f-cost of the next best child. This paper introduces an enhanced version of PEA* (EPEA*). Given a priori domain knowledge, EPEA* generates only the children with the same f-cost as the parent. EPEA* is generalized to its iterative-deepening variant, EPE-IDA*. For some domains, these algorithms yield substantial performance improvements. State-of-the-art results were obtained for the pancake puzzle and for some multi-agent pathfinding instances. Drawbacks of EPEA* are also discussed.

In this paper, we propose two new strategies to design efficient local search algorithms for the minimum vertex cover (MVC) problem. There are two main drawbacks in state-of-the-art MVC local search algorithms: First, they select a pair of vertices to be exchanged simultaneously, which is time consuming; Second, although they use edge weighting techniques, they do not have a strategy to decrease the weights. To address these drawbacks, we propose two new strategies: two stage exchange and edge weighting with forgetting. The two stage exchange strategy selects two vertices to be exchanged separately and performs the exchange in two stages. The strategy of edge weighting with forgetting not only increases weights of uncovered edges, but also decreases some weights for each edge periodically. We utilize these two strategies to design a new algorithm dubbed NuMVC. The experimental results show that NuMVC significantly outperforms existing state-of-the-art heuristic algorithms on most of the hard DIMACS instances and all instances in the hard random BHOSLIB benchmark.