Hybrid Constraint Tightening for Solving Hybrid Scheduling Problems

AAAI Conferences

Hybrid Scheduling Problems (HSPs) contain both temporal and finite-domain variables, as well as constraints between them. A hybrid constraint over temporal and finite-domain variables often models situations where different assignments to a subset of finite-domain variables result in different bounds on temporal constraints. The insight we examine in this paper is that some temporal constraint propagation is possible even before finite-domain variables are assigned, by giving the temporal constraint the tightest bound consistent with all (remaining) feasible finite-domain variable values. We describe a hybrid constraint-tightening algorithm that can proactively prune the search space of HSPs and is run as a preprocessing step independently of the search algorithm used. We examine the efficiency of this algorithm analytically, and give preliminary results showing that it reduces the expected runtime of search by a significant margin in the kinds of HSPs we are studying.


Solving Weighted Constraint Satisfaction Problems with Memetic/Exact Hybrid Algorithms

AAAI Conferences

A weighted constraint satisfaction problem (WCSP) is a constraint satisfaction problem in which preferences among solutions can be expressed. Bucket elimination is a complete technique commonly used to solve this kind of constraint satisfaction problem. When the memory required to apply bucket elimination is too high, a heuristic method based on it (denominated mini-buckets) can be used to calculate bounds for the optimal solution. Nevertheless, the curse of dimensionality makes these techniques impractical on large scale problems. In response to this situation, we present a memetic algorithm for WCSPs in which bucket elimination is used as a mechanism for recombining solutions, providing the best possible child from the parental set. Subsequently, a multilevel model in which this exact/metaheuristic hybrid is further hybridized with branch-and-bound techniques and mini-buckets is studied. As a case study, we have applied these algorithms totheresolution of the maximum density still life problem, a hard constraint optimization problem based on Conway's game of life. The resulting algorithm consistently finds optimal patterns for up to date solved instances in less time than current approaches. Moreover, it is shown that this proposal provides new best known solutions for very large instances.


Non-Systematic Backtracking for Mixed Integer Programs

AAAI Conferences

A variety of hybrids of Constraint Programming, Artificial Intelligence and Operations Research techniques have given impressive results. Three recent approaches are (i) the use of relaxations in constraint systems, (ii) non-systematic backtracking to boost the scalability of constraint solvers, and (iii) non-systematic backtracking to boost the scalability of branch-and-bound search. This paper describes a hybrid of all three approaches that combines non-systematic backtracking, SATbased inference and linear relaxation. It is intended for large MIPs that are hard for reasons of both optimisation and feasibility. Such problems are of practical as well as theoretical interest and we expect the hybrid to find many applications. It is currently under development and results will be reported at the workshop.


Rare skull stored in a museum belonged to the hybrid offspring of a beluga whale and a narwhal

Daily Mail - Science & tech

DNA analysis has confirmed the existence of a hybrid beluga whale and a narwhal. The skull of the animal was first found in 1990 by a hunter in Greenland and resided in a Danish museum for almost two decades. It is believed that, in life, the hybrid may have been grey in colour and possessed a tail like a narwhal but forward flippers like those of a beluga whale. Researchers found that the male hybrid got 54 per cent of its genes from its beluga whale father and 46 per cent from a narwhal mother but had a unique diet. Scientists have confirmed the existence of a hybrid beluga whale and a narwhal.


Finding Still Lifes with Memetic/Exact Hybrid Algorithms

arXiv.org Artificial Intelligence

The maximum density still life problem (MDSLP) is a hard constraint optimization problem based on Conway's game of life. It is a prime example of weighted constrained optimization problem that has been recently tackled in the constraint-programming community. Bucket elimination (BE) is a complete technique commonly used to solve this kind of constraint satisfaction problem. When the memory required to apply BE is too high, a heuristic method based on it (denominated mini-buckets) can be used to calculate bounds for the optimal solution. Nevertheless, the curse of dimensionality makes these techniques unpractical for large size problems. In response to this situation, we present a memetic algorithm for the MDSLP in which BE is used as a mechanism for recombining solutions, providing the best possible child from the parental set. Subsequently, a multi-level model in which this exact/metaheuristic hybrid is further hybridized with branch-and-bound techniques and mini-buckets is studied. Extensive experimental results analyze the performance of these models and multi-parent recombination. The resulting algorithm consistently finds optimal patterns for up to date solved instances in less time than current approaches. Moreover, it is shown that this proposal provides new best known solutions for very large instances.