This paper uses a multicriteria mathematical programming model to estimate the farmer's utility function and simulate different scenarios and policies as well as to make alternative production plans. Application of this model was carried out in the irrigated region of the Xanthi Prefecture in Greece, as well as to three different farm clusters. The three farm clusters -small, medium and large sizes-were the result of a cluster analysis into a sample of farms of the region. In all these four cases, we considered three criteria for the estimation of the utility function; the maximization of total gross margin, the minimization of its variance and the minimization of labor. The estimated utility functions were used as objective functions of Linear or Quadratic (when the variance is considered) Programming models in order to find the optimum production plan of the total region and each farm size separately. These models were used to simulate the impacts on the production plan, income, employment and the environment due to a policy, which increases the price of irrigation water.

Abstract. Max Restricted Path Consistency (maxRPC) is a local consistency for binary constraints that can achieve considerably stronger pruning than arc consistency. However, existing maxRPC algorithms suffer from overheads and redundancies as they can repeatedly perform many constraint checks without triggering any value deletions. In this paper we propose techniques that can boost the performance of maxRPC algorithms. These include the combined use of two data structures to avoid many redundant constraint checks, and heuristics for the efficient ordering and execution of certain operations. Based on these, we propose two closely related maxRPC algorithms. The first one has optimal O(end 3 ) time complexity, displays good performance when used stand-alone, but is expensive to apply during search. The second one has O(en 2 d 4 ) time complexity, but a restricted version with O(end 4 ) complexity can be very efficient when used during search. Both algorithms have O(ed) space complexity when used stand-alone. However, the first algorithm has O(end) space complexity when used during search, while the second retains the O(ed) complexity. Experimental results demonstrate that the resulting methods constantly outperform previous algorithms for maxRPC, often by large margins, and constitute a more than viable alternative to arc consistency.

Max Restricted Path Consistency (maxRPC) is a local consistency for binary constraints that enforces a higher order of consistency than arc consistency. Despite the strong pruning that can be achieved, maxRPC is rarely used because existing maxRPC algorithms suffer from overheads and redundancies as they can repeatedly perform many constraint checks without triggering any value deletions. In this paper we propose and evaluate techniques that can boost the performance of maxRPC algorithms by eliminating many of these overheads and redundancies. These include the combined use of two data structures to avoid many redundant constraint checks, and the exploitation of residues to quickly verify the existence of supports. Based on these, we propose a number of closely related maxRPC algorithms. The first one, maxRPC3, has optimal O(end 3 ) time complexity, displays good performance when used stand-alone, but is expensive to apply during search.

Constraint programming is used for a variety of real-world optimisation problems, such as planning, scheduling and resource allocation problems. At the same time, one continuously gathers vast amounts of data about these problems. Current constraint programming software does not exploit such data to update schedules, resources and plans. We propose a new framework, that we call the Inductive Constraint Programming loop. In this approach data is gathered and analyzed systematically, in order to dynamically revise and adapt constraints and optimization criteria. Inductive Constraint Programming aims at bridging the gap between the areas of data mining and machine learning on the one hand, and constraint programming on the other hand.

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