This article presents integer programming formulations for finding interesting patterns in Conway's game of Life, with accompanying exercises and solutions.
This article presents integer programming formulations for finding interesting patterns in Conway's game of Life, with accompanying exercises and solutions.
Feature selection methods are used in machine learning and data analysis to select a subset of features that may be successfully used in the construction of a model for the data. These methods are applied under the as...
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Feature selection methods are used in machine learning and data analysis to select a subset of features that may be successfully used in the construction of a model for the data. These methods are applied under the assumption that often many of the available features are redundant for the purpose of the analysis. In this paper, we focus on a particular method for feature selection in supervised learning problems, based on a linear, programming model with integer variables. For the solution of the optimization problem associated with this approach, we propose a novel robust metaheuristics algorithm that relies on a Greedy Randomized Adaptive Search Procedure, extended with the adoption of short memory and a local search strategy. The performances of our heuristic algorithm are successfully compared with those of well-established feature selection methods, both on simulated and real data from biological applications. The obtained results suggest that our method is particularly suited for problems with a very large number of binary or categorical features. (C) 2015 Elsevier B.V. and Association of European Operational Research Societies (EURO) within the International Federation of Operational Research Societies (IFORS). All rights reserved.
This paper addresses the problem of designing an optimal micro-hydro power installation in rivers with generic profiles, when micro-hydro schemes are studied. This is geared towards the application of Micro Hydro Powe...
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This paper addresses the problem of designing an optimal micro-hydro power installation in rivers with generic profiles, when micro-hydro schemes are studied. This is geared towards the application of Micro Hydro Power Plants to supply marginal isolated areas using small Pelton wheels, where both technology and resources are limited. For this purpose, a model of a Pelton micro-hydro plant is first developed. Subsequently, a discretization of the river profile is made, on the basis of which a set of integer variables are proposed, being the model transformed then into an integer optimization problem. Finally, the effectiveness of the proposed method is showed through a specific design problem. The application of the developed method is especially interesting when designing micro-hydro plants to provide electricity to isolated populations, where both technology and resources are limited. (C) 2018 Elsevier Ltd. All rights reserved.
In this paper we present an integer programming method for solving the Classroom Assignment Problem in University Course Timetabling. We introduce a novel formulation of the problem which generalises existing models a...
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In this paper we present an integer programming method for solving the Classroom Assignment Problem in University Course Timetabling. We introduce a novel formulation of the problem which generalises existing models and maintains tractability even for large instances. The model is validated through computational results based on our experiences at the University of Auckland, and on instances from the 2007 International Timetabling Competition. We also expand upon existing results into the computational difficulty of room assignment problems. (C) 2014 Elsevier Ltd. All rights reserved.
In 2003, Gusfield introduced the Haplotype Inference by Pure Parsimony (HIPP) problem and presented an integer program (IP) that quickly solved many simulated instances of the problem [1]. Although it solved well on s...
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In 2003, Gusfield introduced the Haplotype Inference by Pure Parsimony (HIPP) problem and presented an integer program (IP) that quickly solved many simulated instances of the problem [1]. Although it solved well on small instances, Gusfield's IP can be of exponential size in the worst case. Several authors [2], [3] have presented polynomial-sized IPs for the problem. In this paper, we further the work on IP approaches to HIPP. We extend the existing polynomial-sized IPs by introducing several classes of valid cuts for the IP. We also present a new polynomial-sized IP formulation that is a hybrid between two existing IP formulations and inherits many of the strengths of both. Many problems that are too complex for the exponential-sized formulations can still be solved in our new formulation in a reasonable amount of time. We provide a detailed empirical comparison of these IP formulations on both simulated and real genotype sequences. Our formulation can also be extended in a variety of ways to allow errors in the input or model the structure of the population under consideration.
We investigate the maximum induced matching problem (MIM), which is the problem of finding an induced matching having the largest cardinality on an undirected graph. The problem is known to be NP-hard for general grap...
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We investigate the maximum induced matching problem (MIM), which is the problem of finding an induced matching having the largest cardinality on an undirected graph. The problem is known to be NP-hard for general graphs. We first propose a vertex-based integer programming formulation for MIM, which is more compact compared to an edge-based formulation found in the literature. We also introduce the maximum weight induced matching problem (MWIM), which generalizes MIM so that vertices and edges have weights. We adapt the edge-based formulation to MWIM, and propose a quadratic programming formulation of MWIM based on our vertex-based formulation. We then linearize our quadratic programming formulation, and devise a Benders decomposition algorithm that exploits a special structure of the linearized formulation. We also propose valid inequalities and formulation tightening procedures to improve the efficiency of our approach. Our computational tests on a large suite of randomly generated graphs show that our vertex-based formulation and decomposition approach significantly improve the solvability of MIM and MWIM, especially on dense graphs.
We present a nevi method to determine whether a Convex region contains any integer points, The method is designed for array subscript analysis in parallel programs. The general problem is whether a system of linear eq...
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We present a nevi method to determine whether a Convex region contains any integer points, The method is designed for array subscript analysis in parallel programs. The general problem is whether a system of linear equalities and inequalities has an integer solution,A set of known techniques is used to transform the problem to that of finding whether a convex region contains any integer points. The main result of the paper is a set of new search procedures that identify an integer solution in a convex region, or prove that no integer solutions exist. They are based on the geometrical properties of convex regions that are not empty, but also do not contain any integer points. The results contribute to exact and efficient dependence and synchronization analysis of parallel programs.
We present an efficient algorithm to find an optimal integer solution of a given system of 2-variable equalities and I-variable inequalities with respect to a given linear objective function. Our algorithm has worst-c...
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We present an efficient algorithm to find an optimal integer solution of a given system of 2-variable equalities and I-variable inequalities with respect to a given linear objective function. Our algorithm has worst-case running time in O(N-2) where N is the number of bits in the input. (C) 2009 Elsevier B.V. All rights reserved.
Mathematical programming discriminant analysis models must be normalised to prevent the generation of discriminant functions in which the variable coefficients and the constant term are zero. This normalisation requir...
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Mathematical programming discriminant analysis models must be normalised to prevent the generation of discriminant functions in which the variable coefficients and the constant term are zero. This normalisation requirement can cause difficulties, and unlike statistical discriminant analysis, variables cannot be selected in a computationally efficient way with mathematical programming discriminant analysis models. Two new integer programming normalisations are proposed in this paper. In the first, binary variables are used to represent the constant term, but with this normalisation functions with a zero constant term cannot be generated and the variable coefficients are not invariant under origin shifts. These limitations are overcome by using integer programming methods to constrain the sum of the absolute values of the variable coefficients to a constant. These new normalisations are extended to allow variable selection with mathematical programming discriminant analysis models. The use of these new applications of integer programming is illustrated using published data.
We propose an algorithm based on Barvinok's counting algorithm for P --> max{ c'x |Ax less than or equal to b;x is an element of Z(n)}. It runs in time polynomial in the input size of P when n is fixed, and...
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We propose an algorithm based on Barvinok's counting algorithm for P --> max{ c'x |Ax less than or equal to b;x is an element of Z(n)}. It runs in time polynomial in the input size of P when n is fixed, and under a condition on c, provides the optimal value of P. We also relate Barvinok's counting formula and Gomory relaxations. (C) 2003 Elsevier B.V. All rights reserved.
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