In the minimum common string partition (MCSP) problem two related input strings are given. "Related" refers to the property that both strings consist of the same set of letters appearing the same number of t...
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In the minimum common string partition (MCSP) problem two related input strings are given. "Related" refers to the property that both strings consist of the same set of letters appearing the same number of times in each of the two strings. The MCSP seeks a minimum cardinality partitioning of one string into non-overlapping substrings that is also a valid partitioning for the second string. This problem has applications in bioinformatics e.g. in analyzing related DNA or protein sequences. For strings with lengths less than about 1000 letters, a previously published integer linear programming (ILP) formulation yields, when solved with a state-of-the-art solver such as CPLEX, satisfactory results. In this work, we propose a new, alternative ILP model that is compared to the former one. While a polyhedral study shows the linearprogramming relaxations of the two models to be equally strong, a comprehensive experimental comparison using real-world as well as artificially created benchmark instances indicates substantial computational advantages of the new formulation.
The Rummikub problem of finding the maximal number or value of the tiles that can be placed from your rack onto the table is very difficult, since the number of possible combinations are enormous. We show that this pr...
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The Rummikub problem of finding the maximal number or value of the tiles that can be placed from your rack onto the table is very difficult, since the number of possible combinations are enormous. We show that this problem can be modeled as an integer linear programming problem. In this way solutions can be found in 1 s. We extend the model such that unnecessary changes of the existing sets on the table are minimized.
The article focuses on PAUL, a protein structural alignment algorithm that uses integer linear programming and Lagrangian relaxation. It notes that the algorithm computes an alignment based on the inter-residue distan...
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The article focuses on PAUL, a protein structural alignment algorithm that uses integer linear programming and Lagrangian relaxation. It notes that the algorithm computes an alignment based on the inter-residue distances of the protein. The distances are used to formulate the problem as an integerlinear program which is subsequently solved utilizing Langrangian relaxation. According to the authors, PAUL is competitive to other state-of-the-art methods and a useful tool for high-quality pairwise structural alignment.
In the present paper a complete procedure for solving Multiple Objective integer linear programming Problems is presented. The algorithm can be regarded as a corrected form and an alternative to the method that was pr...
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In the present paper a complete procedure for solving Multiple Objective integer linear programming Problems is presented. The algorithm can be regarded as a corrected form and an alternative to the method that was proposed by Gupta and Malhotra. A numerical illustration is given to show that this latter can miss some efficient solutions. Whereas, the algorithm stated bellow determines all efficient solutions without missing any one.
Let f : V -> {0, 1, 2} be a function, G = (V, E) be a graph with a vertex set V and a set of edges E and let the weight of the vertex u. V be defined by f (u). A vertex u with property f (u) = 0 is considered to be...
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Let f : V -> {0, 1, 2} be a function, G = (V, E) be a graph with a vertex set V and a set of edges E and let the weight of the vertex u. V be defined by f (u). A vertex u with property f (u) = 0 is considered to be defended with respect to the function f if it is adjacent to a vertex with positive weight. Further, the function f is called a weak Roman dominating function (WRDF) if for every vertex u with property f (u) = 0 there exists at least one adjacent vertex v with positive weight such that the function f : V. {0, 1, 2} defined by f (u) = 1, f (v) = f (v) -1 and f (w) = f (w), w. V \ {u, v} has no undefended vertices. In this paper, an optimization problem of finding the WRDF f such that u. V f (u) is minimal, known as the weak Roman domination problem (WRDP), is considered. Therefore, a new integerlinear programing (ILP) formulation is proposed and compared with the one known from the literature. Comparison between the new and the existing formulation is made through computational experiments on a grid, planar, net and randomly generated graphs known from the literature and up to 600 vertices. Tests were run using standard CPLEX and Gurobi optimization solvers. The obtained results demonstrate that the proposed new ILP formulation clearly outperforms the existing formulation in the sense of solutions' quality and running times.
Vehicular networks are mobile networks designed for the domain of vehicles and pedestrians. These networks are an essential component of intelligent transportation systems and have the potential to ease traffic manage...
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Vehicular networks are mobile networks designed for the domain of vehicles and pedestrians. These networks are an essential component of intelligent transportation systems and have the potential to ease traffic management, lower accident rates, and offer other solutions to smart cities. One of the most challenging aspects in the design of a vehicular network is the distribution of its infrastructure units, which are called roadside units (RSUs). In this work, we tackle the gamma deployment problem that consists of deploying the minimum number of RSUs in a vehicular network in accordance with a quality of service metric called gamma deployment. This metric defines a vehicle as covered if it connects to some RSUs at least once in a given time interval during its whole trip. Then, the metric parameterizes the minimum percentage of covered vehicles necessary to make a deployment acceptable or feasible. In this paper, we prove that the decision version of the gamma deployment problem in grids is NP-complete. Moreover, we correct the multiflow integer linear programming formulation present in the literature and introduce a new formulation based on set covering that is at least as strong as the multiflow formulation. In experiments with a commercial solver, the set covering formulation widely outperforms the multiflow formulation with respect to running time and linearprogramming relaxation gap.
Time, quality, and cost are the most critical performance indicators in project management. It has always been considered a tough challenge for project managers to optimize them simultaneously. This paper aims at esta...
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Time, quality, and cost are the most critical performance indicators in project management. It has always been considered a tough challenge for project managers to optimize them simultaneously. This paper aims at establishing a simulation-based integer linear programming tool that helps project managers, at the preliminary stages, to assess the risks related to the feasibility and profitability of the projects within the framework of a stochastic discrete time-cost-quality tradeoff problem. The computational experiments on a wide range of benchmark instances from the literature were performed, and the results were compared with those of the deterministic version of the problem. The proposed approach is able to assess the impact of the stochastic behavior of the duration and the quality of the tasks on the cost, duration, and quality of the whole project. Moreover, the simplicity and the reduced time required for the computation of large size networks revealed to be very promising for giving a practical solution for real-life projects.
Job-shop scheduling is an important but difficult problem arising in low-volume high-variety manufacturing. It is usually solved at the beginning of each shift with strict computational time requirements. To obtain ne...
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Job-shop scheduling is an important but difficult problem arising in low-volume high-variety manufacturing. It is usually solved at the beginning of each shift with strict computational time requirements. To obtain near-optimal solutions with quantifiable quality within strict time limits, a direction is to formulate them in an integer linear programming (ILP) form so as to take advantages of widely available ILP methods such as Branch-and-Cut (B&C). Nevertheless, computational requirements for ILP methods on existing ILP formulations are high. In this letter, a novel ILP formulation for minimizing total weighted tardiness is presented. The new formulation has much fewer decision variables and constraints, and is proven to be tighter as compared to our previous formulation. For fast resolution of large problems, our recent decomposition-and-coordination method "Surrogate Absolute-Value Lagrangian Relaxation" (SAVLR) is enhanced by using a 3-segment piecewise linear penalty function, which more accurately approximates a quadratic penalty function as compared to an absolute-value function. Testing results demonstrate that our new formulation drastically reduces the computational requirements of B&C as compared to our previous formulation. For large problems where B&C has difficulties, near-optimal solutions are efficiently obtained by using the enhanced SAVLR under the new formulation.
The problem of dividing political territories in electoral process is a very important factor which contributes to the development of democracy in modern political systems. The most significant criteria for fairness o...
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The problem of dividing political territories in electoral process is a very important factor which contributes to the development of democracy in modern political systems. The most significant criteria for fairness of electoral process are demographic, geographic and political. Demographic criterion in the first place refers to the population equality, while the geographic one is mostly represented by compactness, contiguity and integrity. In this paper we propose a new integer linear programming formulation for the problem of political districting. The model is based on the graph representation of political territory, where territorial units are vertices and direct links between them are edges. The correctness of integer linear programming formulation is mathematically proven. In contrast to the most of the previous formulations, all three major criteria, population equality, compactness and contiguity, are completely taken into consideration. There are two models, one which deals with afore mentioned criteria where compactness is taken as an objective function, and the other one which takes into account interests of the decision maker, i.e. the political ruling body which organizes elections. Several numerical examples for the presented models are given which illustrate general aspects of the problem. The experimental results are obtained using CPLEX solver.
A Clique Partitioning Problem (CPP) finds an optimal partition of a given edge-weighted undirected graph, such that the sum of the weights is maximized. This general graph problem has a wide range of real-world applic...
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A Clique Partitioning Problem (CPP) finds an optimal partition of a given edge-weighted undirected graph, such that the sum of the weights is maximized. This general graph problem has a wide range of real-world applications, including correlation clustering, group technology, community detection, and coalition structure generation. Although a CPP is NP-hard, due to the recent advance of integer linear programming (ILP) solvers, we can solve reasonably large problem instances by formulating a CPP as an ILP instance. The first ILP formulation was introduced by Grotschel and Wakabayashi (Mathematical programming, 45(1-3), 59-96,1989). Recently, Miyauchi et al. (2018) proposed a more concise ILP formulation that can significantly reduce transitivity constraints as compared to previously introduced models. In this paper, we introduce a series of concise ILP formulations that can reduce even more transitivity constraints. We theoretically evaluate the amount of reduction based on a simple model in which edge signs (positive/negative) are chosen independently. We show that the reduction can be up to 50% (dependent of the ratio of negative edges) and experimentally evaluate the amount of reduction and the performance of our proposed formulation using a variety of graph data sets. Experimental evaluations show that the reduction can exceed 50% (where edge signs can be correlated), and our formulation outperforms the existing state-of-the-art formulations both in terms of memory usage and computational time for most problem instances.
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