219 research outputs found

    A Cooperative Local Search Method for Solving the Traveling Tournament Problem

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    Constrained optimization is the process of optimizing a certain objective function subject to a set of constraints. The goal is not necessarily to find the global optimum. We try to explore the search space more efficiently in order to find a good approximate solution. The obtained solution should verify the hard constraints that are required to be satisfied. In this paper, we propose a cooperative search method that handles optimality and feasibility separately. We take the traveling tournament problem (TTP) as a case study to show the applicability of the proposed idea. TTP is the problem of scheduling a double round-robin tournament that satisfies a set of related constraints and minimizes the total distance traveled by the teams. The proposed method for TTP consists of two main steps. In the first step, we ignore the optimization criterion. We reduce the search only to feasible solutions satisfying the problem's constraints. For this purpose, we use constraints programming model to ensure the feasibility of solutions. In the second step, we propose a stochastic local search method to handle the optimization criterion and find a good approximate solution that verifies the hard constraints. The overall method is evaluated on benchmarks and compared with other well-known techniques for TTP. The computational results are promising and show the effectiveness of the proposed idea for TTP

    Vehicle Routing Problem with Time Windows: An Evolutionary Algorithmic Approach

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    The Vehicle Routing Problem with Time Windows (VRPTW) is an important problem in logistics, which is an extension of well known Vehicle Routing Problem (VRP), with a central depot. The Objective is to design an optimal set of routes for serving a number of customers without violating the customer’s time window constraints and vehicle capacity constraint. It has received considerable attention in recent years. This paper reviews the research on Evolutionary Algorithms for VRPTW. The main types of evolutionary algorithms for the VRPTW are Genetic Algorithms and Evolutionary Strategies which may also be described as Evolutionary metaheuristics to distinguish them from other metaheuristics. Along with these evolutionary metaheuristics, this paper reviews heuristic search methods that hybridize ideas of evolutionary algorithms with some other search technique, such as tabu search, guided local search, route construction heuristics, ejection chain approach, adaptive large neighborhood search, variable neighborhood search and hierarchal tournament selection. In addition to the basic features of each method, experimental results for the 56 benchmark problem with 100 customers of Solomon (1987) and Gehring and Homberger (1999) are presented and analyzed

    Solving Challenging Real-World Scheduling Problems

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    This work contains a series of studies on the optimization of three real-world scheduling problems, school timetabling, sports scheduling and staff scheduling. These challenging problems are solved to customer satisfaction using the proposed PEAST algorithm. The customer satisfaction refers to the fact that implementations of the algorithm are in industry use. The PEAST algorithm is a product of long-term research and development. The first version of it was introduced in 1998. This thesis is a result of a five-year development of the algorithm. One of the most valuable characteristics of the algorithm has proven to be the ability to solve a wide range of scheduling problems. It is likely that it can be tuned to tackle also a range of other combinatorial problems. The algorithm uses features from numerous different metaheuristics which is the main reason for its success. In addition, the implementation of the algorithm is fast enough for real-world use.Siirretty Doriast

    An Improved Approximation Algorithm for the Traveling Tournament Problem with Maximum Trip Length Two

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    The Traveling Tournament Problem is a complex combinatorial optimization problem in tournament timetabling, which asks a schedule of home/away games meeting specific feasibility requirements, while also minimizing the total distance traveled by all the n teams (n is even). Despite intensive algorithmic research on this problem over the last decade, most instances with more than 10 teams in well-known benchmarks are still unsolved. In this paper, we give a practical approximation algorithm for the problem with constraints such that at most two consecutive home games or away games are allowed. Our algorithm, that generates feasible schedules based on minimum perfect matchings in the underlying graph, not only improves the previous approximation ratio from (1+16/n) to about (1+4/n) but also has very good experimental performances. By applying our schedules on known benchmark sets, we can beat all previously-known results of instances with n being a multiple of 4 by 3% to 10%

    Time Relaxed Round Robin Tournament and the NBA Scheduling Problem

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    This dissertation study was inspired by the National Basketball Association regular reason scheduling problem. NBA uses the time-relaxed round robin tournament format, which has drawn less research attention compared to the other scheduling formats. Besides NBA, the National Hockey League and many amateur leagues use the time-relaxed round robin tournament as well. This dissertation study is the first ever to examine the properties of general time-relaxed round robin tournaments. Single round, double round and multiple round time-relaxed round robin tournaments are defined. The integer programming and constraint programming models for those tournaments scheduling are developed and presented. Because of the complexity of this problem, several decomposition methods are presented as well. Traveling distance is an important factor in the tournament scheduling. Traveling tournament problem defined in the time constrained conditions has been well studied. This dissertation defines the novel problem of time-relaxed traveling tournament problem. Three algorithms has been developed and compared to address this problem. In addition, this dissertation study presents all major constraints for the NBA regular season scheduling. These constraints are grouped into three categories: structural, external and fairness. Both integer programming and constraint programming are used to model these constraints and the computation studies are presente

    Metaheuristic Optimization Frameworks: a Survey and Benchmarking

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    This paper performs an unprecedented comparative study of Metaheuristic optimization frameworks. As criteria for comparison a set of 271 features grouped in 30 characteristics and 6 areas has been selected. These features include the different metaheuristic techniques covered, mechanisms for solution encoding, constraint handling, neighborhood specification, hybridization, parallel and distributed computation, software engineering best practices, documentation and user interface, etc. A metric has been defined for each feature so that the scores obtained by a framework are averaged within each group of features, leading to a final average score for each framework. Out of 33 frameworks ten have been selected from the literature using well-defined filtering criteria, and the results of the comparison are analyzed with the aim of identifying improvement areas and gaps in specific frameworks and the whole set. Generally speaking, a significant lack of support has been found for hyper-heuristics, and parallel and distributed computing capabilities. It is also desirable to have a wider implementation of some Software Engineering best practices. Finally, a wider support for some metaheuristics and hybridization capabilities is needed

    Traveling Salesman Problem

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    The idea behind TSP was conceived by Austrian mathematician Karl Menger in mid 1930s who invited the research community to consider a problem from the everyday life from a mathematical point of view. A traveling salesman has to visit exactly once each one of a list of m cities and then return to the home city. He knows the cost of traveling from any city i to any other city j. Thus, which is the tour of least possible cost the salesman can take? In this book the problem of finding algorithmic technique leading to good/optimal solutions for TSP (or for some other strictly related problems) is considered. TSP is a very attractive problem for the research community because it arises as a natural subproblem in many applications concerning the every day life. Indeed, each application, in which an optimal ordering of a number of items has to be chosen in a way that the total cost of a solution is determined by adding up the costs arising from two successively items, can be modelled as a TSP instance. Thus, studying TSP can never be considered as an abstract research with no real importance

    An Improved Scheduling Algorithm for Traveling Tournament Problem with Maximum Trip Length Two

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    The Traveling Tournament Problem(TTP) is a combinatorial optimization problem where we have to give a scheduling algorithm which minimizes the total distance traveled by all the participating teams of a double round-robin tournament maintaining given constraints. Most of the instances of this problem with more than ten teams are still unsolved. By definition of the problem the number of teams participating has to be even. There are different variants of this problem depending on the constraints. In this problem, we consider the case where number of teams is a multiple of four and a team can not play more than two consecutive home or away matches. Our scheduling algorithm gives better result than the existing best result for number of teams less or equal to 32
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