708 research outputs found

    Algorithm Engineering in Robust Optimization

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    Robust optimization is a young and emerging field of research having received a considerable increase of interest over the last decade. In this paper, we argue that the the algorithm engineering methodology fits very well to the field of robust optimization and yields a rewarding new perspective on both the current state of research and open research directions. To this end we go through the algorithm engineering cycle of design and analysis of concepts, development and implementation of algorithms, and theoretical and experimental evaluation. We show that many ideas of algorithm engineering have already been applied in publications on robust optimization. Most work on robust optimization is devoted to analysis of the concepts and the development of algorithms, some papers deal with the evaluation of a particular concept in case studies, and work on comparison of concepts just starts. What is still a drawback in many papers on robustness is the missing link to include the results of the experiments again in the design

    Generating bounded solutions for multi-demand multidimensional knapsack problems: a guide for operations research practitioners

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    A generalization of the 0-1 knapsack problem that is hard-to-solve both theoretically (NP-hard) and in practice is the multi-demand multidimensional knapsack problem (MDMKP). Solving an MDMKP can be difficult because of its conflicting knapsack and demand constraints. Approximate solution approaches provide no guarantees on solution quality. Recently, with the use of classification trees, MDMKPs were partitioned into three general categories based on their expected performance using the integer programming option of the CPLEX® software package on a standard PC: Category A—relatively easy to solve, Category B—somewhat difficult to solve, and Category C—difficult to solve. However, no solution methods were associated with these categories. The primary contribution of this article is that it demonstrates, customized to each category, how general-purpose integer programming software (CPLEX in this case) can be iteratively used to efficiently generate bounded solutions for MDMKPs. Specifically, the simple sequential increasing tolerance (SSIT) methodology will iteratively use CPLEX with loosening tolerances to efficiently generate these bounded solutions. The real strength of this approach is that the SSIT methodology is customized based on the particular category (A, B, or C) of the MDMKP instance being solved. This methodology is easy for practitioners to use because it requires no time-consuming effort of coding problem specific-algorithms. Statistical analyses will compare the SSIT results to a single-pass execution of CPLEX in terms of execution time and solution quality

    A hybrid genetic algorithm for solving a layout problem in the fashion industry.

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    As of this writing, many success stories exist yet of powerful genetic algorithms (GAs) in the field of constraint optimisation. In this paper, a hybrid, intelligent genetic algorithm will be developed for solving a cutting layout problem in the Belgian fashion industry. In an initial section, an existing LP formulation of the cutting problem is briefly summarised and is used in further paragraphs as the core design of our GA. Through an initial attempt of rendering the algorithm as universal as possible, it was conceived a threefold genetic enhancement had to be carried out that reduces the size of the active solution space. The GA is therefore rebuilt using intelligent genetic operators, carrying out a local optimisation and applying a heuristic feasibility operator. Powerful computational results are achieved for a variety of problem cases that outperform any existing LP model yet developed.Fashion; Industry;

    Xqx Based Modeling For General Integer Programming Problems

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    We present a new way to model general integer programming (IP) problems with in- equality and equality constraints using XQX. We begin with the definition of IP problems folloby their practical applications, and then present the existing XQX based models to handle such problems. We then present our XQX model for general IP problems (including binary IP) with equality and inequality constraints, and also show how this model can be applied to problems with just inequality constraints. We then present the local optima based solution procedure for our XQX model. We also present new theorems and their proofs for our XQX model. Next, we present a detailed literature survey on the 0-1 multidimensional knapsack problem (MDKP) and apply our XQX model using our simple heuristic procedure to solve benchmark problems. The 0-1 MDKP is a binary IP problem with inequality con- straints and variables with binary values. We apply our XQX model using a heuristics we developed on 0-1 MDKP problems of various sizes and found that our model can handle any problem sizes and can provide reasonable quality results in reasonable time. Finally, we apply our XQX model developed for general integer programming problems on the general multi-dimensional knapsack problems. The general MDKP is a general IP problem with inequality constraints where the variables are positive integers. We apply our XQX model on GMDKP problems of various sizes and find that it can provide reasonable quality results in reasonable time. We also find that it can handle problems of any size and provide fea- sible and good quality solutions irrespective of the starting solutions. We conclude with a discussion of some issues related with our XQX model
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