Generalized quadratic multiple knapsack problem and two solution approaches

Saraç, Tuğba; Sipahioglu, Aydin

doi:10.1016/j.cor.2013.08.018

Cited by 22 publications

(26 citation statements)

References 26 publications

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“…As a consequence, an updating mechanism is employed to adjust the model at each generation. First, the superior sub-population that consists of SP_Size elite solutions is determined by the widely-used two-tournament selection strategy [42], where SP_Size = η% · P_Size. Then, probability matrix Q is updated based on the information of the superior sub-population and the historical information of searching.…”

Section: Updating Mechanismmentioning

confidence: 99%

An Estimation of Distribution Algorithm-Based Memetic Algorithm for the Distributed Assembly Permutation Flow-Shop Scheduling Problem

Wang

2016

IEEE Trans. Syst. Man Cybern, Syst.

164

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In this paper, an estimation of distribution algorithm (EDA)-based memetic algorithm (MA) is proposed for solving the distributed assembly permutation flow-shop scheduling problem (DAPFSP) with the objective to minimize the maximum completion time. A novel bi-vector-based method is proposed to represent a solution for the DAPFSP. In the searching phase of the EDA-based MA (EDAMA), the EDA-based exploration and the local-search-based exploitation are incorporated within the MA framework. For the EDA-based exploration phase, a probability model is built to describe the probability distribution of superior solutions. Besides, a novel selective-enhancing sampling mechanism is proposed for generating new solutions by sampling the probability model. For the local-search-based exploitation phase, the critical path of the DAPFSP is analyzed to avoid invalid searching operators. Based on the analysis, a critical-path-based local search strategy is proposed to further improve the potential solutions obtained in the EDA-based searching phase. Moreover, the effect of parameter setting is investigated based on the Taguchi method of design-of-experiment. Suitable parameter values are suggested for instances with different scales. Finally, numerical simulations based on 1710 benchmark instances are carried out. The experimental results and comparisons with existing algorithms show the effectiveness of the EDAMA in solving the DAPFSP. In addition, the best-known solutions of 181 instances are updated by the EDAMA. IndexTerms-Critical path, distributed production scheduling, estimation of distribution algorithm (EDA), memetic algorithm (MA).

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Section: Updating Mechanismmentioning

confidence: 99%

An Estimation of Distribution Algorithm-Based Memetic Algorithm for the Distributed Assembly Permutation Flow-Shop Scheduling Problem

Wang

2016

IEEE Trans. Syst. Man Cybern, Syst.

164

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“…T HE generalized quadratic multiple knapsack problem (GQMKP), as an extension of the classical quadratic multiple knapsack problem with setups and knapsack preferences of the items, is a difficult combinatorial optimization problem recently introduced in [30].…”

Section: Introductionmentioning

confidence: 99%

“…Notice that the above model is modified from the binary quadratic model described in [30] and has the advantage of being more concise.…”

Section: Introductionmentioning

confidence: 99%

“…As shown in the case study of [30], the GQMKP can be encountered in companies producing plastic parts which make use of injection machines. In the studied application, jobs are considered as objects; injection machines are regarded as knapsacks and the given planning period is considered as the capacity of the knapsack.…”

Section: Introductionmentioning

confidence: 99%

“…In [30], the authors showed the first study dealing directly with the GQMKP and proposed three solution approaches to this difficult problem. Based on the 0-1 quadratic model proposed in their paper, the first approach is based on the general Gams/Dicopt framework for solving MINP (mixedinteger nonlinear programming) models by integrating a NLP (Nonlinear Programming) or MIP (Mixed-Integer Programming) solver that runs under the Gams system.…”

Section: Introductionmentioning

confidence: 99%

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Memetic Search for the Generalized Quadratic Multiple Knapsack Problem

Chen

Hao

2016

IEEE Trans. Evol. Computat.

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The generalized quadratic multiple knapsack problem (GQMKP) extends the classical quadratic multiple knapsack problem (QMKP) with setups and knapsack preference of the items. The GQMKP can accommodate a number of real-life applications and is computationally difficult. In this paper, we demonstrate the interest of the memetic search approach for approximating the GQMKP by presenting a highly effective memetic algorithm (denoted by MAGQMK). The algorithm combines a backbone-based crossover operator (to generate offspring solutions) and a multi-neighborhood simulated annealing procedure (to find high quality local optima). To prevent premature convergence of the search, MAGQMK employs a quality-anddistance pool updating strategy. Extensive experiments on two sets of 96 benchmarks show a remarkable performance of the proposed approach. In particular, it discovers improved best solutions in 53 and matches the best known solutions for 39 other cases. A case study on a pseudo real-life problem demonstrates the efficacy of the proposed approach in practical situations. Additional analyses show the important contribution of the novel general-exchange neighborhood, the backbone-based crossover operator as well as the quality-and-distance pool updating rule to the performance of the proposed algorithm.

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