A New Grouping Genetic Algorithm for the Quadratic Multiple Knapsack Problem

Singh, Alok; Baghel, Anurag Singh

doi:10.1007/978-3-540-71615-0_19

Cited by 19 publications

(12 citation statements)

References 6 publications

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“…Although Genetic Algorithms (GA) are often used in solving the QKP and QMKP [13], [14], [9], these publications on GA are not directly applicable to our problem due to the existence of lower bounds on class sizes. Moreover, the existence of lower and upper bounds on class sizes renders classical operations of crossover and mutation inefficient, i.e.…”

Section: Genetic Algorithm Based Matheuristicmentioning

confidence: 99%

A Lagrangian Relaxation-Based Heuristic to Solve Large Extended Graph Partitioning Problems

Czibula

Zinder

2016

WALCOM: Algorithms and Computation

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Abstract. The paper is concerned with the planning of training sessions in large organisations requiring periodic retraining of their staff. The allocation of students must take into account student preferences as well as the desired composition of study groups. The paper presents a bicriteria Quadratic Multiple Knapsack formulation of the considered practical problem, and a novel solution procedure based on Lagrangian relaxation. The paper presents the results of computational experiments aimed at testing the optimisation procedure on real world data originating from Australia's largest electricity distributor. Results are compared and validated against a Genetic Algorithm based matheuristic.

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Section: Genetic Algorithm Based Matheuristicmentioning

confidence: 99%

A Lagrangian Relaxation-Based Heuristic to Solve Large Extended Graph Partitioning Problems

Czibula

Zinder

2016

WALCOM: Algorithms and Computation

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“…• Set I: This set consists of 60 well-known benchmarks which are commonly used for the QMKP algorithm assessment in the literature (Chen & Hao, 2015;García-Martínez et al, 2014a,b;Sundar & Singh, 2010;Saraç & Sipahioglu, 2007;Singh & Baghel, 2007;Hiley & Julstrom, 2006). Built from the quadratic knapsack problem (QKP) instances introduced in (Billionnet & Soutif, 2015) which can be download from: http://cedric.…”

Section: Benchmark Instancesmentioning

confidence: 99%

“…Due to their quadratic nature, these problems are known to be extremely difficult. For this reason, approximate algorithms based on metaheuristics like evolutionary algorithms, constitute a very popular approach for tackling these problems (Misevicius, 2004;Hiley & Julstrom, 2006;Saraç & Sipahioglu, 2007;Singh & Baghel, 2007;Soak & Lee, 2012).…”

Section: Introductionmentioning

confidence: 99%

“…Among these heuristics, neighborhood search and constructive/destructive search approaches are very popular, including hill-climbing (Hiley & Julstrom, 2006), tabu-enhanced iterated greedy search (García-Martínez et al, 2014a), strategic oscillation (García-Martínez et al, 2014b) and responsive iterated threshold search (Chen & Hao, 2015). Population-based algorithms constitute another class of popular tools for addressing the QMKP, such as genetic algorithms (Hiley & Julstrom, 2006;Saraç & Sipahioglu, 2007), memetic algorithms (Singh & Baghel, 2007;Soak & Lee, 2012) and artificial bee colony algorithms (Sundar & Singh, 2010).…”

Section: Introductionmentioning

confidence: 99%

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An evolutionary path relinking approach for the quadratic multiple knapsack problem

Chen

Hao

Glover

2016

Knowledge-Based Systems

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The quadratic multiple knapsack problem (QMKP) is a challenging combinatorial optimization problem with numerous applications. In this paper, we propose the first evolutionary path relinking approach (EPR) for solving the QMKP approximately. This approach combines advanced features both from the path relinking (PR) method and the responsive threshold search algorithm. Thanks to the tunneling property which allows a controlled exploration of infeasible regions, the proposed EPR algorithm is able to identify very high quality solutions. Experimental studies on the set of 60 well-known benchmarks and a new set of 30 large-sized instances show that EPR outperforms several state-ofthe-art algorithms. In particular, it discovers 10 improved results (new lower bounds) and matches the best known result for the remaining 50 cases. More significantly, EPR demonstrates remarkable efficacy on the 30 new larger instances by easily dominating the current best performing algorithms across the whole instance set. Key components of the algorithm are analyzed to shed lights on their impact on the proposed approach.

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“…Singh and Baghel [21] proposed a steady-state grouping genetic algorithm (SB-GGA). They compared SB-GGA with HJ-SHC and HJ-GA.…”

Section: Introductionmentioning

confidence: 99%

A memetic algorithm for the quadratic multiple container packing problem

Soak

Lee

2010

Appl Intell

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In this paper, we propose a new memetic algorithm for the quadratic multiple container packing problem. The proposed memetic algorithm is based on the adaptive link adjustment evolutionary algorithm (ALA-EA) and it incorporates heuristic fitness improvement schemes into the ALA-EA. In addition, we propose a new powerful initialization method for the QMCPP.The proposed algorithm is compared to the previous approaches. We report that it can find much improved final solutions at most benchmark instances. Moreover, even the best solutions of the first generation show better than the previous known best solutions at most of instances especially with density d = 0.75.In addition, we compare the proposed memetic algorithm to the NetKey based evolutionary algorithm for analyzing features of the ALA-EA.Keywords Evolutionary algorithm · Memetic algorithm · Quadratic multiple container packing problem · Adaptive link adjustment

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A New Grouping Genetic Algorithm for the Quadratic Multiple Knapsack Problem

Cited by 19 publications

References 6 publications

A Lagrangian Relaxation-Based Heuristic to Solve Large Extended Graph Partitioning Problems

A Lagrangian Relaxation-Based Heuristic to Solve Large Extended Graph Partitioning Problems

An evolutionary path relinking approach for the quadratic multiple knapsack problem

A memetic algorithm for the quadratic multiple container packing problem

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