A heuristic algorithm for the multidimensional zero-one knapsack problem

Magazine, Michael J.; Oğuz, Osman

doi:10.1016/0377-2217(84)90286-8

Cited by 94 publications

(61 citation statements)

References 14 publications

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“…MA0-8 and MMA-8 perform better over ORlib as compared to the heuristics proposed by Magazine et al [29], Volgenant et al [51] and Pirkul [42] generating an average gap of 7.69%, 6.98% and 1.37%, respectively. Additionally, Chu et al [6] reported that the CPLEX mixed integer programming (MIP) solver attained an average gap of 3.14%.…”

Section: Comparison Of Ma0-8 and Mma-8 To The Previous Approachesmentioning

confidence: 86%

A case study of memetic algorithms for constraint optimization

Özcan

Başaran

2008

Soft Comput

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There is a variety of knapsack problems in the literature. Multidimensional 0-1 Knapsack Problem (MKP) is an NP-hard combinatorial optimization problem having many application areas. Many approaches have been proposed for solving this problem. In this paper, an empirical investigation of memetic algorithms (MAs) that hybridize genetic algorithms (GAs) with hill climbing for solving MKPs is provided. Two distinct sets of experiments are performed.During the initial experiments, MA parameters are tuned. GA and four MAs each using a different hill climbing method based on the same configuration are evaluated. In the second set of experiments, a self-adaptive (co-evolving) multimeme memetic algorithm (MMA) is compared to the best MA from the parameter tuning experiments. MMA utilizes the evolutionary process as a learning mechanism for choosing the appropriate hill climbing method to improve a candidate solution at a given time. Two well-known MKP benchmarks are used during the experiments.

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Section: Comparison Of Ma0-8 and Mma-8 To The Previous Approachesmentioning

confidence: 86%

A case study of memetic algorithms for constraint optimization

Özcan

Başaran

2008

Soft Comput

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“…However, selecting the most efficient process to restore feasibility is not so trivial. Several techniques can be found in the literature: profit-to-weight ratio based on surrogate relaxation [3]; profit-toweight ratio considering the most violated constraint [15]; reduced prices based on Lagrangian relaxation [21]; maximum profit-to-weight ratio [30]; and, penalty functions [25,20].…”

Section: Improvement Methodsmentioning

confidence: 99%

A Scatter Search Method for the Bi-Criteria Multi-dimensional {0,1}-Knapsack Problem using Surrogate Relaxation

Silva

Clímaco

Figueira

2004

Journal of Mathematical Modelling and Algorithms

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Abstract. This paper presents a scatter search (SS) based method for the bi-criteria multi-dimensional knapsack problem. The method is organized according to the usual structure of SS: (1) diversification, (2) improvement, (3) reference set update, (4) subset generation, and (5) solution combination. Surrogate relaxation is used to convert the multi-constraint problem into a single constraint one, which is used in the diversification method and to evaluate the quality of the solutions. The definition of the appropriate surrogate multiplier vector is also discussed. Tests on several sets of large size instances show that the results are of high quality and an accurate description of the entire set of the non-dominated solutions can be obtained within reasonable computational time.Comparisons with other meta-heuristics are also presented. In the tested instances the obtained set of potentially non-dominated solutions dominates the set found with those meta-heuristics. (2000): 90C27. Mathematics Subject Classification

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“…Magazine and Oguz [26] presented a heuristic algorithm which combined the method of Senju and Toyoda [25] with the Generalised Lagrange Multiplier approach of Everett [27] to fix certain variables. This work was improved by Volgenant and Zoon [28].…”

Section: B Genetic Programming As a Hyper-heuristicmentioning

confidence: 99%

“…A number of papers in the literature [25], [26], [33], [41], [42], [43], [44] make use of an add and (or) drop phase to either construct, improve or repair solutions to the multidimensional 0-1 knapsack problem. These techniques more often than not use a utility-weight value to score and sort the objects in order of their relative efficiency.…”

Section: A Genetic Programming Hyper-heuristic For the Multidimenmentioning

confidence: 99%

A genetic programming hyper-heuristic for the multidimensional knapsack problem

et al. 2014

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Abstract-Hyper-heuristics are a class of high-level search techniques which operate on a search space of heuristics rather than directly on a search space of solutions. Early hyperheuristics focussed on selecting and applying a low-level heuristic at each stage of a search. Recent trends in hyper-heuristic research have led to a number of approaches being developed to automatically generate new heuristics from a set of heuristic components. This work investigates the suitability of using genetic programming as a hyper-heuristic methodology to generate constructive heuristics to solve the multidimensional 0-1 knapsack problem. A population of heuristics to rank knapsack items are trained on a subset of test problems and then applied to unseen instances. The results over a set of standard benchmarks show that genetic programming can be used to generate constructive heuristics which yield human-competitive results.

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A heuristic algorithm for the multidimensional zero-one knapsack problem

Cited by 94 publications

References 14 publications

A case study of memetic algorithms for constraint optimization

A case study of memetic algorithms for constraint optimization

A Scatter Search Method for the Bi-Criteria Multi-dimensional {0,1}-Knapsack Problem using Surrogate Relaxation

A genetic programming hyper-heuristic for the multidimensional knapsack problem

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