Where are the hard knapsack problems?
Computers and Operations Research
A Local-Search-Based Heuristic for the Demand-Constrained Multidimensional Knapsack Problem
INFORMS Journal on Computing
Core problems in bi-criteria {0,1}-knapsack problems
Computers and Operations Research
Efficient time-aware prioritization with knapsack solvers
Proceedings of the 1st ACM international workshop on Empirical assessment of software engineering languages and technologies: held in conjunction with the 22nd IEEE/ACM International Conference on Automated Software Engineering (ASE) 2007
International Journal of Mobile Network Design and Innovation
A Steep Thermodynamical Selection Rule for Evolutionary Algorithms
ICCS '07 Proceedings of the 7th international conference on Computational Science, Part IV: ICCS 2007
Hard multidimensional multiple choice knapsack problems, an empirical study
Computers and Operations Research
Avoiding premature convergence in estimation of distribution algorithms
CEC'09 Proceedings of the Eleventh conference on Congress on Evolutionary Computation
Black box scatter search for general classes of binary optimization problems
Computers and Operations Research
Kernel search: A general heuristic for the multi-dimensional knapsack problem
Computers and Operations Research
The Multidimensional Knapsack Problem: Structure and Algorithms
INFORMS Journal on Computing
Journal of Computational Methods in Sciences and Engineering - Special Supplement Issue in Section A and B: Selected Papers from the ISCA International Conference on Software Engineering and Data Engineering, 2009
Development of core to solve the multidimensional multiple-choice knapsack problem
Computers and Industrial Engineering
Hybrid metaheuristics in combinatorial optimization: A survey
Applied Soft Computing
Problem reduction heuristic for the 0-1 multidimensional knapsack problem
Computers and Operations Research
Kernel Search: a new heuristic framework for portfolio selection
Computational Optimization and Applications
The core concept for the multidimensional knapsack problem
EvoCOP'06 Proceedings of the 6th European conference on Evolutionary Computation in Combinatorial Optimization
CORAL: An Exact Algorithm for the Multidimensional Knapsack Problem
INFORMS Journal on Computing
Kernel search for the capacitated facility location problem
Journal of Heuristics
A scalable GPU-based approach to accelerate the multiple-choice knapsack problem
DATE '12 Proceedings of the Conference on Design, Automation and Test in Europe
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Since Balas and Zemel in the 1980s introduced the so-called core problem as an efficient tool for solving the Knapsack Problem, all the most successful algorithms have applied this concept. Balas and Zemel proved that if the weights in the core are uniformly distributed then there is a high probability for finding an optimal solution in the core. Items outside the core may be fathomed because of reduction rules. This paper demonstrates that generally it is not reasonable to assume a uniform distribution of the weights in the core, and it is experimentally shown that the heuristic proposed by Balas and Zemel does not find as good solutions as expected. Also, other algorithms that solve some kind of core problem may be stuck by difficult cores. This behavior has apparently not been noticed before because of unsufficient testing. Capacities leading to difficult problems are identified for several categories of instance types, and it is demonstrated that the hitherto applied test instances are easier than the average. As a consequence we propose a series of new randomly generated test instances and show how recent algorithms behave when applied to these problems.