Mathematical Programming: Series A and B
Formulations and valid inequalities for the node capacitated graph partitioning problem
Mathematical Programming: Series A and B
The zero/one multiple knapsack problem and genetic algorithms
SAC '94 Proceedings of the 1994 ACM symposium on Applied computing
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
A Genetic Algorithm for the Multidimensional Knapsack Problem
Journal of Heuristics
Characterizing Locality in Decoder-Based EAs for the Multidimensional Knapsack Problem
AE '99 Selected Papers from the 4th European Conference on Artificial Evolution
Exact Solution of the Quadratic Knapsack Problem
INFORMS Journal on Computing
Using a Mixed Integer Programming Tool for Solving the 0-1 Quadratic Knapsack Problem
INFORMS Journal on Computing
The quadratic multiple knapsack problem and three heuristic approaches to it
Proceedings of the 8th annual conference on Genetic and evolutionary computation
Improving Image Vector Quantization with a Genetic Accelerated K-Means Algorithm
ACIVS '08 Proceedings of the 10th International Conference on Advanced Concepts for Intelligent Vision Systems
An Artificial Bee Colony Algorithm for the Quadratic Knapsack Problem
ICONIP '09 Proceedings of the 16th International Conference on Neural Information Processing: Part II
A genetic algorithm for the quadratic multiple knapsack problem
BVAI'07 Proceedings of the 2nd international conference on Advances in brain, vision and artificial intelligence
A heuristic approach for allocation of data to RFID tags: A data allocation knapsack problem (DAKP)
Computers and Operations Research
Naive and heuristic permutation-coded genetic algorithms for the quadratic knapsack problem
Proceedings of the 14th annual conference companion on Genetic and evolutionary computation
Solving 0-1 knapsack problems by a discrete binary version of cuckoo search algorithm
International Journal of Bio-Inspired Computation
An effective GRASP and tabu search for the 0-1 quadratic knapsack problem
Computers and Operations Research
A simplified binary artificial fish swarm algorithm for 0-1 quadratic knapsack problems
Journal of Computational and Applied Mathematics
Generalized quadratic multiple knapsack problem and two solution approaches
Computers and Operations Research
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Augmenting an evolutionary algorithm with knowledge of its target problem can yield a more effective algorithm, as this presentation illustrates. The Quadratic Knapsack Problem extends the familiar Knapsack Problem by assigning values not only to individual objects but also to pairs of objects. In these problems, an object's value density is the sum of the values associated with it divided by its weight. Two greedy heuristics for the quadratic problem examine objects for inclusion in the knapsack in descending order of their value densities. Two genetic algorithms encode candidate selections of objects as binary strings and generate only strings whose selections of objects have total weight no more than the knapsack's capacity. One GA is naive; its operators apply no information about the values associated with objects. The second extends the naive GA with greedy techniques from the non-evolutionary heuristics. Its operators examine objects for inclusion in the knapsack in orders determined by tournaments based on objects' value densities. All four algorithms are tested on twenty problem instances whose optimum knapsack values are known. The greedy heuristics do well, as does the naive GA, but the greedy GA exhibits the best performance. In repeated trials on the test instances, it identifies optimum solutions more than nine times out of every ten.