Genetic programming: on the programming of computers by means of natural selection
Genetic programming: on the programming of computers by means of natural selection
Fast Approximation Algorithms for the Knapsack and Sum of Subset Problems
Journal of the ACM (JACM)
A PTAS for the multiple knapsack problem
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
Multi-Objective Optimization Using Evolutionary Algorithms
Multi-Objective Optimization Using Evolutionary Algorithms
A Genetic Algorithm for the Multidimensional Knapsack Problem
Journal of Heuristics
Genetic Algorithms for Multiobjective Optimization: FormulationDiscussion and Generalization
Proceedings of the 5th International Conference on Genetic Algorithms
Genetic Algorithms for the Multiple Container Packing Problem
PPSN V Proceedings of the 5th International Conference on Parallel Problem Solving from Nature
Approximating Multiobjective Knapsack Problems
Management Science
Analysis of a multiobjective evolutionary algorithm on the 0-1 knapsack problem
Theoretical Computer Science
Proceedings of the 9th annual conference on Genetic and evolutionary computation
Particle Swarm Optimization for the Multidimensional Knapsack Problem
ICANNGA '07 Proceedings of the 8th international conference on Adaptive and Natural Computing Algorithms, Part I
Evolving bin packing heuristics with genetic programming
PPSN'06 Proceedings of the 9th international conference on Parallel Problem Solving from Nature
Running time analysis of a multiobjective evolutionary algorithm on simple and hard problems
FOGA'05 Proceedings of the 8th international conference on Foundations of Genetic Algorithms
Multiobjective evolutionary algorithms: a comparative case studyand the strength Pareto approach
IEEE Transactions on Evolutionary Computation
IEEE Transactions on Evolutionary Computation
Evolution of Search Algorithms Using Graph Structured Program Evolution
EuroGP '09 Proceedings of the 12th European Conference on Genetic Programming
Symbiotic coevolutionary genetic programming: a benchmarking study under large attribute spaces
Genetic Programming and Evolvable Machines
Generation of VNS components with grammatical evolution for vehicle routing
EuroGP'13 Proceedings of the 16th European conference on Genetic Programming
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The 0/1 knapsack problem is one of the most exhaustively studied NP-hard combinatorial optimization problems. Many different approaches have been taken to obtain an approximate solution to the problem in polynomial time. Here we consider the biobjective 0/1 knapsack problem. The contribution of this paper is to show that a genetic programming system can evolve a set of heuristics that can give solutions on the Pareto front for multiobjective combinatorial problems. The genetic programming (GP) system outlined here evolves a heuristic which decides whether or not to add an item to the knapsack in such a way that the final solution is one of the Pareto optimal solutions. Moreover, the Pareto front obtained from the GP system is comparable to the front obtained from other human-designed heuristics. We discuss the issue of the diversity of the obtained Pareto front and the application of strongly-typed GP as a means of obtaining better diversity.