Abstract
Multi-objective optimisation is regarded as one of the most promising ways for dealing with constrained optimisation problems in evolutionary optimisation. This paper presents a theoretical investigation of a multi-objective optimisation evolutionary algorithm for solving the 0-1 knapsack problem. Two initialisation methods are considered in the algorithm: local search initialisation and greedy search initialisation. Then the solution quality of the algorithm is analysed in terms of the approximation ratio.
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Notes
- 1.
A feasible solution \(\mathbf {x}\) is called a local optimum if \(f(\mathbf {y})< f(\mathbf {x})\) for any feasible solution \(\mathbf {y}\) within Hamming distance \(d(\mathbf {x},\mathbf {y})= 1\).
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Acknowledgement
This work was partially supported by EPSRC under Grant No. EP/I009809/1 (He), by NSFC under Grant No. 61170081, 61472143 (Zhou), 61273314 and by the Program for New Century Excellent Talents in University under Grant NCET-13-0596 (Wang).
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He, J., Wang, Y., Zhou, Y. (2015). Analysis of Solution Quality of a Multiobjective Optimization-Based Evolutionary Algorithm for Knapsack Problem. In: Ochoa, G., Chicano, F. (eds) Evolutionary Computation in Combinatorial Optimization. EvoCOP 2015. Lecture Notes in Computer Science(), vol 9026. Springer, Cham. https://doi.org/10.1007/978-3-319-16468-7_7
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