Approximation of Pareto optima in multiple-objective, shortest-path problems
Operations Research
Randomized algorithms
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Theoretical Computer Science
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Proceedings of the 10th annual conference on Genetic and evolutionary computation
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IEEE Transactions on Evolutionary Computation
An oriented spanning tree based genetic algorithm for multi-criteria shortest path problems
Applied Soft Computing
Information Sciences: an International Journal
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We present a natural vector-valued fitness function f for the multi-objective shortest path problem, which is a fundamental multi-objective combinatorial optimization problem known to be NP-hard. Thereafter, we conduct a rigorous runtime analysis of a simple evolutionary algorithm (EA) optimizing f. Interestingly, this simple general algorithm is a fully polynomial-time randomized approximation scheme (FPRAS) for the problem under consideration, which exemplifies how EAs are able to find good approximate solutions for hard problems. Furthermore, we present lower bounds for the worst-case optimization time.