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.

Approximation algorithms, combinatorial optimization, evolutionary optimization, fully polynomial-time randomized approximation scheme (FPRAS), multi-objective optimization, runtime analysis, shortest path problem
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© 2010 by the Massachusetts Institute of Technology
2010
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