Abstract
Worst-case performance analysis is one method of characterizing the effectiveness of a heuristic. It provides a guarantee on the maximum relative difference between the solution generated by the heuristic and the optimal solution for any possible problem instance, even those that are not likely to appear in practice. Thus, a heuristic that works well in practice may have a weak worst-case performance, if, for example, it provides very bad solutions for one (or more) pathological instance(s).
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References
Azuma, K. (1967). Weighted sums of certain dependent random variables. Tohoku Mathematical Journal, 19, 357–367.
Coffman, E. G. Jr., & Lueker, G. S. (1991). Probabilistic analysis of packing and partitioning algorithms. New York: Wiley.
Dreyfus, S. E., & Law, A. M. (1977). The art and theory of dynamic programming. New York: Academic Press.
Few, L. (1955). The shortest path and the shortest road through n points. Mathematika, 2, 141–144.
Held, M., & Karp, R. M. (1962). A dynamic programming approach to sequencing problems. SIAM Journal on Applied Mathematics, 10, 196–210.
Jaillet, P. (1985). Probabilistic traveling salesman problem (Ph.D. Dissertation, Operations Research Center, Massachusetts Institute of Technology, Cambridge, MA)
Karlin, S., & Taylor, H. M. (1975). A first course in stochastic processes. San Diego, CA: Academic.
Karp, R. M. (1977). Probabilistic analysis of partitioning algorithms for the traveling salesman problem. Mathematics of Operations Research, 2, 209–224.
Karp, R. M., & Steele, J. M. (1985). Probabilistic analysis of heuristics. In E. L. Lawler, J. K. Lenstra, A. H. G. Rinnooy Kan, D. B. Shmoys (Eds.) The traveling salesman problem: a guided tour of combinatorial optimization (pp. 181–205). New York: Wiley.
Kingman, J. F. C. (1976). Subadditive processes. Lecture Notes in Mathematics 539, 168–222. Berlin: Springer.
Rhee, W. T., & Talagrand, M. (1987). Martingale inequalities and NP-complete problems. Mathematics of Operations Research, 12, 177–181.
Steele, J. M. (1981). Subadditive euclidean functionals and nonlinear growth geometric probability. Annals of Probability, 9, 365–375.
Steele, J. M. (1990). Lecture notes on “probabilistic analysis of algorithms.”
Stout, W. F. (1974). Almost sure convergence. New York: Academic.
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Simchi-Levi, D., Chen, X., Bramel, J. (2014). Average-Case Analysis. In: The Logic of Logistics. Springer Series in Operations Research and Financial Engineering. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-9149-1_5
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DOI: https://doi.org/10.1007/978-1-4614-9149-1_5
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