Abstract
In a multi-objective combinatorial optimization (MOCO) problem, multiple objectives must be optimized simultaneously. In past years, several constraint-based algorithms have been proposed for finding Pareto-optimal solutions to MOCO problems that rely on repeated calls to a constraint solver. Understanding the properties of these algorithms and analyzing their performance is an important problem. Previous work has focused on empirical evaluations on benchmark instances. Such evaluations, while important, have their limitations. Our paper adopts a different, purely theoretical approach, which is based on characterizing the search space into subspaces and analyzing the worst-case performance of a MOCO algorithm in terms of the expected number of calls to the underlying constraint solver. We apply the approach to two important constraint-based MOCO algorithms. Our analysis reveals a deep connection between the search mechanism of a constraint solver and the exploration of the search space of a MOCO problem.
Keywords
- Multi-objective Combinatorial Optimization (MOCO)
- Constraint-based Algorithm
- MOCO Problem
- Underlying Constraint Solver
- Pareto Optimal Solutions
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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Notes
- 1.
From here after, we use solution unqualified to refer to a feasible solution and Pareto-optimal solution to refer to an optimal solution to a MOCO instance.
- 2.
Without loss of generality, we consider minimization problems.
References
Baptiste, P., Le Pape, C., Nuijten, W.: Constraint-Based Scheduling: Applying Constraint Programming to Scheduling Problems. Kluwer, Dordrecht (2001)
Bjørner, N., Phan, A.D.: \(\nu \)Z - maximal satisfaction with Z3. In: Proceedings of the SCSS, pp. 632–647 (2014)
Chakraborty, S., Fremont, D.J., Meel, K.S., Seshia, S.A., Vardi, M.Y.: Distribution-aware sampling and weighted model counting for SAT. In: Proceedings of the AAAI, pp. 1722–1730 (2014)
Chakraborty, S., Meel, K.S., Vardi, M.Y.: A scalable and nearly uniform generator of SAT witnesses. In: Sharygina, N., Veith, H. (eds.) CAV 2013. LNCS, vol. 8044, pp. 608–623. Springer, Heidelberg (2013). doi:10.1007/978-3-642-39799-8_40
Chakraborty, S., Meel, K.S., Vardi, M.Y.: Balancing scalability and uniformity in sat witness generator. In: Proceedings of the DAC, pp. 1–6 (2014)
Dechter, R., Kask, K., Bin, E., Emek, R.: Generating random solutions for constraint satisfaction problems. In: Proceedings of the AAAI, pp. 15–21 (2002)
Ehrgott, M.: Multicriteria Optimization, 2nd edn. Springer, Heidelberg (2005)
Gavanelli, M.: An algorithm for multi-criteria optimization in CSPs. In: Proceedings of the ECAI, pp. 136–140 (2002)
Gomes, C., Selman, B., Kautz, H.: Boosting combinatorial search through randomization. In: Proceedings of the AAAI, pp. 431–437 (1998)
Gomes, C.P., Sabharwal, A., Selman, B.: Near-uniform sampling of combinatorial spaces using XOR constraints. In: Proceedings of the NIPS, pp. 481–488 (2006)
Hartert, R., Schaus, P.: A support-based algorithm for the bi-objective pareto constraint. In: Proceedings of the AAAI, pp. 2674–2679 (2014)
Le Pape, C., Couronné, P., Vergamini, D., Gosselin, V.: Time-versus-capacity compromises in project scheduling. In: Proceedings of the Thirteenth Workshop of the UK Planning Special Interest Group, Strathclyde, UK (1994)
Lukasiewycz, M., Glaß, M., Haubelt, C., Teich, J.: Solving multi-objective Pseudo-Boolean problems. In: Marques-Silva, J., Sakallah, K.A. (eds.) SAT 2007. LNCS, vol. 4501, pp. 56–69. Springer, Heidelberg (2007). doi:10.1007/978-3-540-72788-0_9
Papadimitriou, C., Steiglitz, K.: Combinatorial Optimization: Algorithms and Complexity. Dover, Mineola (1998)
Rayside, D., Estler, H.C., Jackson, D.: The guided improvement algorithm for exact, general purpose, many-objective combinatorial optimization. Technical report, MIT-CSAIL-TR-2009-033 (2009)
Rossi, F., van Beek, P., Walsh, T. (eds.): Handbook of Constraint Programming. Elsevier, Amsterdam (2006)
Sadeh, N., Fox, M.: Variable and value ordering heuristics for the job shop scheduling constraint satisfaction problem. Artif. Intell. 86(1), 1–41 (1996)
Spielman, D., Teng, S.H.: Smoothed analysis of algorithms: why the simplex algorithm usually takes polynomial time. J. ACM 51(3), 385–463 (2004)
Van Hentenryck, P.: Constraint Satisfaction in Logic Programming. MIT Press, Cambridge (1989)
van Wassenhove, L., Gelders, L.: Solving a bicriterion scheduling problem. Eur. J. Oper. Res. 4(1), 42–48 (1980)
Acknowledgments
This work has been partially supported by Shanghai Municipal Natural Science Foundation (No. 17ZR1406900) and NSERC Discovery Grant.
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Guo, J., Blais, E., Czarnecki, K., van Beek, P. (2017). A Worst-Case Analysis of Constraint-Based Algorithms for Exact Multi-objective Combinatorial Optimization. In: Mouhoub, M., Langlais, P. (eds) Advances in Artificial Intelligence. Canadian AI 2017. Lecture Notes in Computer Science(), vol 10233. Springer, Cham. https://doi.org/10.1007/978-3-319-57351-9_16
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