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Evaluating the quality of online optimization algorithms by discrete event simulation

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Abstract

A key feature of dynamic problems which offer degrees of freedom to the decision maker is the necessity for a goal-oriented decision making routine which is employed every time the logic of the system requires a decision. In this paper, we look at optimization procedures which appear as subroutines in dynamic problems and show how discrete event simulation can be used to assess the quality of algorithms: after establishing a general link between online optimization and discrete event systems, we address performance measurement in dynamic settings and derive a corresponding tool kit. We then analyze several control strategies using the methodologies discussed previously in two real world examples of discrete event simulation models: a manual order picking system and a pickup and delivery service.

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References

  • Angelopoulos S, Dorrigiv R, López-Ortiz A (2007) On the separation and equivalence of paging strategies. In: Proceedings of the 18th annual ACM-SIAM symposium on discrete algorithms, pp 229–237

  • Becchetti L, Leonardi S, Marchetti-Spaccamela A, Schäfer G, Vredeveld T (2006) Average-case and smoothed competitive analysis of the multilevel feedback algorithm. Math Oper Res 31(1):85–108

    Article  Google Scholar 

  • Ben-David S, Borodin A (1994) A new measure for the study of on-line algorithms. Algorithmica 11(1):73–91

    Article  Google Scholar 

  • Blom M, Krumke S, de Paepe W, Stougie L (2000) The online TSP against fair adversaries. In: Bongiovanni G, Petreschi R, Gambosi G (eds) Algorithms and complexit. Springer, Berlin, pp 137–149

    Chapter  Google Scholar 

  • Borodin A, El-Yaniv R (1998) Online computation and competitive analysis. Cambridge University Press, Cambridge

    Google Scholar 

  • Boyar J, Favrholdt L (2007) The relative worst order ratio for online algorithms. In: ACM transactions on algorithms, 3(2), article no. 22

  • Boyar J, Favrholdt L, Larsen K, Nielsen M (2003) Extending the accommodating function. Acta Inform 40(1):3–35

    Article  Google Scholar 

  • Boyar J, Larsen K, Nielsen M (2002) The accommodating function: a generalization of the competitive ratio. SIAM J Comput 31(1):233–258

    Article  Google Scholar 

  • Cassandras C, Lafortune S (2008) Introduction to discrete event systems, 2nd edn. Springer, Berlin

    Book  Google Scholar 

  • Coffman E, So K, Hofri M, Yao A (1980) A stochastic model of bin-packing. Inf Control 44(2):105–115

    Article  Google Scholar 

  • Cordeau J, Laporte G (2003) A tabu search heuristic for the static multi-vehicle dial-a-ride problem. Transp Res B Methodol 37(6):579–594

    Article  Google Scholar 

  • Croes GA (1958) A method for solving traveling-salesman problems. Oper Res 6(6):791–812

    Article  Google Scholar 

  • Csirik J, Woeginger G (2002) Resource augmentation for online bounded space bin packing. J Algorithms 44(2):308–320

    Article  Google Scholar 

  • Dorrigiv R, Lopez-Ortiz A (2007) Adaptive analysis of on-line algorithms. In: Fekete S, Fleischer R, Klein R, Lopez-Ortiz A (eds) Robot navigation, number 06421 in Dagstuhl Seminar Proceedings, Internationales Begegnungs- und Forschungszentrum für Informatik (IBFI). Schloss Dagstuhl, Germany

  • Dorrigiv R, López-Ortiz A (2008) Closing the gap between theory and practice: new measures for on-line algorithm analysis. In: Proceedings of the 2nd international conference on algorithms and computation, pp 13–24

  • Dorrigiv R, López-Ortiz A, Munro J (2009) On the relative dominance of paging algorithms. Theor Comput Sci 410(38–40):3694–3701

    Article  Google Scholar 

  • Dunke F (2014) Online Optimization with Lookahead. Ph.D. thesis, Karlsruhe Institute of Technology

  • Fiat A, Woeginger G (1998) Competitive odds and ends. In: Fiat A, Woeginger G (eds) Online algorithms: the state of the art. Springer, Berlin, pp 385–394

    Chapter  Google Scholar 

  • Franaszek P, Wagner T (1974) Some distribution-free aspects of paging algorithm performance. J ACM 21(1):31–39

    Article  Google Scholar 

  • Ghiani G, Laporte G, Musmanno R (2004) Introduction to logistics systems planning and control. Wiley, Hoboken

    Google Scholar 

  • Grötschel M, Krumke S, Rambau J (eds) (2001) Online optimization of large scale systems, Springer

  • Grötschel M, Krumke S, Rambau J, Winter T, Zimmermann U (2001) Combinatorial online optimization in real time. In: Grötschel M, Krumke S, Rambau J (eds) Online optimization of large scale systems. Springer, Berlin, pp 679–704

    Chapter  Google Scholar 

  • Henn S, Koch S, Wäscher G (2012) Order batching in order picking warehouses: a survey of solution approaches. In: Manzini R (ed) Warehousing in the global supply chain. Springer, Berlin, pp 105–137

    Chapter  Google Scholar 

  • Hiller B (2009) Online optimization: probabilistic analysis and algorithm engineering. Ph.D. thesis, Technische Universität Berlin

  • Huber C (2011) Throughput analysis of manual order picking systems with congestion consideration. Ph.D. thesis, Karlsruher Institut für Technologie

  • Jaynes E (1957) Information theory and statistical mechanics. Phys Rev 106(4):620–630

    Article  Google Scholar 

  • Jaynes E (1957) Information theory and statistical mechanics II. Phys Rev 108(2):171–190

    Article  Google Scholar 

  • Kallrath J (2005) Online storage systems and transportation problems with applications: optimization models and mathematical solutions. Springer, Berlin

    Google Scholar 

  • Kalyanasundaram B, Pruhs K (2000) Speed is as powerful as clairvoyance. J ACM 47(4):617–643

    Article  Google Scholar 

  • Karlin A, Manasse M, Rudolph L, Sleator D (1988) Competitive snoopy caching. Algorithmica 3(1–4):79–119

    Article  Google Scholar 

  • Karlin A, Phillips S, Raghavan P (2000) Markov paging. SIAM J Comput 30(3):906–922

    Article  Google Scholar 

  • Kenyon C (1996) Best-fit bin-packing with random order. In: Proceedings of the 7th annual ACM-SIAM symposium on discrete algorithms, pp 359–364

  • Kirkpatrick S, Gelatt CD, Vecchi P (1983) Optimization by simulated annealing. Science 220(4598):671–680

    Article  Google Scholar 

  • Koutsoupias E, Papadimitriou C (2000) Beyond competitive analysis. SIAM J Comput 30(1):300–317

    Article  Google Scholar 

  • Krumke S, Laura L, Lipmann M, Marchetti-Spaccamela A, Paepe Wd, Poensgen D, Stougie L (2002) Non-abusiveness helps: An o(1)-competitive algorithm for minimizing the maximum flow time in the online traveling salesman problem. In: Proceedings of the 5th international workshop on approximation algorithms for combinatorial oimization, APPROX ’02, 200–214, Springer

  • Lawler E, Lenstra J, Rinnooy Kan A, Shmoys D (eds.) (1985) The traveling salesman problem: a guided tour of combinatorial optimization. Wiley

  • Miller C, Tucker A, Zemlin R (1960) Integer programming formulation of traveling salesman problems. J ACM 7(4):326–329

    Article  Google Scholar 

  • Müller A, Stoyan D (2002) Comparison methods for stochastic models and risks. Wiley, Hoboken

    Google Scholar 

  • März L, Krug W (2011) Kopplung von Simulation und Optimierung. In: Krug W, Rose O, Weigert G (eds) Simulation und Optimierung in Produktion und Logistik: Praxisorientierter Leitfaden mit Fallbeispielen. Springer, Berlin, pp 41–45

    Chapter  Google Scholar 

  • Psaraftis H (1995) Dynamic vehicle routing: status and prospects. Ann Oper Res 61(1):143–164

    Article  Google Scholar 

  • Raghavan P (1991) A statistical adversary for on-line algorithms. DIMACS Ser Discrete Math Theor Comput Sci 7:79–83

    Article  Google Scholar 

  • Scharbrodt M, Schickinger T, Steger A (2006) A new average case analysis for completion time scheduling. J ACM 53(1):121–146

    Article  Google Scholar 

  • Sleator D, Tarjan R (1985) Amortized efficiency of list update and paging rules. Commun ACM 28(2):202–208

    Article  Google Scholar 

  • Spielman D, Teng S (2004) Smoothed analysis of algorithms: why the simplex algorithm usually takes polynomial time. J ACM 51(3):385–463

    Article  Google Scholar 

  • Stadtler H, Kilger C (eds.) (2008) Supply chain management and advanced planning: concepts, models, sftware, and case studies. Springer, 4th edn

  • Toth PM, Vigo D (eds.) (2002) The vehicle routing problem. SIAM

  • Verein Deutscher Ingenieure (VDI) (1996) VDI-Richtlinie 3633. Simulation von Logistik-, Materialfluß- und Produktionssystemen: Begriffsdefinitionen. In: VDI-Handbuch Materialfluß und Fördertechnik, Beuth

  • Young N (1994) The k-server dual and loose competitiveness for paging. Algorithmica 11(6):525–541

    Article  Google Scholar 

Download references

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Authors and Affiliations

  1. Institute of Operations Research, Discrete Optimization and Logistics, Karlsruhe Institute of Technology, Kaiserstr. 12, 76131, Karlsruhe, Germany

    Fabian Dunke & Stefan Nickel

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  1. Fabian Dunke
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  2. Stefan Nickel
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Correspondence to Fabian Dunke.

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Dunke, F., Nickel, S. Evaluating the quality of online optimization algorithms by discrete event simulation. Cent Eur J Oper Res 25, 831–858 (2017). https://doi.org/10.1007/s10100-016-0455-6

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  • DOI: https://doi.org/10.1007/s10100-016-0455-6

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