Evaluating the quality of online optimization algorithms by discrete event simulation

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.

[1]  Wilfried Krug,et al.  Kopplung von Simulation und Optimierung , 2011 .

[2]  Harilaos N. Psaraftis,et al.  Dynamic vehicle routing: Status and prospects , 1995, Ann. Oper. Res..

[3]  Gilbert Laporte,et al.  A Tabu Search Heuristic for the Static Multi-Vehicle Dial-a-Ride Problem , 2002 .

[4]  Hartmut Stadtler,et al.  Supply Chain Management and Advanced Planning , 2000 .

[5]  Joan Boyar,et al.  The Accommodating Function: A Generalization of the Competitive Ratio , 2001, SIAM J. Comput..

[6]  Fabian Dunke,et al.  Online Optimization with Lookahead , 2014 .

[7]  Allan Borodin,et al.  Online computation and competitive analysis , 1998 .

[8]  Alejandro López-Ortiz,et al.  Adaptive Analysis of On-line Algorithms , 2006, Robot Navigation.

[9]  Alejandro López-Ortiz,et al.  Closing the Gap Between Theory and Practice: New Measures for On-Line Algorithm Analysis , 2008, WALCOM.

[10]  C. Kenyon Best-fit bin-packing with random order , 1996, SODA '96.

[11]  Christos G. Cassandras,et al.  Introduction to Discrete Event Systems , 1999, The Kluwer International Series on Discrete Event Dynamic Systems.

[12]  D. Spielman,et al.  Smoothed analysis of algorithms: Why the simplex algorithm usually takes polynomial time , 2004 .

[13]  R. A. Zemlin,et al.  Integer Programming Formulation of Traveling Salesman Problems , 1960, JACM.

[14]  Anna R. Karlin,et al.  Competitive snoopy caching , 1986, 27th Annual Symposium on Foundations of Computer Science (sfcs 1986).

[15]  Neal E. Young,et al.  Thek-server dual and loose competitiveness for paging , 1994, Algorithmica.

[16]  Christos H. Papadimitriou,et al.  Beyond competitive analysis [on-line algorithms] , 1994, Proceedings 35th Annual Symposium on Foundations of Computer Science.

[17]  Luca Becchetti,et al.  Average-Case and Smoothed Competitive Analysis of the Multilevel Feedback Algorithm , 2006, Math. Oper. Res..

[18]  Allan Borodin,et al.  A new measure for the study of on-line algorithms , 2005, Algorithmica.

[19]  Anna R. Karlin,et al.  Markov Paging , 2000, SIAM J. Comput..

[20]  Eugene L. Lawler,et al.  The Traveling Salesman Problem: A Guided Tour of Combinatorial Optimization , 1985 .

[21]  János Csirik,et al.  Resource augmentation for online bounded space bin packing , 2000, J. Algorithms.

[22]  Leen Stougie,et al.  The Online-TSP against Fair Adversaries , 2000, CIAC.

[23]  Alejandro López-Ortiz,et al.  On the Separation and Equivalence of Paging Strategies and Other Online Algorithms , 2018, Algorithmica.

[24]  Gerhard Wäscher,et al.  Order Batching in Order Picking Warehouses: A Survey of Solution Approaches , 2012 .

[25]  G. Croes A Method for Solving Traveling-Salesman Problems , 1958 .

[26]  Leen Stougie,et al.  Non-abusiveness Helps: An O(1)-Competitive Algorithm for Minimizing the Maximum Flow Time in the Online Traveling Salesman Problem , 2002, APPROX.

[27]  Martin Grötschel,et al.  Online optimization of large scale systems , 2001 .

[28]  Robert E. Tarjan,et al.  Amortized efficiency of list update and paging rules , 1985, CACM.

[29]  Bala Kalyanasundaram,et al.  Speed is as powerful as clairvoyance , 2000, JACM.

[30]  E. Jaynes Information Theory and Statistical Mechanics , 1957 .

[31]  Paolo Toth,et al.  The Vehicle Routing Problem , 2002, SIAM monographs on discrete mathematics and applications.

[32]  Julia Kallrath Online Storage Systems and Transportation Problems with Applications: Optimization Models and Mathematical Solutions , 2004 .

[33]  Joan Boyar,et al.  The relative worst order ratio for online algorithms , 2007, TALG.

[34]  Benjamin Hiller,et al.  Online Optimization: Probabilistic Analysis and Algorithm Engineering , 2010, OR.

[35]  Roberto Musmanno,et al.  Introduction to Logistics Systems Planning and Control , 2004 .

[36]  Martin Grötschel,et al.  Combinatorial Online Optimization in Real Time , 2001 .

[37]  Joan Boyar,et al.  Extending the accommodating function , 2003, Acta Informatica.

[38]  C. D. Gelatt,et al.  Optimization by Simulated Annealing , 1983, Science.

[39]  Peter A. Franaszek,et al.  Some Distribution-Free Aspects of Paging Algorithm Performance , 1974, JACM.

[40]  Prabhakar Raghavan,et al.  A Statistical Adversary for On-line Algorithms , 1991, On-Line Algorithms.

[41]  Micha Hofri,et al.  A Stochastic Model of Bin-Packing , 1980, Inf. Control..

[42]  A. Müller,et al.  Comparison Methods for Stochastic Models and Risks , 2002 .

[43]  Gerhard J. Woeginger,et al.  Competitive Odds and Ends , 1996, Online Algorithms.

[44]  Leen Stougie,et al.  Non-abusiveness Helps: An % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfKttLearuqr1ngBPrgarmWu51MyVXgatC% vAUfeBSjuyZL2yd9gzLbvyNv2CaeHbuLwBLnhiov2DGi1BTfMBaeHb% d9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbb% L8F4rqqrFfpeea0xe9Lq-Jc9vqaqpepm0xbba9pwe9Q8fs0-yqaqpe% pae9pg0FirpepeKkFr0xfr-xfr , 2002 .

[45]  Christian Huber,et al.  Throughput Analysis of Manual Order Picking Systems with Congestion Consideration , 2012 .

[46]  Alejandro López-Ortiz,et al.  On the relative dominance of paging algorithms , 2009, Theor. Comput. Sci..