Online Optimization: Probabilistic Analysis and Algorithm Engineering

This article gives an overview on some of the results of the authors’ PhD thesis [3]. The subject of this thesis is online optimization, which deals with making decisions in an environment where the data describing the process to optimize becomes available over time, i. e., online. In particular, we study algorithms for combinatorial online optimization problems involving discrete decisions both from a practical and a theoretical point of view. Here we sketch our results related to the control of elevators in high-rise buildings.

[1]  János Csirik,et al.  On the worst-case performance of the NkF bin-packing heuristic , 1989, Acta Cybern..

[2]  Sven Oliver Krumke,et al.  Euler is standing in line dial-a-ride problems with precedence-constraints , 2001, Discret. Appl. Math..

[3]  Tobias Achterberg,et al.  Constraint integer programming , 2007 .

[4]  David Simchi-Levi,et al.  A New Generation of Vehicle Routing Research: Robust Algorithms, Addressing Uncertainty , 1996, Oper. Res..

[5]  Michael Mitzenmacher,et al.  Improved results for route planning in stochastic transportation , 2000, SODA '01.

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

[7]  Frank Thomson Leighton,et al.  Some unexpected expected behavior results for bin packing , 1984, STOC '84.

[8]  Tjark Vredeveld,et al.  Probabilistic Analysis of Online Bin Coloring Algorithms Via Stochastic Comparison , 2008, ESA.

[9]  Peter J. Denning,et al.  Operating Systems Theory , 1973 .

[10]  M. Doisy,et al.  A coupling technique for stochastic comparison of functions of Markov Processes , 2000, Adv. Decis. Sci..

[11]  Leen Stougie,et al.  Online Bin Coloring , 2001, ESA.

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

[13]  Lisa D. Nicklas,et al.  A parallel solution to the cutting stock problem for a cluster of workstations , 1996, Proceedings of 5th IEEE International Symposium on High Performance Distributed Computing.

[14]  Alexander Souza,et al.  On adequate performance measures for paging , 2006, STOC '06.

[15]  Giovanni Righini,et al.  New dynamic programming algorithms for the resource constrained elementary shortest path problem , 2008, Networks.

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

[17]  Michael Mitzenmacher,et al.  Bounds on the greedy routing algorithm for array networks , 1994, SPAA '94.

[18]  Marek Chrobak,et al.  SIGACT news online algorithms column 8 , 2005, SIGA.

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

[20]  Alexander Souza,et al.  The Expected Competitive Ratio for Weighted Completion Time Scheduling , 2004, STACS.

[21]  William J. Cook,et al.  Exact solutions to linear programming problems , 2007, Oper. Res. Lett..

[22]  Gerhard J. Woeginger,et al.  On-line bin packing — A restricted survey , 1995, Math. Methods Oper. Res..

[23]  Lyle A. McGeoch,et al.  A strongly competitive randomized paging algorithm , 1991, Algorithmica.

[24]  Jörg Rambau,et al.  Online-optimization of multi-elevator transport systems with reoptimization algorithms based on set-partitioning models , 2006, Discret. Appl. Math..

[25]  Neal Young,et al.  The K-Server Dual and Loose Competitiveness for Paging , 1991, On-Line Algorithms.

[26]  Wayne E. Smith.  Various optimizers for single‐stage production , 1956 .

[27]  Edward G. Coffman,et al.  Markov chains, computer proofs, and average-case analysis of best fit bin packing , 1993, STOC '93.

[28]  Alfred V. Aho,et al.  Principles of Optimal Page Replacement , 1971, J. ACM.

[29]  Hyung Lee-Kwang,et al.  Design and implementation of a fuzzy elevator group control system , 1998, IEEE Trans. Syst. Man Cybern. Part A.

[30]  David S. Johnson,et al.  Fast Algorithms for Bin Packing , 1974, J. Comput. Syst. Sci..

[31]  Yuval Rabani,et al.  Biased random walks, Lyapunov functions, and stochastic analysis of best fit bin packing , 1996, SODA '96.

[32]  Matthew Brand,et al.  Decision-Theoretic Group Elevator Scheduling , 2003, ICAPS.

[33]  Jana Koehler,et al.  An AI-Based Approach to Destination Control in Elevators , 2002, AI Mag..

[34]  Martin L. Puterman,et al.  Markov Decision Processes: Discrete Stochastic Dynamic Programming , 1994 .

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

[36]  Christos G. Cassandras,et al.  Design and implementation of an adaptive dispatching controller for elevator systems during uppeak traffic , 1998, IEEE Trans. Control. Syst. Technol..

[37]  Gerhard J. Woeginger,et al.  Online Algorithms , 1998, Lecture Notes in Computer Science.

[38]  Christos G. Cassandras,et al.  Optimal dispatching control for elevator systems during uppeak traffic , 1997, IEEE Trans. Control. Syst. Technol..

[39]  T. Lindvall.  Lectures on the Coupling Method , 1992 .

[40]  Shang-Hua Teng,et al.  Smoothed analysis of algorithms: why the simplex algorithm usually takes polynomial time , 2001, STOC '01.

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

[42]  Tobias Achterberg,et al.  SCIP: solving constraint integer programs , 2009, Math. Program. Comput..

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

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

[45]  Prakash V. Ramanan.  Average-Case Analysis of the Smart Next Fit Algorithm , 1989, Inf. Process. Lett..

[46]  D. T. Lee,et al.  A simple on-line bin-packing algorithm , 1985, JACM.

[47]  Benjamin Hiller,et al.  Real-Time Destination-Call Elevator Group Control on Embedded Microcontrollers , 2007, OR.

[48]  Jana Koehler,et al.  Online Synthese von Aufzugssteuerungen als Planungsproblem , 1999, Planen und Konfigurieren.

[49]  Peter J. Denning,et al.  Working Sets Past and Present , 1980, IEEE Transactions on Software Engineering.

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

[51]  Lutfi Al-Sharif,et al.  Elevator Traffic Handbook: Theory and Practice , 2003 .

[52]  Barun Chandra.  Does Randomization Help in On-Line Bin Packing? , 1992, Inf. Process. Lett..

[53]  David S. Johnson,et al.  Bounded Space On-Line Bin Packing: Best Is Better than First , 1991, SODA '91.

[54]  Susanne Albers,et al.  On paging with locality of reference , 2002, STOC '02.

[55]  Neal E. Young,et al.  On-Line Paging Against Adversarially Biased Random Inputs , 2000, J. Algorithms.

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

[57]  Sven Oliver Krumke,et al.  Real-Time Dispatching of Guided and Unguided Automobile Service Units with Soft Time Windows , 2002, ESA.

[58]  Moshe Shaked,et al.  Stochastic orders and their applications , 1994 .

[59]  Leon S. Lasdon,et al.  Optimization Theory of Large Systems , 1970 .

[60]  Edward G. Coffman,et al.  Approximation algorithms for bin packing: a survey , 1996 .

[61]  Tapio Tyni,et al.  Evolutionary bi-objective optimisation in the elevator car routing problem , 2006, Eur. J. Oper. Res..

[62]  Harri Ehtamo,et al.  Optimal control of double-deck elevator group using genetic algorithm , 2003 .

[63]  Susanne Albers,et al.  Online algorithms: a survey , 2003, Math. Program..

[64]  Allan Borodin,et al.  An optimal on-line algorithm for metrical task system , 1992, JACM.

[65]  Angelika Steger,et al.  A new average case analysis for completion time scheduling , 2002, STOC '02.

[66]  Raphael Rom,et al.  Average Case Analysis of Bounded Space Bin Packing Algorithms , 2007, Algorithmica.

[67]  Amos Fiat,et al.  Truly online paging with locality of reference , 1997, Proceedings 38th Annual Symposium on Foundations of Computer Science.

[68]  Eric Torng,et al.  A Unified Analysis of Paging and Caching , 1995, Proceedings of IEEE 36th Annual Foundations of Computer Science.

[69]  Jeffrey D. Ullman,et al.  Worst-Case Performance Bounds for Simple One-Dimensional Packing Algorithms , 1974, SIAM J. Comput..

[70]  Amos Fiat,et al.  Competitive Paging Algorithms , 1991, J. Algorithms.

[71]  Sven Oliver Krumke,et al.  The Online Dial-a-Ride Problem under Reasonable Load , 2000, CIAC.

[72]  Sven Oliver Krumke,et al.  Online Dial-a-Ride Problems: Minimizing the Completion Time , 2000, STACS.

[73]  J. Fourneau,et al.  Increasing Convex Monotone Markov Chains: Theory, Algorithm and Applications , 2005 .

[74]  Martin Grötschel,et al.  Online-Dispatching of Automobile Service Units , 2002, OR.

[75]  D. Daley.  Stochastically monotone Markov Chains , 1968 .

[76]  Andrew G. Barto,et al.  Elevator Group Control Using Multiple Reinforcement Learning Agents , 1998, Machine Learning.

[77]  Shunji Tanaka,et al.  Dynamic optimization of the operation of single-car elevator systems with destination hall call registration: Part II. The solution algorithm , 2005, Eur. J. Oper. Res..

[78]  Allan Borodin,et al.  Competitive paging with locality of reference , 1991, STOC '91.

[79]  Mihalis Yannakakis,et al.  Perfect Packing Theorems and the Average-Case Behavior of Optimal and Online Bin Packing , 2002, SIAM Rev..

[80]  Sven Oliver Krumke,et al.  Reoptimization gaps versus model errors in online-dispatching of service units for ADAC , 2006, Discret. Appl. Math..

[81]  Luca Becchetti,et al.  Modeling Locality: A Probabilistic Analysis of LRU and FWF , 2004, ESA.

[82]  Alejandro López-Ortiz,et al.  On Certain New Models for Paging with Locality of Reference , 2008, WALCOM.

[83]  Sandy Irani,et al.  Strongly competitive algorithms for paging with locality of reference , 1992, SODA '92.

[84]  Alejandro López-Ortiz,et al.  A Survey of Performance Measures for On-line Algorithms , 2005, SIGACT News.

[85]  Peter J. Denning,et al.  The working set model for program behavior , 1968, CACM.

[86]  P.W. Shor,et al.  The average-case analysis of some on-line algorithms for bin packing , 1984, Comb..

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

[88]  Kenny Qili Zhu,et al.  A reactive method for real time dynamic vehicle routing problem , 2000, Proceedings 12th IEEE Internationals Conference on Tools with Artificial Intelligence. ICTAI 2000.

[89]  Alistair Sinclair,et al.  Algorithms for Random Generation and Counting: A Markov Chain Approach , 1993, Progress in Theoretical Computer Science.

[90]  Weizhen Mao,et al.  Tight Worst-Case Performance Bounds for Next-k-Fit Bin Packing , 1993, SIAM J. Comput..

[91]  Paolo Toth,et al.  State-space relaxation procedures for the computation of bounds to routing problems , 1981, Networks.

[92]  Susanne Albers,et al.  Average-case analyses of first fit and random fit bin packing , 2000, SODA '98.