Heuristic algorithms for the inverse mixed integer linear programming problem

The recent development in inverse optimization, in particular the extension from the inverse linear programming problem to the inverse mixed integer linear programming problem (InvMILP), provides more powerful modeling tools but also presents more challenges to the design of efficient solution techniques. The only reported InvMILP algorithm, referred to as AlgInvMILP, although finitely converging to global optimality, suffers two limitations that greatly restrict its applicability: it is time consuming and does not generate a feasible solution except for the optimal one. This paper presents heuristic algorithms that are designed to be implemented and executed in parallel with AlgInvMILP in order to alleviate and overcome its two limitations. Computational experiments show that implementing the heuristic algorithm on one auxiliary processor in parallel with AlgInvMILP on the main processor significantly improves its computational efficiency, in addition to providing a series of improving feasible upper bound solutions. The additional speedup of parallel implementation on two or more auxiliary processors appears to be incremental, but the upper bound can be improved much faster.

[1]  W. Menke.  Geophysical data analysis : discrete inverse theory , 1984 .

[2]  Yong He,et al.  Constrained Inverse Minimum Spanning Tree Problems under the Bottleneck-Type Hamming Distance , 2006, J. Glob. Optim..

[3]  Lizhi Wang,et al.  Cutting plane algorithms for the inverse mixed integer linear programming problem , 2009, Oper. Res. Lett..

[4]  András Faragó,et al.  Inverse Optimization in High-speed Networks , 2003, Discret. Appl. Math..

[5]  Ravindra K. Ahuja,et al.  Inverse Optimization , 2001, Oper. Res..

[6]  Chao Yang,et al.  A column generation method for inverse shortest path problems , 1995, Math. Methods Oper. Res..

[7]  A. Tarantola.  Inverse problem theory : methods for data fitting and model parameter estimation , 1987 .

[8]  S. Awerbuch.  Portfolio-Based Electricity Generation Planning: Policy Implications For Renewables And Energy Security , 2006 .

[9]  Robert B. Dial,et al.  MINIMAL-REVENUE CONGESTION PRICING PART II: AN EFFICIENT ALGORITHM FOR THE GENERAL CASE , 2000 .

[10]  Clemens Heuberger,et al.  Inverse Combinatorial Optimization: A Survey on Problems, Methods, and Results , 2004, J. Comb. Optim..

[11]  O. Rho,et al.  Dual-point design of transonic airfoils using the hybrid inverse optimization method , 1997 .

[12]  Jianzhon Zhang,et al.  Two general methods for inverse optimization problems , 1999 .

[13]  L. Wein,et al.  An Inverse-Optimization-Based Auction Mechanism to Support a Multi-Attribute Rfq Process , 2001 .

[14]  Robert B. Dial,et al.  Minimal-revenue congestion pricing part I: A fast algorithm for the single-origin case , 1999 .

[15]  Mao-cheng Cai,et al.  The Complexity Analysis of the Inverse Center Location Problem , 1999, J. Glob. Optim..

[16]  Philippe L. Toint,et al.  On an instance of the inverse shortest paths problem , 1992, Math. Program..

[17]  V. Chandru,et al.  Inverse Optimization: An Application to the Capacitated Plant Location Problem , 1981 .

[18]  C. Hurkmans,et al.  High-dose simultaneously integrated breast boost using intensity-modulated radiotherapy and inverse optimization. , 2006, International journal of radiation oncology, biology, physics.

[19]  Thorsten Koch,et al.  Konrad-zuse-zentrum F ¨ Ur Informationstechnik Berlin Miplib 2003 , 2022 .

[20]  T. Moser.  Shortest path calculation of seismic rays , 1991 .

[21]  M. Mazumdar,et al.  Using a System Model to Decompose the Effects of Influential Factors on Locational Marginal Prices , 2007, IEEE Transactions on Power Systems.

[22]  Lawrence M. Wein,et al.  An Inverse-Optimization-Based Auction Mechanism to Support a Multiattribute RFQ Process , 2003, Manag. Sci..