A General D.C. Approach to Location Problems

We show that many important location problems (Weber’s problem with attraction and repulsion, constrained multisource and multifacility problems,…) can be formulated as d.c. optimization problems in low-dimensional spaces and thereby can be solved practically by recently developed d.c. optimization techniques. Two typical algorithms are described in detail.

[1]  H. Tuy.  A General Deterministic Approach to Global Optimization VIA D.C. Programming , 1986 .

[2]  Reuven Chen.  Solution of minisum and minimax location–allocation problems with Euclidean distances , 1983 .

[3]  Faiz A. Al-Khayyal,et al.  Global optimization of a nonconvex single facility location problem by sequential unconstrained convex minimization , 1992, J. Glob. Optim..

[4]  Hoang Tuy,et al.  The complementary convex structure in global optimization , 1992, J. Glob. Optim..

[5]  Hoang Tuy,et al.  D.C. Optimization: Theory, Methods and Algorithms , 1995 .

[6]  Phan Thien Thach,et al.  The design centering problem as a D.C. programming problem , 1988, Math. Program..

[7]  H. Tuy.  Global Minimization of a Difference of Two Convex Functions , 1987 .

[8]  Stephen W. Director,et al.  A Design Centering Algorithm for Nonconvex Regions of Acceptability , 1982, IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems.

[9]  Hoang Tuy,et al.  Polyhedral annexaton, dualization and dimension reduction technique in global optimization , 1991, J. Glob. Optim..

[10]  Pierre Hansen,et al.  The Minisum and Minimax Location Problems Revisited , 1985, Oper. Res..

[11]  Christodoulos A Floudas,et al.  Global minimum potential energy conformations of small molecules , 1994, J. Glob. Optim..

[12]  B. Jaumard,et al.  WEBER'S PROBLEM WITH ATTRACTION AND REPULSION , 1991 .

[13]  Jacques-François Thisse,et al.  An Algorithm for a Constrained Weber Problem , 1982 .

[14]  Reuven Chen,et al.  Conditional Minisum and Minimax Location-Allocation Problems in Euclidean Space , 1988, Transp. Sci..

[15]  G. O. Wesolowsky,et al.  The Weber Problem On The Plane With Some Negative Weights , 1991 .

[16]  Nimrod Megiddo,et al.  On the Complexity of Some Common Geometric Location Problems , 1984, SIAM J. Comput..

[17]  Jean-Jacques Strodiot,et al.  Computing a global optimal solution to a design centering problem , 1992, Math. Program..

[18]  Aimo A. Törn,et al.  Global Optimization , 1999, Science.

[19]  K. Rosing.  An Optimal Method for Solving the (Generalized) Multi-Weber Problem , 1992 .

[20]  F. Plastria.  GBSSS: The generalized big square small square method for planar single-facility location , 1992 .

[21]  P. Loridan,et al.  Approximation of solutions for location problems , 1988 .

[22]  Phan Thien Thach.  D.c. sets, d.c. functions and nonlinear equations , 1993, Math. Program..

[23]  Hoang Tuy,et al.  On nonconvex optimization problems with separated nonconvex variables , 1992, J. Glob. Optim..

[24]  Mahmut Parlar,et al.  Technical Note - Algorithms for Weber Facility Location in the Presence of Forbidden Regions and/or Barriers to Travel , 1994, Transp. Sci..

[25]  Christodoulos A. Floudas,et al.  A Global Optimization Method For Weber’s Problem With Attraction And Repulsion , 1994 .

[26]  Hoang Tuy,et al.  On the global minimization of a convex function under general nonconvex constraints , 1988 .