Computer graphical solutions of constrained minimax location problems

Abstract This paper introduces interactive computer graphical optimization to location analysis. An interactive graphical program is described for solving single-facility minimax location problems with nonconvex feasible regions. The core of the program is a well-defined algorithm with a simple, human-executed pattern recognition task as one of its steps. Globally optimal solutions are assured under very mild assumptions on human performance, and the program is reasonably fast.

[1]  J. B. Schneider,et al.  Planning transportation terminal systems in urban regions: A man-machine interactive problem-solving approach , 1972 .

[2]  G. O. Wesolowsky.  Rectangular Distance Location under the Minimax Optimality Criterion , 1972 .

[3]  Richard Walker.  The Captains' Meeting: Finding an Optimal Rendezvous for n Ships , 1978 .

[4]  D. Hearn,et al.  Geometrical Solutions for Some Minimax Location Problems , 1972 .

[5]  Michael Ian Shamos,et al.  Closest-point problems , 1975, 16th Annual Symposium on Foundations of Computer Science (sfcs 1975).

[6]  K. Nair,et al.  Optimal location of a single service center of certain types , 1971 .

[7]  Richard L. Francis,et al.  Letter to the Editor - Some Aspects of a Minimax Location Problem , 1967, Oper. Res..

[8]  M. Rao,et al.  The m-Center Problem: Minimax Facility Location , 1977 .

[9]  T. Tsuda.  Interactive search for the global maximum of a function of many variables , 1977 .

[10]  Timothy J. Lowe,et al.  A subgradient algorithm for certain minimax and minisum problems , 1978, Math. Program..

[11]  Matthias H. Rapp,et al.  Man-machine interactive transit system planning , 1972 .

[12]  V. Klee,et al.  Combinatorial Geometry in the Plane , 1964 .

[13]  R. L. Francis,et al.  A Network Flow Solution to a Multifacility Minimax Location Problem Involving Rectilinear Distances , 1974 .

[14]  Timothy J. Lowe,et al.  Convex Location Problems on Tree Networks , 1976, Oper. Res..

[15]  A. J. Goldman.  Minimax Location of a Facility in a Network , 1972 .

[16]  Patrick D. Krolak,et al.  A man-machine approach toward solving the traveling salesman problem , 1970, DAC '70.

[17]  M H Rapp,et al.  THE PLANNING OF NODE ORIENTED TRANSIT SYSTEMS. AN APPLICATION OF MAN-MACHINE INTERACTIVE PROBLEM SOLVING , 1970 .

[18]  Victor B. Godin,et al.  Interactive Scheduling: Historical Survey and State of the Art , 1978 .

[19]  Jerry B. Schneider,et al.  Locating and sizing park-ride lots with interactive computer graphs , 1976 .

[20]  D. Hearn,et al.  Minimax Multifacility Location with Euclidean Distances , 1976 .

[21]  Patrick D. Krolak,et al.  A Man-Machine Approach Toward Solving the Generalized Truck-Dispatching Problem , 1972 .

[22]  R. Courant,et al.  What Is Mathematics , 1943 .

[23]  D. Hearn,et al.  Letter to the Editor—A Note on a Minimax Location Problem , 1973 .