bbberghman / infof424-pcenters

INFOF424 Combinatorial Optimization Project

The p-Center Problem

Authors : Erica Berghman & Charles Hamesse

Implementation in Julia language combined with the JuMP package of two formulations of the p-Center Problem:

• The formulation proposed by Daskin (1995).
• The formulation proposed by Calik and Tansel (2013).

These formulations can be found in [1], pages 2992 and 2993 respectively.

All the information on this project can be found in report/INFO-F424-P.pdf.

Example run

julia main. jl −i INPUT −f FORMULATION −s SOLVER [−o OUTPUT] [−d DIVISOR] [−c INITIAL−CANDIDATE] [−v VERBOSE] [−h]

Where :

• INPUT is the input instance file (which has to respect the format of the ones in the instances folder),
• FORMULATION is either P1 or P3,
• SOLVER is either Cbc or Gurobi,
• OUTPUT is the output file, if not specified the output will be stdout
• DIVISOR is the divisor used to compute valid inequalities (leaving blank does not add any VI)
• INITIAL-CANDIDATE is the heuristic method for the hot start (random or 2approx)
• VERBOSE is the verbosity level, 0 or 1.

References

[1] Calik H, Tansel BC (2013) Double bound method for solving the p-center location problem. Computers & Operations Research 40 pp.2991–2999

[2] Daskin Mark S. (1995) Network and discrete location: models, algorithms, and applications, Wiley Interscience, New York

[3] Wolsey Laurence A. (1998) Integer Programming. Wiley Interscience, New York