Heuristics for integer programs
Year: 2007
Type: dissertation
Abstract: Many real world optimization problems can be formulated as mixed integer programs. In general, finding optimal, or even feasible, solutions to such problems is computationally intractable. For this reason, there is interest in developing heuristic algorithms for these problems.
In this thesis we present three new mixed integer program heuristic algorithms.
The first, PIVOT AND GOMORY CUT (PGC), is a feasibility heuristic, namely one that tries only to find a feasible solution. PGC integrates Gomory cuts into the bounded variable revised simplex pivoting framework similar to that used in the classic PIVOT AND COMPLEMENT heuristic of Balas and Martin.
The second, DISTANCE INDUCED NEIGHBOURHOOD SEARCH (DINS), is an improvement heuristic, namely one that starts with a feasible solution and tries to improve it as much as possible. DINS performs neighbourhood search at different nodes of the mixed integer program search tree where the mixed integer program search tree is the tree generated by either a branch-and-bound or a branch-and-cut solver. DINS defines the neighbourhoods by modeling a distance metric between the current mixed integer feasible solution and the relaxation solution at the node of the mixed integer program search tree.
The third, NEIGHBOURHOOD PIVOT AND GOMORY CUT (NPGC), is a 'find-and-improve' heuristic. Such a heuristic tries to find the best possible feasible solution. NPGC, an extention of PGC, uses Gomory cuts to define neighbourhoods, searches the neighbourhoods for feasible solutions, and improves any found feasible solutions by applying the LOCAL BRANCHING heuristic of Fischetti and Lodi.
We also present a new class of hard 0-1 integer programs for which instances are easy to generate pseudo-randomly. These pseudo-randomly generated instances are useful in comparing the performance of different heuristics.
DOI: 10.7939/r3-h0wa-jn47
Author: Ghosh, Shubhashis
Institution: University of Alberta
Language: English
Subfield: Numerical Analysis
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2522711078