Assessing the Finite-Time Performance of Local Search Algorithms

Identifying a globally optimal solution for an intractable discrete optimization problem is often cost prohibitive. Therefore, solutions that are within a predetermined threshold are often acceptable in practice. This dissertation introduces the concept of B-acceptable solutions where B is a predetermined threshold for the objective function value. It is difficult to assess a priori the effectiveness of local search algorithms, which makes the process of choosing parameters to improve their performance difficult. This dissertation introduces the B-acceptable solution probability in terms of B-acceptable solutions as a finite-time performance measure for local search algorithms. The B-acceptable solution probability reflects how effectively an algorithm has performed to date and how effectively an algorithm can be expected to perform in the future. The B-acceptable solution probability is also used to obtain necessary asymptotic convergence (with probability one) conditions. Upper and lower bounds for the B-acceptable solution probability are presented. These expressions assume particularly simple forms when applied to specific local search strategies such as Monte Carlo search and threshold accepting. Moreover, these expressions provide guidelines on how to manage the execution of local search algorithm runs. Computational experiments are reported to estimate the probability of reaching a B-acceptable solution for a fixed number of iterations. Logistic regression is applied as a tool to estimate the probability of reaching a B-acceptable solution for values of B close to the objective function value of a globally optimal solution as well as to estimate this objective function value. Computational experiments are reported with logistic regression for pure local search, simulated annealing and threshold accepting applied to instances of the TSP with known optimal solutions.

Name thesis:degree_name

Ph. D.

Level thesis:degree_level

doctoral

Discipline thesis:degree_discipline

Industrial and Systems Engineering

Department dc:contributor.department

Industrial and Systems Engineering

Grantor dc:publisher

Virginia Tech

Year dc:date.issued

2001

Author dc:creator

• Henderson, Darrall

Chairs dc:contributor.committeechair

• Jacobson, Sheldon H.
• Koelling, C. Patrick

Committee members dc:contributor.committeemember

• Wakefield, Ronald R.
• Bish, Ebru K.
• Sherali, Hanif D.

• hill climbing algorithms
• heuristics
• finite-time performance
• discrete optimization
• combinatorial optimization
• simulated annealing
• convergence
• local search

Statement dc:rights

• In Copyright

Licence dc:rights.uri

• http://rightsstatements.org/vocab/InC/1.0/

Dc Identifier Other

etd-04172001-135808

OAI identifier oai:identifier

oai:vtechworks.lib.vt.edu:10919/26926