Title page for ETD etd-04172001-135808


Type of Document Dissertation
Author Henderson, Darrall
Author's Email Address darrall@stanfordalumni.org
URN etd-04172001-135808
Title Assessing the Finite-Time Performance of Local Search Algorithms
Degree PhD
Department Industrial and Systems Engineering
Advisory Committee
Advisor Name Title
Jacobson, Sheldon H. Committee Co-Chair
Koelling, Charles Patrick Committee Co-Chair
Bish, Ebru K. Committee Member
Sherali, Hanif D. Committee Member
Wakefield, Ronald R. Committee Member
Keywords
  • hill climbing algorithms
  • heuristics
  • finite-time performance
  • discrete optimization
  • combinatorial optimization
  • simulated annealing
  • convergence
  • local search
Date of Defense 2001-05-13
Availability unrestricted
Abstract
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.

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