In this thesis we study constraint relaxations of various nonlinear programming (NLP) algorithms in order to improve their performance. For both stochastic and deterministic algorithms, we study the relationship between the expected time to find a feasible solution and the constraint relaxation level, build an exponential model based on this relationship, and develop a constraint relaxation schedule in such a way that the total time spent to find a feasible solution for all the relaxation levels is of the same order of magnitude as the time spent for finding a solution of similar quality using the last relaxation level alone. When the objective and constraint functions are stochastic, we define new criteria of constraint satisfaction and similar constraint relaxation schedules. Similar to the case when functions are deterministic, we build an exponential model between the expected time to find a feasible solution and the associated constraint relaxation level. We develop an anytime constraint relaxation schedule in such a way that the total time spent to solve a problem for all constraint relaxation levels is of the same order of magnitude as the time spent for finding a feasible solution using the last relaxation level alone. Finally, we study the asymptotic
|
4828
|
Genetic Algorithms
– Goldberg
- 1989
|
|
2322
|
Stochastic relaxation, Gibbs distributions and the Bayesian restoration of images
– Geman, Geman
- 1984
|
|
2172
|
Optimization by simulated annealing
– Kirkpatrick, Gelatt, et al.
- 1983
|
|
1316
|
Genetic Algorithms + Data Structures = Evolution Programs. AI Series
– Michalewicz
- 1992
|
|
686
|
and Nonlinear Programming
– Luenberger, Linear
- 1984
|
|
541
|
Numerical Optimization
– Nocedal, Wright
|
|
354
|
Tabu search
– Glover, Laguna
- 1995
|
|
347
|
Global Optimization Using Interval Analysis
– HANSEN, WALSTER
- 2004
|
|
279
|
Constrained Optimization and Lagrange Multiplier Methods. Athena Scientific
– Bertsekas
- 1996
|
|
268
|
An overview of evolutionary algorithms for parameter optimization
– Back, Schwefel
- 1993
|
|
259
|
Primal-Dual Interior-Point Methods
– WRIGHT
- 1997
|
|
195
|
DomainIndependent Extensions to GSAT: Solving Large Structured Satisfiability
– Selman, Kautz
- 1993
|
|
188
|
Local Search Strategies for Satisfiability Testing
– Selman, Kautz, et al.
- 1995
|
|
175
|
Random perturbations of dynamical systems
– Freidlin, Wentzell
- 1984
|
|
172
|
A Survey of Evolution Strategies
– Back, Hoffmeister, et al.
- 1991
|
|
168
|
The Breakout Method For Escaping From Local Minima
– Morris
- 1993
|
|
164
|
The reactive tabu search
– Battiti, Tecchiolli
- 1994
|
|
157
|
Modeling genetic algorithms with Markov chains
– Nix, Vose
- 1992
|
|
156
|
Evolutionary Algorithms for Constrained Parameter Optimization Problems
– Michalewicz, Schoenauer
- 1996
|
|
144
|
Global optimization: deterministic approaches, 2nd ed
– Horst, Tuy
- 1993
|
|
140
|
Partitioning procedures for solving mixed-variables programming problems
– Benders
- 1962
|
|
137
|
Zilinskas. Global optimization
– Törn
- 1989
|
|
129
|
An Introduction to Simulated Evolutionary Optimization
– Fogel
- 1994
|
|
128
|
Some Guidelines for Genetic Algorithms with Penalty Functions
– Richardson, Palmer, et al.
- 1989
|
|
128
|
Convergence analysis of canonical genetic algorithms
– Rudolph
- 1994
|
|
94
|
MIMIC: Finding optima by estimating probability densities
– Bonet, Jr, et al.
- 1997
|
|
88
|
A genetic algorithm for the set covering problem
– Beasley, Chu
- 1996
|
|
79
|
On the use of non-stationary penalty functions to solve nonlinear constrained optimization problems with GAs
– Joines, Houck
- 1994
|
|
71
|
Generalized Benders decomposition
– Geoffrion
- 1972
|
|
70
|
Pardalos, Handbook of global optimization
– Horst, M
- 1995
|
|
70
|
1993�. Using Genetic Algorithms in Engineering Design Optimization with Non�linear Constraints
– Powell�, Skolnick
|
|
67
|
Minimization by random search techniques
– Solis, Wets
- 1981
|
|
66
|
Interior methods for constrained optimization
– Wright
- 1992
|
|
65
|
Real-coded genetic algorithms and interval schemata
– Eshelman, Schaffer
|
|
65
|
Lagrangean relaxation for integer programming
– Geoffrion
- 1974
|
|
64
|
An outer approximation algorithm for a class of mixed integer nonlinear programs
– Duran, Grossmann
- 1986
|
|
61
|
Handling constraints in genetic algorithms
– Michalewicz, Janikow
- 1991
|
|
58
|
Sequential quadratic programming
– BOGGS, TOLLE
- 1995
|
|
57
|
Co�evolutionary Constraint Satisfaction. In Pro� ceedings of the 3rd Conference on Parallel Problem Solving from Na� ture� New York� Springer�Verlag� 46�55
– Paredis�
- 1993
|
|
55
|
An interior point algorithm for large scale nonlinear programming
– Byrd, Hribar, et al.
- 1999
|
|
53
|
1993�. Shall We Repair� Genetic Algo� rithms� Combinatorial Optimization� and Feasibility Constraints
– Orvosh�, Davis
|
|
49
|
A discrete Lagrangian-based global search method for solving satisfiability problems
– Shang, Wah
- 1998
|
|
48
|
An Empirical Comparison of Seven Iterative and Evolutionary Function Optimization Heuristics
– Baluja
- 1995
|
|
48
|
1994�. Constrained Optimization via Genetic Algorithms
– Lai, Qi
|
|
46
|
Genocop III� A Co�evolutionary Al� gorithm for Numerical Optimization Problems with Nonlinear Constraints
– Michalewicz�, Nazhiyath�
- 1995
|
|
45
|
User’s guide for snopt 5.3: A fortran package for large-scale nonlinear programming
– Gill, Murray, et al.
- 1997
|
|
43
|
Learning evaluation functions for global optimization and boolean satisfiability
– Boyan, Moore
- 1998
|
|
42
|
Constrained ga optimization
– Schoenauer, Xanthakis
- 1993
|
|
41
|
a computer code for the multistage stochastic linear programming problem
– MSLIP
- 1990
|
|
40
|
Constrained Global Optimization: Algorithms and Applications
– PARDALOS, ROSEN
- 1987
|
|
