Pseudo-Cut Strategies for Global Optimization

2011 ◽  
Vol 2 (4) ◽  
pp. 1-12 ◽  
Author(s):  
Fred Glover ◽  
Leon Lasdon ◽  
John Plummer ◽  
Abraham Duarte ◽  
Rafael Marti ◽  
...  
Keyword(s):  
Global Optimization ◽  
Tabu Search ◽  
Nonconvex Optimization ◽  
Cutting Planes ◽  
Solution Process ◽  
Global Optimum ◽  
Fundamental Idea ◽  
Feasible Solutions

Motivated by the successful use of a pseudo-cut strategy within the setting of constrained nonlinear and nonconvex optimization in Lasdon et al. (2010), we propose a framework for general pseudo-cut strategies in global optimization that provides a broader and more comprehensive range of methods. The fundamental idea is to introduce linear cutting planes that provide temporary, possibly invalid, restrictions on the space of feasible solutions, as proposed in the setting of the tabu search metaheuristic in Glover (1989), in order to guide a solution process toward a global optimum, where the cutting planes can be discarded and replaced by others as the process continues. These strategies can be used separately or in combination, and can also be used to supplement other approaches to nonlinear global optimization. Our strategies also provide mechanisms for generating trial solutions that can be used with or without the temporary enforcement of the pseudo-cuts.

Pseudo-Cut Strategies for Global Optimization

2012 ◽  
pp. 188-198
Author(s):  
Fred Glover ◽  
Leon Lasdon ◽  
John Plummer ◽  
Abraham Duarte ◽  
Rafael Marti ◽  
...  
Keyword(s):  
Global Optimization ◽  
Tabu Search ◽  
Nonconvex Optimization ◽  
Cutting Planes ◽  
Solution Process ◽  
Global Optimum ◽  
Fundamental Idea ◽  
Feasible Solutions

Motivated by the successful use of a pseudo-cut strategy within the setting of constrained nonlinear and nonconvex optimization in Lasdon et al. (2010), we propose a framework for general pseudo-cut strategies in global optimization that provides a broader and more comprehensive range of methods. The fundamental idea is to introduce linear cutting planes that provide temporary, possibly invalid, restrictions on the space of feasible solutions, as proposed in the setting of the tabu search metaheuristic in Glover (1989), in order to guide a solution process toward a global optimum, where the cutting planes can be discarded and replaced by others as the process continues. These strategies can be used separately or in combination, and can also be used to supplement other approaches to nonlinear global optimization. Our strategies also provide mechanisms for generating trial solutions that can be used with or without the temporary enforcement of the pseudo-cuts.

scholarly journals Global optimization based on active preference learning with radial basis functions

2020 ◽  
Author(s):  
Alberto Bemporad ◽  
Dario Piga
Keyword(s):  
Global Optimization ◽  
Objective Function ◽  
Decision Maker ◽  
Optimization Problems ◽  
Global Optimum ◽  
Bayesian Optimization ◽  
Preference Learning ◽  
Global Optimizer ◽  
Radial Basis ◽  
Decision Vector

AbstractThis paper proposes a method for solving optimization problems in which the decision-maker cannot evaluate the objective function, but rather can only express a preference such as “this is better than that” between two candidate decision vectors. The algorithm described in this paper aims at reaching the global optimizer by iteratively proposing the decision maker a new comparison to make, based on actively learning a surrogate of the latent (unknown and perhaps unquantifiable) objective function from past sampled decision vectors and pairwise preferences. A radial-basis function surrogate is fit via linear or quadratic programming, satisfying if possible the preferences expressed by the decision maker on existing samples. The surrogate is used to propose a new sample of the decision vector for comparison with the current best candidate based on two possible criteria: minimize a combination of the surrogate and an inverse weighting distance function to balance between exploitation of the surrogate and exploration of the decision space, or maximize a function related to the probability that the new candidate will be preferred. Compared to active preference learning based on Bayesian optimization, we show that our approach is competitive in that, within the same number of comparisons, it usually approaches the global optimum more closely and is computationally lighter. Applications of the proposed algorithm to solve a set of benchmark global optimization problems, for multi-objective optimization, and for optimal tuning of a cost-sensitive neural network classifier for object recognition from images are described in the paper. MATLAB and a Python implementations of the algorithms described in the paper are available at http://cse.lab.imtlucca.it/~bemporad/glis.

scholarly journals An Algorithm for Global Optimization Inspired by Collective Animal Behavior

2012 ◽  
Vol 2012 ◽  
pp. 1-24 ◽  
Author(s):  
Erik Cuevas ◽  
Mauricio González ◽  
Daniel Zaldivar ◽  
Marco Pérez-Cisneros ◽  
Guillermo García
Keyword(s):  
Global Optimization ◽  
Animal Behavior ◽  
Food Source ◽  
Collective Motion ◽  
Global Optimum ◽  
Migration Routes ◽  
Collective Behaviors ◽  
Biological Laws ◽  
Harvesting Efficiency ◽  
Collective Animal Behavior

A metaheuristic algorithm for global optimization called the collective animal behavior (CAB) is introduced. Animal groups, such as schools of fish, flocks of birds, swarms of locusts, and herds of wildebeest, exhibit a variety of behaviors including swarming about a food source, milling around a central locations, or migrating over large distances in aligned groups. These collective behaviors are often advantageous to groups, allowing them to increase their harvesting efficiency, to follow better migration routes, to improve their aerodynamic, and to avoid predation. In the proposed algorithm, the searcher agents emulate a group of animals which interact with each other based on the biological laws of collective motion. The proposed method has been compared to other well-known optimization algorithms. The results show good performance of the proposed method when searching for a global optimum of several benchmark functions.

On Global Feasible Search for Global Design Optimization With Application to Generalized Polynomial Models

1992 ◽  
Author(s):  
Chihsiung Lo ◽  
Panos Y. Papalambros
Keyword(s):  
Global Optimization ◽  
Design Optimization ◽  
Model Transformation ◽  
Special Problem ◽  
Search Algorithms ◽  
Deterministic Global Optimization ◽  
Generalized Polynomial ◽  
Polynomial Models ◽  
Feasible Solutions ◽  
Global Design Optimization

Abstract A powerful idea for deterministic global optimization is the use of global feasible search, namely, algorithms that guarantee finding feasible solutions of nonconvex problems or prove that none exists. In this article, a set of conditions for global feasible search algorithms is established. The utility of these conditions is demonstrated on two algorithms that solve special problem classes globally. Also, a new model transformation is shown to convert a generalized polynomial problem into one of the special classes above. A flywheel design example illustrates the approach. A sequel article provides further computational details and design examples.

scholarly journals Stable scheduling of single machine with probabilistic parameters

2017 ◽  
Vol 65 (2) ◽  
pp. 219-231 ◽  
Author(s):  
W. Bożejko ◽  
P. Rajba ◽  
M. Wodecki
Keyword(s):  
Tabu Search ◽  
Single Machine ◽  
Random Variables ◽  
Global Optimum ◽  
Total Weighted Tardiness ◽  
Independent Random Variables ◽  
Stochastic Version ◽  
Weighted Tardiness ◽  
Deterministic Problem ◽  
Erlang Distributions

Abstract We consider a stochastic variant of the single machine total weighted tardiness problem jobs parameters are independent random variables with normal or Erlang distributions. Since even deterministic problem is NP-hard, it is difficult to find global optimum for large instances in the reasonable run time. Therefore, we propose tabu search metaheuristics in this work. Computational experiments show that solutions obtained by the stochastic version of metaheuristics are more stable (i.e. resistant to data disturbance) than solutions generated by classic, deterministic version of the algorithm.

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