Journal of Global Optimization
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A System for Distance Studies and Applications of Metaheuristics
Journal of Global Optimization - Tập 35 - Trang 637-651 - 2006
The efficiency of metaheuristics depends on parameters. Often this relation is defined by statistical simulation and have many local minima. Therefore, methods of stochastic global optimization are needed to optimize the parameters. The traditional numerical analysis considers optimization algorithms that guarantee some accuracy for all functions to be optimized. This includes the exact algorithms......
Simple linkage: Analysis of a threshold-accepting global optimization method
Journal of Global Optimization - Tập 9 - Trang 95-111 - 1996
In a recent paper the authors introduced an infinite class of global optimization algorithms based upon random sampling from the feasible region and local searches started from selected sample points, based upon an acceptance/rejection criterion. All of the algorithms of that class possess strong theoretical properties. Here we analyze a member of that family, which, although being significantly s......
Self-adaptive velocity particle swarm optimization for solving constrained optimization problems
Journal of Global Optimization - Tập 41 - Trang 427-445 - 2007
Particle swarm optimization (PSO) is originally developed as an unconstrained optimization technique, therefore lacks an explicit mechanism for handling constraints. When solving constrained optimization problems (COPs) with PSO, the existing research mainly focuses on how to handle constraints, and the impact of constraints on the inherent search mechanism of PSO has been scarcely explored. Motiv......
Optimal learning with a local parametric belief model
Journal of Global Optimization - Tập 63 - Trang 401-425 - 2015
We are interested in maximizing smooth functions where observations are noisy and expensive to compute, as might arise in computer simulations or laboratory experimentations. We derive a knowledge gradient policy, which chooses measurements which maximize the expected value of information, while using a locally parametric belief model that uses linear approximations with radial basis functions. Th......
Curvature-constrained directional-cost paths in the plane
Journal of Global Optimization - Tập 53 - Trang 663-681 - 2011
This paper looks at the problem of finding the minimum cost curvature-constrained path between two directed points where the cost at every point along the path depends on the instantaneous direction. This generalises the results obtained by Dubins for curvature-constrained paths of minimum length, commonly referred to as Dubins paths. We conclude that if the reciprocal of the directional-cost func......
Augmented Lagrangian Duality and Nondifferentiable Optimization Methods in Nonconvex Programming
Journal of Global Optimization - - 2002
In this paper we present augmented Lagrangians for nonconvex minimization problems with equality constraints. We construct a dual problem with respect to the presented here Lagrangian, give the saddle point optimality conditions and obtain strong duality results. We use these results and modify the subgradient and cutting plane methods for solving the dual problem constructed. Algorithms proposed ......
On the hierarchical structure of Pareto critical sets
Journal of Global Optimization - Tập 73 - Trang 891-913 - 2019
In this article we show that the boundary of the Pareto critical set of an unconstrained multiobjective optimization problem (MOP) consists of Pareto critical points of subproblems where only a subset of the set of objective functions is taken into account. If the Pareto critical set is completely described by its boundary (e.g., if we have more objective functions than dimensions in decision spac......
A bisection-extreme point search algorithm for optimizing over the efficient set in the linear dependence case
Journal of Global Optimization - Tập 3 - Trang 95-111 - 1993
The algorithms and algorithmic ideas currently available for globally optimizing linear functions over the efficient sets of multiple objective linear programs either use nonstandard subroutines or cannot yet be implemented for lack of sufficient development. In this paper a Bisection-Extreme Point Search Algorithm is presented for globally solving a large class of such problems. The algorithm fin......
Semidefinite relaxation bounds for bi-quadratic optimization problems with quadratic constraints
Journal of Global Optimization - Tập 49 - Trang 293-311 - 2010
This paper studies the relationship between the so-called bi-quadratic optimization problem and its semidefinite programming (SDP) relaxation. It is shown that each r-bound approximation solution of the relaxed bi-linear SDP can be used to generate in randomized polynomial time an
$${\mathcal{O}(r)}$$
-ap......
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