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This paper surveys several applications of biased random-key genetic algorithms (BRKGA) in optimization problems that arise in telecommunications. We first review the basic concepts of BRKGA. This is followed by a description of BRKGA-based heuristics for routing in IP networks, design of survivable IP networks, redundant server location for content distribution, regenerator location in optical networks,...
We study a simple, yet unconventional approach to the global optimization of unconstrained nonlinear least-squares problems. Non-convexity of the sum of least-squares objective in parameter estimation problems may often lead to the presence of multiple local minima. Here, we focus on the spatial branch-and-bound algorithm for global optimization and experiment with one of its implementations, BARON...
A standard quadratic optimization problem (StQP) consists of finding the largest or smallest value of a (possibly indefinite) quadratic form over the standard simplex which is the intersection of a hyperplane with the positive orthant. This NP-hard problem has several immediate real-world applications like the Maximum Clique Problem, and it also occurs in a natural way as a subproblem in quadratic...
In this paper, we consider a dynamic Lagrangian dual optimization procedure for solving mixed-integer 0–1 linear programming problems. Similarly to delayed relax-and-cut approaches, the procedure dynamically appends valid inequalities to the linear programming relaxation as induced by the Reformulation-Linearization Technique (RLT). A Lagrangian dual algorithm that is augmented with a primal solution...
This paper describes a generalized variable neighborhood search heuristic for the Capacitated Vehicle Routing Problem with Stochastic Service Times, in which the service times at vertices are stochastic. The heuristic is tested on randomly generated instances and compared with two other heuristics and with an alternative solution strategy. Computational results show the superiority and effectiveness...
Linear programming with linear complementarity constraints (LPLCC) is an area of active research in Optimization, due to its many applications, algorithms, and theoretical existence results. In this paper, a number of formulations for important nonconvex optimization problems are first reviewed. The most relevant algorithms for computing a complementary feasible solution, a stationary point, and a...
Generalized Order-Value Optimization (GOVO) problems involve functions whose evaluation depends on order relations on some representation functional set. We give examples of GOVO problems that may be analyzed in the context of Piecewise-Smooth Optimization. Generalizations of algorithms that have been proved to be effective for proving special classes of GOVO problems are introduced. The case of Low...
In this paper, we address the global optimization of functions subject to bound and linear constraints without using derivatives of the objective function. We investigate the use of derivative-free models based on radial basis functions (RBFs) in the search step of direct-search methods of directional type. We also study the application of algorithms based on difference of convex (d.c.) functions...
We consider the semi-infinite optimization problem: $$f^*:=\min_{\mathbf{x}\in\mathbf{X}} \bigl\{f(\mathbf{x}):g(\mathbf{x},\mathbf{y}) \leq 0, \forall\mathbf{y}\in\mathbf {Y}_\mathbf{x}\bigr\},$$ where f,g are polynomials and X⊂ℝn as well as Yx⊂ℝp, x∈X, are compact basic semi-algebraic sets. To approximate f∗ we proceed in two steps. First, we use the “joint+marginal” approach of Lasserre...
Discretized formulations have proved to be useful for modeling combinatorial optimizations. The main focus of this work is on how to strengthen the linear programming relaxation of a given discretized formulation. More precisely, we will study and strengthen subproblems that arise in these formulations. In one case we will focus on the so-called knapsack reformulation which is based on viewing these...
In this paper, we deal with the cost allocation problem arising in an inventory transportation system with a single item and multiple agents that place joint orders using an EOQ policy. In our problem, the fixed-order cost of each agent is the sum of a first component (common to all agents) plus a second component which depends on the distance from the agent to the supplier. We assume that agents...
In this work we show some relations between ε-efficiency sets obtained through well-known approximate solution concepts of vector optimization problems. In particular, we prove that various of these concepts are equivalent, in the sense that they give the same ε-efficiency sets by choosing suitable parameters. The obtained results are illustrated in the Pareto context.
In this paper we study solution methods for solving the dual problem corresponding to the Lagrangian Decomposition of two-stage stochastic mixed 0-1 models. We represent the two-stage stochastic mixed 0-1 problem by a splitting variable representation of the deterministic equivalent model, where 0-1 and continuous variables appear at any stage. Lagrangian Decomposition (LD) is proposed for satisfying...
We study generic variational principles in optimization when the underlying topological space X is not necessarily metrizable. It turns out that, to ensure the validity of such a principle, instead of having a complete metric which generates the topology in the space X (which is the case of most variational principles), it is enough that we dispose of a complete metric on X which is stronger than...
The problem of finding a feasible solution to a linear inequality system arises in numerous contexts. In González-Gutiérrez and Todorov (Optim. Lett. doi: 10.1007/s11590-010-0244-4 , 2011), an algorithm, called extended relaxation method, for solving the feasibility problem has been proposed by the authors. Convergence of the algorithm has been proven. In this paper, we consider a class of extended...
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