Multidirectional Physarum Solver: an Innovative Bio-inspired Algorithm for Optimal Discrete Decision Making

Categories Combinatorial Optimization Tags , , , , ,

This paper introduces a new bio-inspired algorithm for optimal discrete decision making, able to incrementally grow and explore decision graphs in multiple directions. The heuristic draws inspiration from the idea that building decision sequences from multiple directions and then combining the sequences is an optimal choice if compared with a unidirectional approach. The behaviour of … Read more

Well-posedness for Lexicographic Vector Equilibrium Problems

Categories Multi-Criteria Optimization, Nonsmooth Optimization Tags , ,

We consider lexicographic vector equilibrium problems in metric spaces. Sufficient conditions for a family of such problems to be (uniquely) well-posed at the reference point are established. As an application, we derive several results on well-posedness for a class of variational inequalities. CitationPublished in Constructive Nonsmooth Analysis and Related Topics (Vladimir Demyanov, Panos M. Pardalos, … Read more

Biased and unbiased random-key genetic algorithms: An experimental analysis

Categories Meta Heuristics, Optimization Software Benchmark, Stochastic Approaches Tags , , , , , ,

We study the runtime performance of three types of random-key genetic algorithms: the unbiased algorithm of Bean (1994); the biased algorithm of Gonçalves and Resende (2011); and a greedy version of Bean’s algorithm on 12 instances from four types of covering problems: general-cost set covering, Steiner triple covering, general-cost set K-covering, and unit-cost covering by … Read more

Calmness modulus of linear semi-infinite programs

Categories Linear Programming, Semi-infinite Programming Tags , , , ,

Our main goal is to compute or estimate the calmness modulus of the argmin mapping of linear semi-infinite optimization problems under canonical perturbations, i.e., perturbations of the objective function together with continuous perturbations of the right-hand side of the constraint system (with respect to an index ranging in a compact Hausdorff space). Specifically, we provide … Read more

On the Augmented Lagrangian Dual for Integer Programming

Categories (Mixed) Integer Linear Programming Tags , ,

We consider the augmented Lagrangian dual for integer programming, and provide a primal characterization of the resulting bound. As a corollary, we obtain proof that the augmented Lagrangian is a strong dual for integer programming. We are able to show that the penalty parameter applied to the augmented Lagrangian term may be placed at a … Read more

Approximate-KKT stopping criterion when Lagrange multipliers are not available

Categories Nonlinear Optimization Tags , ,

In this paper we investigate how to efficiently apply Approximate-Karush-Kuhn-Tucker (AKKT) proximity measures as stopping criteria for optimization algorithms that do not generate approximations to Lagrange multipliers, in particular, Genetic Algorithms. We prove that for a wide range of constrained optimization problems the KKT error measurement tends to zero. We also develop a simple model … Read more

A SMOOTHING MAJORIZATION METHOD FOR hBc$ MATRIX MINIMIZATION

Categories Convex and Nonsmooth Optimization, Linear, Cone and Semidefinite Programming Tags , , , ,

We discuss the $l_2$-$l_p$ (with $p\in (0,1)$ matrix minimization for recovering low rank matrix. A smoothing approach is developed for solving this non-smooth, non-Lipschitz and non-convex optimization problem, in which the smoothing parameter is used as a variable and a majorization method is adopted to solve the smoothing problem. The convergence theorem shows that any … Read more

BILEVEL OPTIMIZATION AS A REGULARIZATION APPROACH TO PSEUDOMONOTONE EQUILIBRIUM PROBLEMS

Categories Convex and Nonsmooth Optimization, Generalized Convexity/Monoticity, Global Optimization Tags , , , ,

We investigate some properties of an inexact proximal point method for pseudomonotone equilibrium problems in a real Hilbert space. Un- like monotone case, in pseudomonotone case, the regularized subprob- lems may not be strongly monotone, even not pseudomonotone. How- ever, every proximal trajectory weakly converges to the same limit, We use these properties to extend … Read more

STOCHASTIC OPTIMIZATION OVER A PARETO SET ASSOCIATED WITH A STOCHASTIC MULTI-OBJECTIVE OPTIMIZATION PROBLEM

Categories Multi-Criteria Optimization, Stochastic Approaches Tags , , , ,

We deal with the problem of minimizing the expectation of a real valued random function over the weakly Pareto or Pareto set associated with a Stochastic Multi-Objective Optimization Problem (SMOP) whose objectives are expectations of random functions. Assuming that the closed form of these expectations is difficult to obtain, we apply the Sample Average Approximation … Read more

Robust Least Square Semidefinite Programming with Applications to Correlation Stress Testing

Categories Convex and Nonsmooth Optimization, Linear, Cone and Semidefinite Programming, Robust Optimization Tags , ,

In this paper, we consider a least square semidefinite programming problem under ellipsoidal data uncertainty. We show that the robustification of this uncertain problem can be reformulated as a semidefinite linear programming problem with an additional second-order cone constraint. We then provide an explicit quantitative sensitivity analysis on how the solution under the robustification depends … Read more