This work discusses the following general packing problem-class: given a finite collection of d-dimensional spheres with arbitrarily chosen radii, find the smallest sphere in R^d that contains the entire collection of these spheres in a non-overlapping arrangement. Generally speaking, analytical solution approaches cannot be expected to apply to this general problem-type, except for very small … Read more
We propose an algorithm for solving nonsmooth, nonconvex, constrained optimization problems as well as a new set of visualization tools for comparing the performance of optimization algorithms. Our algorithm is a sequential quadratic optimization method that employs Broyden-Fletcher-Goldfarb-Shanno (BFGS) quasi-Newton Hessian approximations and an exact penalty function whose parameter is controlled using a steering strategy. … Read more
A very important part of research in Mathematical Optimization field is to benchmark optimization packages because it is one of the ways to compare solvers. During benchmarking, one usually obtains a large amount of information, like CPU time, number of functions evaluations, number of iterations and much more. This information, if presented as tables, can … Read more
Though empirical testing is broadly used to evaluate heuristics, there are shortcomings with how it is often applied in practice. In a systematic review of Max-Cut and Quadratic Unconstrained Binary Optimization (QUBO) heuristics papers, we found only 4% publish source code, only 14% compare heuristics with identical termination criteria, and most experiments are performed with … Read more
We introduce a novel metaheuristic methodology to improve the initialization of a given deterministic or stochastic optimization algorithm. Our objective is to improve the performance of the considered algorithm, called core optimization algorithm, by reducing its number of cost function evaluations, by increasing its success rate and by boosting the precision of its results. In … Read more
This paper concerns some practical issues associated with the formulation of sequential quadratic programming (SQP) methods for large-scale nonlinear optimization. SQP methods find an approximate solution of a sequence of quadratic programming (QP) subproblems in which a quadratic model of the objective function is minimized subject to the linearized constraints. Extensive numerical results are given … Read more
Nonlinear optimization (NLO) per definitionem covers a vast range of problems, from trivial to practically intractable. For this reason, it is impossible to offer “guaranteed” advice to NLO software users. This fact becomes especially obvious, when facing unusually hard and/or previously unexplored NLO challenges. In the present study we offer some related practical observations, propose … Read more
The goal of this paper is to identify the most promising sets of closest assignment constraints from the literature, in order to improve mixed integer linear programming formulations for exploration of information flow within a social network. The direct comparison between proposed formulations is performed on standard single source capacitated facility location problem instances. Therefore, … Read more
The Conic Benchmark Library (CBLIB 2014) is a collection of more than a hundred conic optimization instances under a free and open license policy. It is the first extensive benchmark library for the advancing field of conic mixed-integer and continuous optimization, which is already supported by all major commercial solvers and spans a wide range … Read more
Traditionally, two variants of the L-shaped method based on Benders’ decomposition principle are used to solve two-stage stochastic programming problems: the single-cut and the multi-cut version. The concept of an oracle with on-demand accuracy was originally proposed in the context of bundle methods for unconstrained convex optimzation to provide approximate function data and subgradients. In … Read more