Optimization Software Benchmark

A BFGS-SQP Method for Nonsmooth, Nonconvex, Constrained Optimization and its Evaluation using Relative Minimization Profiles

  • Frank E. Curtis
  • Tim Mitchell
  • Michael L. Overton
    • Categories Control Applications, Nonsmooth Optimization, Optimization Software Benchmark

    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

    Perprof-py: a Python package for performance profile of mathematical optimization software

  • Luiz-Rafael Santos
  • Raniere Gaia Costa da Silva
  • Abel Soares Siqueira
    • Categories Optimization Software Benchmark

    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

    What Works Best When? A Systematic Evaluation of Heuristics for Max-Cut and QUBO

  • Iain Dunning
  • Swati Gupta
  • John Silberholz
    • Categories Meta Heuristics, Optimization Software Benchmark Tags , , , , , , ,

    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

    A Multi-Layer Line Search Method to Improve the Initialization of Optimization Algorithms

  • Benjamin Ivorra
  • Bijan Mohammadi
  • Ángel M. Ramos
    • Categories Global Optimization, Meta Heuristics, Optimization Software Benchmark

    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

    On the Performance of SQP Methods for Nonlinear Optimization

  • Philip E. Gill
  • Michael A. Saunders
  • Elizabeth Wong
    • Categories Constrained Nonlinear Optimization, Optimization Software Benchmark Tags , , ,

    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

    How Difficult is Nonlinear Optimization? A Practical Solver Tuning Approach, with Illustrative Results

  • János Pintér
    • Categories Global Optimization Applications, Nonlinear Optimization, Optimization Software Benchmark

    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

    A several new mixed integer linear programming formulations for exploration of online social networks

  • Zoran Gajic
    • Categories (Mixed) Integer Linear Programming, Facility Planning and Design, Optimization Software Benchmark Tags , ,

    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

    CBLIB 2014: A benchmark library for conic mixed-integer and continuous optimization

  • Henrik A. Friberg
    • Categories Integer Programming, Linear, Cone and Semidefinite Programming, Optimization Software Benchmark Tags , , , , ,

    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

    Applying oracles of on-demand accuracy in two-stage stochastic programming – a computational study

  • Csaba I. Fábián
  • Achim Koberstein
  • Leena Suhl
  • Christian Wolf
    • Categories Optimization Software Benchmark, Stochastic Programming Tags , , ,

    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

    Computing in Operations Research using Julia

  • Iain Dunning
  • Miles Lubin
    • Categories Modeling Languages and Systems, Optimization Software Benchmark, Optimization Software Design Principles

    The state of numerical computing is currently characterized by a divide between highly efficient yet typically cumbersome low-level languages such as C, C++, and Fortran and highly expressive yet typically slow high-level languages such as Python and MATLAB. This paper explores how Julia, a modern programming language for numerical computing which claims to bridge this … Read more