Integer Programming

Complete mixed integer linear programming formulations for modularity density based clustering

  • Alberto Costa
  • Lin Xuan Foo
  • Tsan Sheng Ng
    • Categories (Mixed) Integer Linear Programming, Network Optimization, Nonlinear Optimization

    Modularity density maximization is a clustering method that improves some issues of the commonly-used modularity maximization approach. Recently, some Mixed-Integer Linear Programming (MILP) reformulations have been proposed in the literature for the modularity density maximization problem, but they require as input the solution of a set of auxiliary binary Non-Linear Programs (NLPs). These can become … Read more

    A parametric programming approach to redefine the global configuration of resource constraints of 0-1-Integer Linear Programming problems.

  • Alejandro Crema
    • Categories (Mixed) Integer Linear Programming, Applications - OR and Management Sciences, Multi-Criteria Optimization Tags , , , ,

    A mathematical programming approach to deal with the global configuration of resource constraints is presented. A specialized parametric programming algorithm to obtain the pareto set for the biobjective problem that appears to deal with the global configuration for 0-1-Integer Linear Programing problems is presented and implemented. Computational results for Multiconstrained Knapsack problems and Bounded Knapsack … Read more

    Ambiguous Chance-Constrained Binary Programs under Mean-Covariance Information

  • Ruiwei Jiang
  • Siqian Shen
  • Yiling Zhang
    • Categories 0-1 Programming, Second-Order Cone Programming, Stochastic Programming

    We consider chance-constrained binary programs, where each row of the inequalities that involve uncertainty needs to be satis ed probabilistically. Only the information of the mean and covariance matrix is available, and we solve distributionally robust chance-constrained binary programs (DCBP). Using two different ambiguity sets, we equivalently reformulate the DCBPs as 0-1 second-order cone (SOC) programs. … Read more

    Mixed Integer Quadratic Optimization Formulations for Eliminating Multicollinearity Based on Variance Inflation Factor

  • Ken Kobayashi
  • Tomomi Matsui
  • Ryuhei Miyashiro
  • Kazuhide Nakata
  • Yuichi Takano
  • Ryuta Tamura
    • Categories Applications - Science and Engineering, Integer Programming, Statistics Tags , , , , ,

    The variance inflation factor, VIF, is the most frequently used indicator for detecting multicollinearity in multiple linear regression models. This paper proposes two mixed integer quadratic optimization formulations for selecting the best subset of explanatory variables under upper-bound constraints on VIF of selected variables. Computational results illustrate the effectiveness of our optimization formulations based on … Read more

    The Multilinear polytope for acyclic hypergraphs

  • Alberto Del Pia
  • Aida Khajavirad
    • Categories (Mixed) Integer Linear Programming, (Mixed) Integer Nonlinear Programming, Global Optimization Theory Tags , , , ,

    We consider the Multilinear polytope defined as the convex hull of the set of binary points satisfying a collection of multilinear equations. Such sets are of fundamental importance in many types of mixed-integer nonlinear optimization problems, such as binary polynomial optimization. Utilizing an equivalent hypergraph representation, we study the facial structure of the Multilinear polytope … Read more

    Improving the Randomization Step in Feasibility Pump

  • Santanu S. Dey
  • Andres Iroume
  • Marco Molinaro
  • Domenico Salvagnin
    • Categories 0-1 Programming, Stochastic Programming Tags , , ,

    Feasibility pump (FP) is a successful primal heuristic for mixed-integer linear programs (MILP). The algorithm consists of three main components: rounding fractional solution to a mixed-integer one, projection of infeasible solutions to the LP relaxation, and a randomization step used when the algorithm stalls. While many generalizations and improvements to the original Feasibility Pump have … Read more

    Maximizing a class of utility functions over the vertices of a polytope

  • Alper Atamturk
  • Andrés Gómez
    • Categories (Mixed) Integer Nonlinear Programming, Robust Optimization, Stochastic Programming Tags , , , , , , , ,

    Given a polytope X, a monotone concave univariate function g, and two vectors c and d, we study the discrete optimization problem of finding a vertex of X that maximizes the utility function c’x + g(d’x). This problem has numerous applications in combinatorial optimization with a probabilistic objective, including estimation of project duration with stochastic … Read more

    An Effective Dynamic Programming Algorithm for the Minimum-Cost Maximal Knapsack Packing

  • Fabio Furini
  • Ivana Ljubić
  • Markus Sinnl
    • Categories Combinatorial Optimization, Dynamic Programming, Integer Programming

    Given a set of n items with profits and weights and a knapsack capacity C, we study the problem of finding a maximal knapsack packing that minimizes the profit of selected items. We propose for the first time an effective dynamic programming (DP) algorithm which has O(nC) time complexity and O(n+C) space complexity. We demonstrate … Read more

    Pseudo basic steps: Bound improvement guarantees from Lagrangian decomposition in convex disjunctive programming

  • Dimitri J. Papageorgiou
  • Francisco Trespalacios
    • Categories (Mixed) Integer Nonlinear Programming Tags , , , ,

    An elementary, but fundamental, operation in disjunctive programming is a basic step, which is the intersection of two disjunctions to form a new disjunction. Basic steps bring a disjunctive set in regular form closer to its disjunctive normal form and, in turn, produce relaxations that are at least as tight. An open question is: What … Read more

    A generalized simplex method for integer problems given by verification oracles

  • Sergei Chubanov
    • Categories Integer Programming, Linear Programming Tags , , ,

    We consider a linear problem over a finite set of integer vectors and assume that there is a verification oracle, which is an algorithm being able to verify whether a given vector optimizes a given linear function over the feasible set. Given an initial solution, the algorithm proposed in this paper finds an optimal solution … Read more