Alejandro Crema

Robust combinatorial optimization problems with knapsack constraints under interdiction uncertainty

  • Alejandro Crema
    • Categories Approximation Algorithms, Combinatorial Optimization, Robust Optimization Tags , , , ,

    We present an algorithm for finding near-optimal solutions to robust combinatorial optimization problems with knapsack constraints under interdiction uncertainty. We incorporate a heuristic for generating feasible solutions in a standard row generation approach. Experimental results are presented for set covering, simple plant location, and min-knapsack problems under a discrete-budgeted interdiction uncertainty set introduced in this … Read more

    Absolute regret of implicitly defined sets for combinatorial optimization problems

  • Alejandro Crema
    • Categories Robust Optimization Tags , , ,

    We consider combinatorial optimization problems with interval uncertainty in the cost vector. Recently a new approach was developed to deal with such uncertainties: instead of a single one absolute robust solution, obtained by solving a min max problem, a set of cardinality predefined and minimal absolute regret, obtained by solving a min max min problem, … Read more

    Min max (relative) set-regret combinatorial optimization

  • Alejandro Crema
    • Categories 0-1 Programming, Combinatorial Optimization, Robust Optimization Tags , , ,

    We consider combinatorial optimization problems with uncertainty in the cost vector. Recently a novel approach was developed to deal such uncertainties: instead of a single one robust solution, obtained by solving a min max problem, the authors consider a set of solutions obtained by solving a min max min problem. In this new approach the … Read more

    Generalized average shadow prices and bottlenecks

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

    We present a generalization of the average shadow price in 0-1-Mixed Integer Linear Programming problems and its relation with bottlenecks including the analysis relative to the coefficients matrix of resource constraints. A mathematical programming approach to find the strategy for investment in resources is presented. CitationEscuela de Computación, Facultad de Ciencias, Universidad Central de VenezuelaArticleDownload … 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

    Mathematical programming approach to tighten a Big-$ formulation

  • Alejandro Crema
    • Categories Integer Programming Tags ,

    In this paper we present a mathematical programming approach to tighten a Big-$M$ formulation ($P_M$) of a Mixed Integer Problem with Logical Implications ($P$). If $M_0$ is a valid vector (the optimal solutions of $P$ belong to the feasible solutions set of $P_{M_0}$) our procedures find a valid vector $M$ such that $M \leq M_0$. … Read more

    Approximating the solution for the multiparametric 0-1-mixed integer linear programming problem with interval data

  • Alejandro Crema
  • Fernando Crema
  • Edgar Hugo Peraza
    • Categories (Mixed) Integer Linear Programming Tags , ,

    In this paper we present algorithms to approximate the solution for the multiparametric 0-1-mixed integer linear programming problem relative to the objective function. We consider the uncertainty for the parameters that de fine the cost vector corresponding to a subset of 0-1-variables by assuming that each parameter belongs to a known interval. We suppose that we … Read more