Integer Programming

On Refinement Strategies for Solving MINLPs by Piecewise Linear Relaxations: A Generalized Red Refinement

  • Robert Burlacu
    • Categories (Mixed) Integer Nonlinear Programming Tags , , ,

    We investigate the generalized red refinement for n-dimensional simplices that dates back to Freudenthal in a mixed-integer nonlinear program (MINLP) context. We show that the red refinement meets sufficient convergence conditions for a known MINLP solution framework that is essentially based on solving piecewise linear relaxations. In addition, we prove that applying this refinement procedure … Read more

    An Adaptive Patch Approximation Algorithm for Bicriteria Convex Mixed Integer problems

  • Erik Diessel
    • Categories (Mixed) Integer Nonlinear Programming, Multi-Criteria Optimization Tags , , ,

    Pareto frontiers of bicriteria continuous convex problems can be efficiently computed and optimal theoretical performance bounds have been established. In the case of bicriteria mixed-integer problems, the approximation of the Pareto frontier becomes, however, significantly harder. In this paper, we propose a new algorithm for approximating the Pareto frontier of bicriteria mixed-integer programs with convex … Read more

    An Almost Exact Solution to the Min Completion Time Variance in a Single Machine

  • Stefano Nasini
  • Rabia Nessah
    • Categories 0-1 Programming, Combinatorial Optimization, Scheduling Tags , , ,

    We consider a single machine scheduling problem to minimize the completion time variance of n jobs. This problem is known to be NP-hard and our contribution is to establish a novel bounding condition for a characterization of an optimal sequence. Specifically, we prove a necessary and sufficient condition (which can be verified in O(n\log n)) … Read more

    A Separation Heuristic for 2-Partition Inequalities for the Clique Partitioning Problem

  • Michael M. Sørensen
    • Categories Branch and Cut Algorithms, Cutting Plane Approaches, Polyhedra

    We consider the class of 2-partition inequalities for the clique partitioning problem associated with complete graphs. We propose a heuristic separation algorithm for the inequalities and evaluate its usefulness in a cutting-plane algorithm. Our computational experiments fall into two parts. In the first part, we compare the LP objective values obtained by the proposed separator … Read more

    Multi-period investment pathways – Modeling approaches to design distributed energy systems under uncertainty

  • Markus Bohlayer
  • Marco Braun
  • Adrian Bürger
  • Markus Fleschutz
  • Gregor Zöttl
    • Categories (Mixed) Integer Linear Programming, Applications - OR and Management Sciences, Stochastic Programming

    Multi-modal distributed energy system planning is applied in the context of smart grids, industrial energy supply, and in the building energy sector. In real-world applications, these systems are commonly characterized by existing system structures of different age where monitoring and investment are conducted in a closed-loop, with the iterative possibility to invest. The literature contains … Read more

    The confined primal integral

  • Timo Berthold
  • Zsolt Csizmadia
    • Categories (Mixed) Integer Nonlinear Programming, Optimization Software Benchmark Tags , ,

    It is a challenging task to fairly compare local solvers and heuristics against each other and against global solvers. How does one weigh a faster termination time against a better quality of the found solution? In this paper, we introduce the confined primal integral, a new performance measure that rewards a balance of speed and … Read more

    Conflict Analysis for MINLP

  • Timo Berthold
  • Jakob Witzig
    • Categories (Mixed) Integer Nonlinear Programming

    The generalization of MIP techniques to deal with nonlinear, potentially non-convex, constraints have been a fruitful direction of research for computational MINLP in the last decade. In this paper, we follow that path in order to extend another essential subroutine of modern MIP solvers towards the case of nonlinear optimization: the analysis of infeasible subproblems … Read more

    Improved optimization models for potential-driven network flow problems via ASTS orientations

  • Kai Helge Becker
  • Benjamin Hiller
    • Categories (Mixed) Integer Nonlinear Programming, Network Optimization Tags , , , ,

    The class of potential-driven network flow problems provides important models for a range of infrastructure networks that lead to hard-to-solve MINLPs in real-world applications. On large-scale meshed networks the relaxations usually employed are rather weak due to cycles in the network. To address this situation, we introduce the concept of ASTS orientations, a generalization of … Read more

    On a generalization of the Chvatal-Gomory closure

  • Sanjeeb Dash
  • Oktay Gunluk
  • Dabeen Lee
    • Categories Cutting Plane Approaches, Integer Programming Tags , , , , ,

    Many practical integer programming problems involve variables with one or two-sided bounds. Dunkel and Schulz (2012) considered a strengthened version of Chvatal-Gomory (CG) inequalities that use 0-1 bounds on variables, and showed that the set of points in a rational polytope that satisfy all these strengthened inequalities is a polytope. Recently, we generalized this result … Read more

    Formulations and Valid Inequalities for Optimal Black Start Allocation in Power Systems

  • Ignacio Aravena
  • Shmuel Oren
  • Deepak Rajan
  • Georgios Patsakis
    • Categories (Mixed) Integer Linear Programming, Energy Tags , , ,

    The restoration of a power system after an extended blackout starts around units with enhanced technical capabilities, referred to as black start units (BSUs). We examine the planning problem of optimally allocating these units on the grid subject to a budget constraint. We present a mixed integer programming model based on current literature in power … Read more