(Mixed) Integer Nonlinear Programming

Multi-objective Optimization Based Algorithms for Solving Mixed Integer Linear Minimum Multiplicative Programs

  • Hadi Charkhgard
  • Vahid Mahmoodian
  • Yu Zhang
    • Categories (Mixed) Integer Nonlinear Programming, Branch and Cut Algorithms, Global Optimization

    We present two new algorithms for a class of single-objective non-linear optimization problems, the so-called Mixed Integer Linear minimum Multiplicative Programs (MIL-mMPs). This class of optimization problems has a desirable characteristic: a MIL-mMP can be viewed as a special case of the problem of optimization over the efficient set in multi-objective optimization. The proposed algorithms … Read more

    A Polynomial-time Algorithm with Tight Error Bounds for Single-period Unit Commitment Problem

  • S.C. Fang
  • Ruotian Gao
  • Wenxun Xing
  • Cheng Lu
    • Categories (Mixed) Integer Nonlinear Programming, Approximation Algorithms, Scheduling Tags , , , ,

    This paper proposes a Lagrangian dual based polynomial-time approximation algorithm for solving the single-period unit commitment problem, which can be formulated as a mixed integer quadratic programming problem and proven to be NP-hard. Tight theoretical bounds for the absolute errors and relative errors of the approximate solutions generated by the proposed algorithm are provided. Computational … Read more

    A Strictly Contractive Peaceman-Rachford Splitting Method for the Doubly Nonnegative Relaxation of the Minimum Cut Problem

  • Xinxin Li
  • Ting Kei Pong
  • Hao Sun
  • Henry Wolkowicz
    • Categories (Mixed) Integer Nonlinear Programming, Linear, Cone and Semidefinite Programming, Optimization Software Benchmark Tags , , , , , ,

    The minimum cut problem, MC, and the special case of the vertex separator problem, consists in partitioning the set of nodes of a graph G into k subsets of given sizes in order to minimize the number of edges cut after removing the k-th set. Previous work on this topic uses eigenvalue, semidefinite programming, SDP, … Read more

    Single Allocation Hub Location with Heterogeneous Economies of Scale

  • Okan Arslan
  • Masoud Chitsaz
  • Gilbert Laporte
  • Andrea Lodi
  • Borzou Rostami
    • Categories (Mixed) Integer Nonlinear Programming, Applications - OR and Management Sciences, Combinatorial Optimization Tags , , , , ,

    We study the single allocation hub location problem with heterogeneous economies of scale (SAHLP-h). The SAHLP-h is a generalization of the classical single allocation hub location problem (SAHLP), in which the hub-hub connection costs are piecewise linear functions of the amounts of flow. We model the problem as an integer non-linear program, which we then … Read more

    On Mixed-Integer Optimal Control with Constrained Total Variation of the Integer Control

  • Sebastian Sager
  • Clemens Zeile
    • Categories (Mixed) Integer Linear Programming, (Mixed) Integer Nonlinear Programming, Systems governed by Differential Equations Optimization

    The combinatorial integral approximation (CIA) decomposition suggests to solve mixed-integer optimal control problems (MIOCPs) by solving one continuous nonlinear control problem and one mixed-integer linear program (MILP). Unrealistic frequent switching can be avoided by adding a constraint on the total variation to the MILP. Within this work, we present a fast heuristic way to solve … Read more

    A counterexample to an exact extended formulation for the single-unit commitment problem

  • Tiziano Bacci
  • Antonio Frangioni
  • Claudio Gentile
    • Categories (Mixed) Integer Nonlinear Programming, Applications - OR and Management Sciences Tags , , ,

    Recently, Guan, Pan, and Zohu presented a MIP model for the thermal single- unit commitment claiming that provides an integer feasible solution for any convex cost function. In this note we provide a counterexample to this statement and we produce evidence that the perspective function is needed for this aim. Citation Research Report 19-03, Istituto … Read more

    New MINLP Formulations for the Unit Commitment Problems with Ramping Constraints

  • Tiziano Bacci
  • Antonio Frangioni
  • Claudio Gentile
  • Kostas Tavlaridis-Gyparakis
    • Categories (Mixed) Integer Nonlinear Programming, Applications - OR and Management Sciences Tags , , , ,

    The Unit Commitment (UC) problem in electrical power production requires to optimally operate a set of power generation units over a short time horizon (one day to a week). Operational constraints of each unit depend on its type (e.g., thermal, hydro, nuclear, …), and can be rather complex. For thermal units, typical ones concern minimum … Read more

    Experimental operation of a solar-driven climate system with thermal energy storages using mixed-integer nonlinear MPC

  • Adrian Bürger
  • Daniel Bull
  • Parantapa Sawant
  • Markus Bohlayer
  • Angelika Altmann-Dieses
  • Marco Braun
  • Moritz Diehl
    • Categories (Mixed) Integer Nonlinear Programming, Control Applications, Systems governed by Differential Equations Optimization Tags , , , ,

    This work presents the results of experimental operation of a solar-driven climate system using mixed-integer nonlinear Model Predictive Control (MPC). The system is installed in a university building and consists of two solar thermal collector fields, an adsorption cooling machine with different operation modes, a stratified hot water storage with multiple inlets and outlets as … Read more

    Mixed-Integer Optimal Control under Minimum Dwell Time Constraints

  • Nicolò Robuschi
  • Sebastian Sager
  • Clemens Zeile
    • Categories (Mixed) Integer Linear Programming, (Mixed) Integer Nonlinear Programming, Systems governed by Differential Equations Optimization Tags , , , , ,

    Tailored mixed-integer optimal control policies for real-world applications usually have to avoid very short successive changes of the active integer control. Minimum dwell time constraints express this requirement and can be included into the combinatorial integral approximation decomposition, which solves mixed-integer optimal control problems by solving one continuous nonlinear program and one mixed-integer linear program. … Read more

    Tight compact extended relaxations for nonconvex quadratic programming problems with box constraints

  • Sven de Vries
  • Bernd Perscheid
    • Categories (Mixed) Integer Nonlinear Programming, Graphs and Matroids, Quadratic Programming Tags ,

    Cutting planes from the Boolean Quadric Polytope (BQP) can be used to reduce the optimality gap of the NP-hard nonconvex quadratic program with box constraints (BoxQP). It is known that all cuts of the Chvátal-Gomory closure of the BQP are A-odd cycle inequalities. We obtain a compact extended relaxation of all A-odd cycle inequalities, which … Read more