(Mixed) Integer Nonlinear Programming

Endogenous Price Zones and Investment Incentives in Electricity Markets: An Application of Multilevel Optimization with Graph Partitioning

  • Mirjam Ambrosius
  • Veronika Grimm
  • Thomas Kleinert
  • Frauke Liers
  • Martin Schmidt
  • Gregor Zöttl
    • Categories (Mixed) Integer Nonlinear Programming, Applications - OR and Management Sciences, Global Optimization Tags , , , ,

    In the course of the energy transition, load and supply centers are growing apart in electricity markets worldwide, rendering regional price signals even more important to provide adequate locational investment incentives. This paper focuses on electricity markets that operate under a zonal pricing market design. For a fixed number of zones, we endogenously derive the … Read more

    Resilient layout, design and operation of energy-efficient water distribution networks for high-rise buildings using MINLP

  • Lena C. Altherr
  • Marc E. Pfetsch
  • Andreas Schmitt
  • Philipp Leise
    • Categories (Mixed) Integer Nonlinear Programming, Mechanical Engineering, Robust Optimization Tags , , , , , , ,

    Water supply of high-rise buildings requires pump systems to ensure pressure requirements. The design goal of these systems are energy and cost efficiency, both in terms of fixed cost as well as during operation. In this paper, cost optimal decentralized and tree-shaped water distribution networks are computed, where placements of pumps at different locations in … Read more

    A Branch-and-Cut Algorithm for Solving Mixed-integer Semidefinite Optimization Problems

  • Ken Kobayashi
  • Yuichi Takano
    • Categories (Mixed) Integer Nonlinear Programming, Global Optimization, Semi-definite Programming Tags , , ,

    This paper is concerned with a cutting-plane algorithm for solving mixed-integer semidefinite optimization (MISDO) problems. In this algorithm, the positive semidefinite constraint is relaxed, and the resultant mixed-integer linear optimization problem is repeatedly solved with valid inequalities for the relaxed constraint. We prove convergence properties of the algorithm. Moreover, to speed up the computation, we … Read more

    On robust fractional 0-1 programming

  • Colin Gillen
  • Andrés Gómez
  • Oleg A. Prokopyev
  • Erfan Mehmanchi
    • Categories (Mixed) Integer Linear Programming, (Mixed) Integer Nonlinear Programming, Robust Optimization Tags , ,

    We study single- and multiple-ratio robust fractional 0-1 programming problems (RFPs). In particular, this work considers RFPs under a wide-range of disjoint and joint uncertainty sets, where the former implies separate uncertainty sets for each numerator and denominator, and the latter accounts for different forms of inter-relatedness between them. First, we demonstrate that, unlike the … Read more

    Location and Capacity Planning of Facilities with General Service-Time Distributions Using Conic Optimization

  • Ahmadi-Javid Amir
  • Oded Berman
  • Pooya Hoseinpour
    • Categories (Mixed) Integer Nonlinear Programming, Applications - OR and Management Sciences, Facility Planning and Design

    This paper studies a stochastic congested location problem in the network of a service system that consists of facilities to be established in a finite number of candidate locations. Population zones allocated to each open service facility together creates a stream of demand that follows a Poisson process and may cause congestion at the facility. … Read more

    A mixed-integer fractional optimization approach to best subset selection

  • Andrés Gómez
  • Oleg A. Prokopyev
    • Categories (Mixed) Integer Nonlinear Programming, Branch and Cut Algorithms, Statistics Tags , , ,

    We consider the best subset selection problem in linear regression, i.e., finding a parsimonious subset of the regression variables that provides the best fit to the data according to some predefined criterion. We show that, for a broad range of criteria used in the statistics literature, the best subset selection problem can be modeled as … Read more

    On Subadditive Duality for Conic Mixed-Integer Programs

  • Burak Kocuk
  • Diego Moran Ramirez
    • Categories (Mixed) Integer Nonlinear Programming

    In this paper, we show that the subadditive dual of a feasible conic mixed-integer program (MIP) is a strong dual whenever it is feasible. Moreover, we show that this dual feasibility condition is equivalent to feasibility of the conic dual of the continuous relaxation of the conic MIP. In addition, we prove that all known … Read more

    Outer Approximation With Conic Certificates For Mixed-Integer Convex Problems

  • Chris Coey
  • Miles Lubin
  • Juan Pablo Vielma
    • Categories (Mixed) Integer Nonlinear Programming, Linear, Cone and Semidefinite Programming, Optimization Software Benchmark Tags , ,

    A mixed-integer convex (MI-convex) optimization problem is one that becomes convex when all integrality constraints are relaxed. We present a branch-and-bound LP outer approximation algorithm for an MI-convex problem transformed to MI-conic form. The polyhedral relaxations are refined with K* cuts} derived from conic certificates for continuous primal-dual conic subproblems. Under the assumption that all … Read more

    Mixed-integer bilevel representability

  • Amitabh Basu
  • Christopher Thomas Ryan
  • Sriram Sankaranarayanan
    • Categories (Mixed) Integer Nonlinear Programming, Integer Programming Tags ,

    We study the representability of sets that admit extended formulations using mixed-integer bilevel programs. We show that feasible regions modeled by continuous bilevel constraints (with no integer variables), complementarity constraints, and polyhedral reverse convex constraints are all finite unions of polyhedra. Conversely, any finite union of polyhedra can be represented using any one of these … Read more

    Branching with Hyperplanes in the Criterion Space: the Frontier Partitioner Algorithm for Biobjective Integer Programming

  • Marianna De Santis
  • Giorgio Grani
  • Laura Palagi
    • Categories (Mixed) Integer Nonlinear Programming, Branch and Cut Algorithms, Multi-Criteria Optimization

    We present an algorithm for finding the complete Pareto frontier of biobjective integer programming problems. The method is based on the solution of a finite number of integer programs. The feasible sets of the integer programs are built from the original feasible set, by adding cuts that separate efficient solutions. Providing the existence of an … Read more