Multi-Criteria Optimization

The stochastic multi-gradient algorithm for multi-objective optimization and its application to supervised machine learning

  • Suyun Liu
  • Luis Nunes Vicente
    • Categories Convex Optimization, Multi-Criteria Optimization, Stochastic Programming Tags , , ,

    Optimization of conflicting functions is of paramount importance in decision making, and real world applications frequently involve data that is uncertain or unknown, resulting in multi-objective optimization (MOO) problems of stochastic type. We study the stochastic multi-gradient (SMG) method, seen as an extension of the classical stochastic gradient method for single-objective optimization. At each iteration … Read more

    Quantifying the value of flexibility: demand response versus storage

  • Ana Paula Chorobura
  • Claudia Sagastizábal
  • Wim van Ackooij
  • Hasnaa Zidani
    • Categories Energy, Multi-Criteria Optimization

    Intermittent sources of energy represent a challenge for electrical networks, particularly regarding demand satisfaction at peak times. Energy management tools such as load shaving or storage systems can be used to mitigate abrupt variations in the network.The value of different mechanisms to move energy through time is determined by a multi-objective programming approach, that aims … Read more

    Line-Prioritized Environmental Selection and Normalization Scheme for Many-Objective Optimization using Reference-Line-based Framework

  • Deepak Sharma
  • Pradyumn Kumar Shukla
    • Categories Multi-Criteria Optimization

    The Pareto-dominance-basedmulti-objective evolutionary algorithms (MOEAs) have been successful in solving many test problems and other engineering optimization problems. However, their performance gets affected when solving more than 3-objective optimization problems due to lack of sufficient selection pressure. Many attempts have been made by the researchers toward improving the environmental selection of those MOEAs. One such … Read more

    Solving Multiobjective Mixed Integer Convex Optimization Problems

  • Marianna De Santis
  • Gabriele Eichfelder
  • Julia Niebling
  • Stefan Rocktäschel
    • Categories (Mixed) Integer Nonlinear Programming, Global Optimization, Multi-Criteria Optimization Tags , ,

    Multiobjective mixed integer convex optimization refers to mathematical programming problems where more than one convex objective function needs to be optimized simultaneously and some of the variables are constrained to take integer values. We present a branch-and-bound method based on the use of properly defined lower bounds. We do not simply rely on convex relaxations, … Read more

    Multi-Objective Optimization for Politically Fair Districting: A Scalable Multilevel Approach

  • Rahul Swamy
  • Douglas King
  • Sheldon Jacobson
    • Categories (Mixed) Integer Linear Programming, Applications - OR and Management Sciences, Multi-Criteria Optimization Tags , , , , , , ,

    Political districting in the United States is a decennial process of redrawing the boundaries of congressional and state legislative districts. The notion of fairness in political districting has been an important topic of subjective debate, with district maps having consequences to multiple stakeholders. Even though districting as an optimization problem has been well-studied, existing models … Read more

    Subdifferentials and SNC property of scalarization functionals with uniform level sets and applications

  • Christiane Tammer
  • Bao Q. Truong
    • Categories Constrained Nonlinear Optimization, Multi-Criteria Optimization, Nonsmooth Optimization

    This paper deals with necessary conditions for minimal solutions of constrained and unconstrained optimization problems with respect to general domination sets by using a well-known nonlinear scalarization functional with uniform level sets (called Gerstewitz’ functional in the literature). The primary objective of this work is to establish revised formulas for basic and singular subdifferentials of … Read more

    Learning to Project in Multi-Objective Binary Linear Programming

  • Hadi Charkhgard
  • Iman Dayarian
  • Ali Eshragh
  • Sorna Javadi
  • Alvaro Sierra-Altamiranda
    • Categories (Mixed) Integer Linear Programming, Multi-Criteria Optimization, Other Topics Tags , , , ,

    In this paper, we investigate the possibility of improving the performance of multi-objective optimization solution approaches using machine learning techniques. Specifically, we focus on multi-objective binary linear programs and employ one of the most effective and recently developed criterion space search algorithms, the so-called KSA, during our study. This algorithm computes all nondominated points of … Read more

    The Sard theorem for essentially smooth locally Lipschitz maps and applications in optimization

  • Xuan Duc Ha Truong
    • Categories Convex and Nonsmooth Optimization, Multi-Criteria Optimization Tags , , , ,

    The classical Sard theorem states that the set of critical values of a $C^{k}$-map from an open set of $\R^n$ to $\R^p$ ($n\geq p$) has Lebesgue measure zero provided $k\geq n-p+1$. In the recent paper by Barbet, Dambrine, Daniilidis and Rifford, the so called “preparatory Sard theorem” for a compact countable set $I$ of $C^k$ … Read more

    On prime and minimal representations of a face of a polyhedron

  • Ta Van Van Tu
    • Categories Combinatorial Optimization, Multi-Criteria Optimization, Polyhedra

    In this paper, a new method for determining all minimal representations of a face of a polyhedron is proposed. A main difficulty for determining prime and minimal representations of a face is that the deletion of one redundant constraint can change the redundancy of other constraints. To reduce computational efforts in finding all minimal representations … Read more

    An Algorithmic Approach to Multiobjective Optimization with Decision Uncertainty

  • Gabriele Eichfelder
  • Julia Niebling
  • Stefan Rocktäschel
    • Categories Global Optimization, Multi-Criteria Optimization, Robust Optimization Tags , ,

    In real life applications optimization problems with more than one objective function are often of interest. Next to handling multiple objective functions, another challenge is to deal with uncertainties concerning the realization of the decision variables. One approach to handle these uncertainties is to consider the objectives as set-valued functions. Hence, the image of one … Read more