An Environmentally Sustainable Feasible Policy for Dynamic Lot Sizing Model with Remanufacturing and Separate Setup Costs: Time Complexity and Optimality

Categories Dynamic Programming, Production and Logistics Tags , , ,

We consider a dynamic lot sizing model in which end products to satisfy demands are obtained by remanufacturing m core types of differing quality, where m ≥ 1, or manufacturing from raw materials. In the model, we have separate setup costs associated with manufacturing and remanufacturing. As is widely known, remanufacturing is an environmental preferable … Read more

The Undirected Team Orienteering Arc Routing Problem: Formulations, Valid Inequalities, and Exact Algorithms

Categories Branch and Cut Algorithms, Combinatorial Optimization, Network Optimization Tags , , ,

We address the Undirected Team Orienteering Arc Routing Problem (UTOARP). In this problem, demand is placed at some edges of a given undirected graph and served demand edges produce a profit. Feasible routes must start and end at a given depot and there is a time limit constraint on the maximum duration of each route. … Read more

The improvement function reformulation for graphs of minimal point mappings

Categories Constrained Nonlinear Optimization, Game Theory, Global Optimization Theory Tags , , , , ,

Graphs of minimal point mappings of parametric optimization problems appear in the definition of feasible sets of bilevel optimization problems and of semi-infinite optimization problems, and the intersection of multiple such graphs defines (generalized) Nash equilibria. This paper shows how minimal point graphs of nonconvex parametric optimization problems can be written with the help of … Read more

Rank-one convexification for convex quadratic optimization with step function penalties

Categories (Mixed) Integer Nonlinear Programming, Data Science Applications, Semi-definite Programming Tags ,

We investigate convexification in convex quadratic optimization with step function penalties. Such problems can be cast as mixed-integer quadratic optimization problems, where binary variables are used to encode the non-convex step function. First, we derive the convex hull for the epigraph of a quadratic function defined by a rank-one matrix. Using this rank-one convexification, we … Read more

A Foundational Perspective for Partitional Clustering on Networks

Categories Data Science Theory, Data-Mining, Optimization in Data Science Tags , , ,

This study presents a theoretical analysis of partitional clustering on networks. Different versions of the problem are studied considering different assignment schemes (hard and soft) and different objective functions. Cluster centers are not restricted to only the set of nodes, it is assumed that centers can also be at the edges of the network. Four … Read more

Mathematical programs with complementarity constraints and application to hyperparameter tuning

Categories Bilevel Optimization, Complementarity and Variational Inequalities, Optimization in Data Science Tags , , , , ,

We consider the Mathematical Program with Complementarity Constraints (MPCC). One of the main challenges in solving this problem is the systematic failure of standard constraint qualifications. Carefully accounting for the combinatorial nature of the complementarity constraints, tractable versions of the Mangasarian-Fromovitz Constraint Qualification (MFCQ) have been designed and widely studied in the literature.  This paper … Read more

An interactive optimization framework for incorporating a broader range of human feedback into stochastic multi-objective mixed integer linear programs

Categories (Mixed) Integer Linear Programming, Multi-Criteria Optimization, Stochastic Programming Tags , , , ,

Interactive optimization leverages the strengths of optimization frameworks alongside the expertise of human users. Prior research in this area tends to either ask human users for the same type of information, or when varying information is requested, users must manually modify the optimization model directly. These limitations restrict the incorporation of wider human knowledge into … Read more

Pareto Leap: An Algorithm for Biobjective Mixed-Integer Programming

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

Many real-life optimization problems need to make decisions with discrete variables and multiple, conflicting objectives. Due to this need, the ability to solve such problems is an important and active area of research. We present a new algorithm, called Pareto Leap, for identifying the (weak) Pareto slices of biobjective mixed-integer programs (BOMIPs), even when Pareto … Read more

Globally Converging Algorithm for Multistage Stochastic Mixed-Integer Programs via Enhanced Lagrangian Cuts

Categories (Mixed) Integer Linear Programming, Stochastic Programming Tags , ,

This paper proposes a globally converging cutting-plane algorithm for solving multistage stochastic mixed-integer programs with general mixed-integer state variables. We demonstrate the generation process of Lagrangian cuts and show that Lagrangian cuts capture the convex envelope of value functions on a restricted region. To approximate nonconvex value functions to exactness, we propose to iteratively add … Read more

Superiorization and Perturbation Resilience of Algorithms: A Continuously Updated Bibliography

Categories Applications - Science and Engineering, Constrained Nonlinear Optimization Tags , , ,

This document presents a (mostly) chronologically-ordered bibliography of scientific publications on the superiorization methodology and perturbation resilience of algorithms which is compiled and continuously updated by us at: http://math.haifa.ac.il/yair/bib-superiorization-censor.html. Since the beginnings of this topic we try to trace the work that has been published about it since its inception. To the best of our … Read more