Solving the three-dimensional open-dimension rectangular packing problem: a constraint programming model
In this paper, we address the three-dimensional open-dimension rectangular packing problem (3D-ODRPP). This problem addresses a set of rectangular boxes of given dimensions and a rectangular container of open dimensions. The objective is to pack all boxes orthogonally into the container while minimizing the container volume. Real-world applications of the 3D-ODRPP arise in production systems … Read more
On Packing a Submodular Knapsack of Unknown Capacity
Consider the problem of maximizing a monotone-increasing submodular function defined on a set of weighted items under an unknown knapsack capacity. Assume that items are packed sequentially into the knapsack and that the capacity of the knapsack is accessed through an oracle that answers whether an item fits into the currently packed knapsack. If an … Read more
A Subspace Minimization Barzilai-Borwein Method for Multiobjective Optimization Problems
Nonlinear conjugate gradient methods have recently garnered significant attention within the multiobjective optimization community. These methods aim to maintain consistency in conjugate parameters with their single-objective optimization counterparts. However, the preservation of the attractive conjugate property of search directions remains uncertain, even for quadratic cases, in multiobjective conjugate gradient methods. This loss of interpretability of … Read more
Convex Ternary Quartics Are SOS-Convex
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The Bipartite Implication Polytope: Conditional Relations over Multiple Sets of Binary Variables
Inspired by its occurrence as a substructure in a stochastic railway timetabling model, we study in this work a special case of the bipartite boolean quadric polytope. It models conditional relations across three sets of binary variables, where selections within two implying sets imply a choice in a corresponding implied set. We call this polytope … Read more
The Multi-Stop Station Location Problem: Exact Approaches
The multi-stop station location problem (MSLP) aims to place stations such that a set of trips is feasible with respect to length bounds while minimizing cost. Each trip consists of a sequence of stops that must be visited in a given order, and a length bound that controls the maximum length that is possible without … Read more
New cuts and a branch-cut-and-price model for the Multi Vehicle Covering Tour Problem
The Multi-Vehicle Covering Tour Problem (m-CTP) involves a graph in which the set of vertices is partitioned into a depot and three distinct subsets representing customers, mandatory facilities, and optional facilities. Each customer is linked to a specific subset of optional facilities that define its coverage set. The goal is to determine a set of … Read more
A Clustering-based uncertainty set for Robust Optimization
Robust optimization is an approach for handling uncertainty in optimization problems, in which the uncertainty set determines the conservativeness of the solutions. In this paper, we propose a data-driven uncertainty set using a type of volume-based clustering, which we call Minimum-Volume Norm-Based Clustering (MVNBC). MVNBC extends the concept of minimum-volume ellipsoid clustering by allowing clusters … Read more
Heuristic Methods for Γ-Robust Mixed-Integer Linear Bilevel Problems
Due to their nested structure, bilevel problems are intrinsically hard to solve–even if all variables are continuous and all parameters of the problem are exactly known. In this paper, we study mixed-integer linear bilevel problems with lower-level objective uncertainty, which we address using the notion of Γ-robustness. To tackle the Γ-robust counterpart of the bilevel … Read more