Dual Bounds from Decision Diagram-Based Route Relaxations: An Application to Truck-Drone Routing

For vehicle routing problems, strong dual bounds on the optimal value are needed to develop scalable exact algorithms, as well as to evaluate the performance of heuristics. In this work, we propose an iterative algorithm to compute dual bounds motivated by connections between decision diagrams (DDs) and dynamic programming (DP) models used for pricing in … Read more

Relaxations and Duality for Multiobjective Integer Programming

Multiobjective integer programs (MOIPs) simultaneously optimize multiple objective functions over a set of linear constraints and integer variables. In this paper, we present continuous, convex hull and Lagrangian relaxations for MOIPs and examine the relationship among them. The convex hull relaxation is tight at supported solutions, i.e., those that can be derived via a weighted-sum … Read more

A Novel Model for Transfer Synchronization in Transit Networks and a Lagrangian-based Heuristic Solution Method

To realize the benefits of network connectivity in transfer-based transit networks, it is critical to minimize transfer disutility for passengers by synchronizing timetables of intersecting routes. We propose a mixed-integer linear programming timetable synchronization model that incorporates new features, such as dwell time determination and vehicle capacity limit consideration, which have been largely overlooked in … Read more

Some heuristic methods for the p-median problem with maximum distance constraints. Application to a bi-objective problem.

In this work we study the p-median problem with maximum distance constraints (PMPDC) which is a variant of the classical p-median problem (PMP). First of all, we provide some different formulations for (PMPDC) because the heuristics procedures for the (PMPDC) with a formulation based on the approach that modifies the distance matrix that leads to … Read more

Single Allocation Hub Location with Heterogeneous Economies of Scale

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

Multistage Stochastic Demand-side Management for Price-Making Major Consumers of Electricity in a Co-optimized Energy and Reserve Market

In this paper we take an optimization-driven heuristic approach, motivated by dynamic programming, to solve a multistage stochastic optimization of energy consumption for a large manufacturer who is a price-making major consumer of electricity. We introduce a mixed-integer program that co-optimizes consumption bids and interruptible load reserve offers, for such a major consumer over a … Read more

A decomposition approach for single allocation hub location problems with multiple capacity levels

In this paper we consider an extended version of the classical capacitated single allocation hub location problem in which the size of the hubs must be chosen from a finite and discrete set of allowable capacities. We develop a Lagrangian relaxation approach that exploits the problem structure and decomposes the problem into a set of … Read more

Lagrangian relaxation for SVM feature selection

We discuss a Lagrangian-relaxation-based heuristics for dealing with feature selection in a standard L1 norm Support Vector Machine (SVM) framework for binary classification. The feature selection model we adopt is a Mixed Binary Linear Programming problem and it is suitable for a Lagrangian relaxation approach. Based on a property of the optimal multiplier setting, we … Read more

The Uncapacitated Single Allocation p-Hub Median Problem with Stepwise Cost Function

In this paper, we address a new version of the Uncapacitated Single Allocation p-Hub Median Problem (USApHMP) in which transportation costs on each edge are given by piecewise constant cost functions. In the classical USApHMP, transportation costs are modelled as linear functions of the transport volume, where a fixed discount factor on hub-hub connections is … Read more

A Stabilised Scenario Decomposition Algorithm Applied to Stochastic Unit Commitment Problems

In recent years the expansion of energy supplies from volatile renewable sources has triggered an increased interest in stochastic optimization models for hydro-thermal unit commitment. Several studies have modelled this as a two-stage or multi-stage stochastic mixed-integer optimization problem. Solving such problems directly is computationally intractable for large instances, and alternative approaches are required. In … Read more