showing 14 related works from this author
Stabilized branch-price-and-cut for the commodity-constrained split delivery vehicle routing problem
2019
Abstract In the commodity-constrained split delivery vehicle routing problem (C-SDVRP), customer demands are composed of sets of different commodities. The C-SDVRP asks for a minimum-distance set of routes such that all customer demands are met and vehicle capacities are respected. Moreover, whenever a commodity is delivered by a vehicle to a customer, the entire amount requested by this customer must be provided. Different commodities demanded by one customer, however, can be delivered by different vehicles. Thus, the C-SDVRP is a relaxation of the capacitated vehicle routing problem and a restriction of the split delivery vehicle routing problem. For its exact solution, we propose a branc…
Bidirectional labeling in column-generation algorithms for pickup-and-delivery problems
2018
Abstract For the exact solution of many types of vehicle-routing problems, column-generation based algorithms have become predominant. The column-generation subproblems are then variants of the shortest-path problem with resource constraints which can be solved well with dynamic-programming labeling algorithms. For vehicle-routing problems with a pickup-and-delivery structure, the strongest known dominance between two labels requires the delivery triangle inequality (DTI) for reduced costs to hold. When the direction of labeling is altered from forward labeling to backward labeling, the DTI requirement becomes the pickup triangle inequality (PTI). DTI and PTI cannot be guaranteed at the sam…
Maximum weight relaxed cliques and Russian Doll Search revisited
2015
Trukhanov et al. [Trukhanov S, Balasubramaniam C, Balasundaram B, Butenko S (2013) Algorithms for detecting optimal hereditary structures in graphs, with application to clique relaxations. Comp. Opt. and Appl., 56(1), 113–130] used the Russian Doll Search (RDS) principle to effectively find maximum hereditary structures in graphs. Prominent examples of such hereditary structures are cliques and some clique relaxations intensely discussed and studied in network analysis. The effectiveness of the tailored RDS by Trukhanov et al. for s-plex and s-defective clique can be attributed to their cleverly designed incremental verification procedures used to distinguish feasible from infeasible struct…
Adaptive Large Neighborhood Search with a Constant-Time Feasibility Test for the Dial-a-Ride Problem
2019
In the dial-a-ride problem, user-specified transport requests from origin to destination points have to be served by a fleet of homogeneous vehicles. The problem variant we consider aims at finding a set of minimum-cost routes satisfying constraints on vehicle capacity, time windows, maximum route duration, and maximum user ride times. We propose an adaptive large neighborhood search (ALNS) for its solution. The key novelty of the approach is an exact amortized constant-time algorithm for evaluating the feasibility of request insertions in the repair steps of the ALNS. In addition, we use two optional improvement techniques: a local-search-based intraroute improvement of routes of promisin…
A note on symmetry reduction for circular traveling tournament problems
2011
Abstract The traveling tournament problem (TTP) consists of finding a distance-minimal double round-robin tournament where the number of consecutive breaks is bounded. Easton et al. (2001) introduced the so-called circular TTP instances, where venues of teams are located on a circle. The distance between neighboring venues is one, so that the distance between any pair of teams is the distance on the circle. It is empirically proved that these instances are very hard to solve due to the inherent symmetry. This note presents new ideas to cut off essentially identical parts of the solution space. Enumerative solution approaches, e.g. relying on branch-and-bound, benefit from this reduction. We…
Advances in vehicle routing and logistics optimization
2019
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Dual Inequalities for Stabilized Column Generation Revisited
2014
Column generation (CG) models have several advantages over compact formulations: they provide better linear program bounds, may eliminate symmetry, and can hide nonlinearities in their subproblems. However, users also encounter drawbacks in the form of slow convergence, also known as the tailing-off effect, and the oscillation of the dual variables. Among different alternatives for stabilizing the CG process, Ben Amor et al. [Ben Amor H, Desrosiers J, Valério de Carvalho JM (2006) Dual-optimal inequalities for stabilized column generation. Oper. Res. 54(3):454–463] suggest the use of dual-optimal inequalities (DOIs) in the context of cutting stock and bin packing problems. We generalize th…
Stabilized branch-and-price algorithms for vector packing problems
2018
Abstract This paper considers packing and cutting problems in which a packing/cutting pattern is constrained independently in two or more dimensions. Examples are restrictions with respect to weight, length, and value. We present branch-and-price algorithms to solve these vector packing problems (VPPs) exactly. The underlying column-generation procedure uses an extended master program that is stabilized by (deep) dual-optimal inequalities. While some inequalities are added to the master program right from the beginning (static version), other violated dual-optimal inequalities are added dynamically. The column-generation subproblem is a multidimensional knapsack problem, either binary, boun…
A branch-and-price framework for decomposing graphs into relaxed cliques
2021
We study the family of problems of partitioning and covering a graph into/with a minimum number of relaxed cliques. Relaxed cliques are subsets of vertices of a graph for which a clique-defining property—for example, the degree of the vertices, the distance between the vertices, the density of the edges, or the connectivity between the vertices—is relaxed. These graph partitioning and covering problems have important applications in many areas such as social network analysis, biology, and disease-spread prevention. We propose a unified framework based on branch-and-price techniques to compute optimal decompositions. For this purpose, new, effective pricing algorithms are developed, and new…
Asymmetry matters: Dynamic half-way points in bidirectional labeling for solving shortest path problems with resource constraints faster
2017
Abstract With their paper “Symmetry helps: Bounded bi-directional dynamic programming for the elementary shortest path problem with resource constraints” [Discrete Optimization 3, 2006, pp. 255–273] Righini and Salani introduced bounded bidirectional dynamic programming (DP) as an acceleration technique for solving variants of the shortest path problem with resource constraints (SPPRC). SPPRCs must be solved iteratively when vehicle routing and scheduling problems are tackled via Lagrangian relaxation or column-generation techniques. Righini and Salani and several subsequent works have shown that bounded bidirectional DP algorithms are often superior to their monodirectional counterparts, s…
Effective Handling of Dynamic Time Windows and Its Application to Solving the Dial-a-Ride Problem
2015
A dynamic time window relates to two operations that must be executed within a given time meaning that the difference between the points in time when the two operations are performed is bounded from above. The most prevalent context of dynamic time windows is when precedence is given for the two operations so that it is a priori specified that one operation must take place before the other. A prominent vehicle routing problem with dynamic time windows and precedence is the dial-a-ride problem (DARP), where user-specified transportation requests from origin to destination points must be serviced. The paper presents a new branch-and-cut-and-price solution approach for the DARP, the prototypi…
Upper and lower bounds for the vehicle-routing problem with private fleet and common carrier
2019
Abstract The vehicle-routing problem with private fleet and common carrier (VRPPC) extends the capacitated VRP by considering the option of outsourcing customers to subcontractors at a customer-dependent cost instead of serving them with the private fleet. The VRPPC has important applications in small package shipping and manufacturing, but despite its relevance, no exact solution approach has been introduced so far. We propose a branch-price-and-cut algorithm that is able to solve small to medium-sized instances and provides tight lower bounds for larger instances from the literature. In addition, we develop a large neighborhood search that shows a decent solution quality and competitive r…
A comparison of column-generation approaches to the Synchronized Pickup and Delivery Problem
2015
Abstract In the Synchronized Pickup and Delivery Problem (SPDP), user-specified transportation requests from origin to destination points have to be serviced by a fleet of homogeneous vehicles. The task is to find a set of minimum-cost routes satisfying pairing and precedence, capacities, and time windows. Additionally, temporal synchronization constraints couple the service times at the pickup and delivery locations of the customer requests in the following way: a request has to be delivered within prespecified minimum and maximum time lags (called ride times) after it has been picked up. The presence of these ride-time constraints severely complicates the subproblem of the natural column-…
Variable Fixing for Two-Arc Sequences in Branch-Price-and-Cut Algorithms on Path-Based Models
2020
Variable fixing by reduced costs is a popular technique for accelerating the solution process of mixed-integer linear programs. For vehicle-routing problems solved by branch-price-and-cut algorithms, it is possible to fix to zero the variables associated with all routes containing at least one arc from a subset of arcs determined according to the dual solution of a linear relaxation. This is equivalent to removing these arcs from the network used to generate the routes. In this paper, we extend this technique to routes containing sequences of two arcs. Such sequences or their arcs cannot be removed directly from the network because routes traversing only one arc of a sequence might still b…