Browsing by Subject "Branch-and-price"

Now showing 1 - 7 of 7

Open Access
A decomposable branch-and-price formulation for optimal classification trees
(2024-07) Yöner, Elif Rana
Construction of Optimal Classification Trees (OCTs) using mixed-integer programs, is a promising approach as it returns a tree with minimum classification error. Yet solving integer programs to optimality is known to be computationally costly, especially as the size of the instance and the depth of the tree grow, calling for efficient solution methods. Our research presents a new, decomposable model which lends itself to efficient solution algorithms such as Branch-and-Price. We model the classification tree using a “patternbased” formulation, deciding which feature should be used to split data at each branching node of each leaf. Our results are promising, illustrating the potential of decomposition in the domain of binary OCTs.
Open Access
A branch-and-price algorithm for the vehicle routing problem with roaming delivery locations
(Elsevier Ltd, 2017) Ozbaygin G.; Ekin Karasan O.; Savelsbergh M.; Yaman, H.
We study the vehicle routing problem with roaming delivery locations in which the goal is to find a least-cost set of delivery routes for a fleet of capacitated vehicles and in which a customer order has to be delivered to the trunk of the customer's car during the time that the car is parked at one of the locations in the (known) customer's travel itinerary. We formulate the problem as a set-covering problem and develop a branch-and-price algorithm for its solution. The algorithm can also be used for solving a more general variant in which a hybrid delivery strategy is considered that allows a delivery to either a customer's home or to the trunk of the customer's car. We evaluate the effectiveness of the many algorithmic features incorporated in the algorithm in an extensive computational study and analyze the benefits of these innovative delivery strategies. The computational results show that employing the hybrid delivery strategy results in average cost savings of nearly 20% for the instances in our test set. © 2017 Elsevier Ltd
Open Access
Exact solution approaches for non-Hamiltonian vehicle routing problems
(2017-07) Özbaygın, Amine Gizem
In this thesis, we study di erent non-Hamiltonian vehicle routing problem variants and concentrate on developing e cient optimization algorithms to solve them. First, we consider the split delivery vehicle routing problem (SDVRP).We provide a vehicle-indexed ow formulation for the problem, and then, a relaxation obtained by aggregating the vehicle-indexed variables over all vehicles. This relaxation may have optimal solutions where several vehicles exchange loads at some customers. We cut-o such solutions either by extending the formulation locally with vehicle-indexed variables or by node splitting. We compare these approaches using instances from the literature and new randomly generated instances. Additionally, we introduce two new extensions of the SDVRP by restricting the number of splits and by relaxing the depot return requirement, and modify our algorithms to handle these extensions. Second, we focus on a problem unifying the notion of coverage and routing. In some real-life applications, it may not be viable to visit every single customer separately due to resource limitations or e ciency concerns. In such cases, utilizing the notion of coverage; i.e., satisfying the demand of multiple customers by visiting a single customer location, may be advantageous. With this motivation, we study the time constrained maximal covering salesman problem (TCMCSP) in which the aim is to nd a tour visiting a subset of customers so that the amount of demand covered within a limited time is maximized. We provide ow and cut formulations and derive valid inequalities. Since the connectivity constraints and the proposed valid inequalities are exponential in the size of the problem, we devise di erent branch-and-cut schemes. Computational experiments performed on a set of problem instances demonstrate the e ectiveness of the proposed valid inequalities in terms of strengthening the linear relaxation bounds as well as speeding up the solution procedure. Moreover, the results indicate the superiority of using a branch-and-cut methodology over a ow-based formulation. Finally, we discuss the relation between the problem parameters and the structure of optimal solutions based on the results of our experiments. Third, we study the vehicle routing problem with roaming delivery locations (VRPRDL) in which a customer order has to be delivered to the trunk of the customer's car during the time that the car is parked at one of the locations in the (known) customer's travel itinerary. We formulate the problem as a set covering problem and develop a branch-and-price algorithm for its solution. The algorithm can also be used for solving a more general variant in which a hybrid delivery strategy is considered that allows a delivery to either a customer's home or to the trunk of the customer's car. We evaluate the e ectiveness of the many algorithmic features incorporated in the algorithm in an extensive computational study and analyze the bene ts of these innovative delivery strategies. The computational results show that employing the hybrid delivery strategy results in average cost savings of nearly 20% for the instances in our test set.Finally, we consider the dynamic version of the VRPRDL in which customer itineraries may change during the execution of the planned delivery schedule, which can become infeasible or suboptimal as a result. We refer to this problem as the dynamic VRPRDL (D-VRPRDL) and propose an iterative solution framework in which the previously planned vehicle routes are re-optimized whenever an itinerary update is revealed. We use the branch-and-price algorithm developed for the static VRPRDL both for solving the planning problem (to obtain an initial delivery schedule) and for solving the re-optimization problems. Since many re-optimization problems may have to be solved during the execution stage, it is critical to produce solutions to these problems quickly. To this end, we devise heuristic procedures through which the columns generated during the previous branch-and-price executions can be utilized when solving a re-optimization problem. In this way, we may be able to save time that would otherwise be spent in generating columns which have already been (partially) generated when solving the previous problems, and nd optimal solutions or at least solutions of good quality reasonably quickly. We perform preliminary computational experiments and report the results.
Embargo
One-dimensional bin packing with pattern-dependent processing time
(Elsevier B.V., 2025-05-01) Marinelli, Fabrizio; Pizzuti, Andrea; Wu, Wei; Yagiura, Mutsunori
In this paper the classical one-dimensional bin packing problem is integrated with scheduling elements: a due date is assigned to each item and the time required to process each bin depends on the pattern being used. The objective is to minimize a convex combination of the material waste and the delay costs, both significant in many real-world contexts. We present a novel pattern-based mixed integer linear formulation suitable for different classical scheduling objective functions, and focus on the specific case where the delay cost corresponds to the maximum tardiness. The formulation is tackled by a branch-and-price algorithm where the pricing of the column generation scheme is a quadratic problem solved by dynamic programming. A sequential value correction heuristic (SVC) is used to feed with warm starting solutions the column generation which, in turn, feeds the SVC with optimal prices so as to compute refined feasible solutions during the enumeration. Computational tests show that both column generation and branch-and-price substantially outperform standard methods in computing dual bounds and exact solutions. Additional tests are presented to analyze the sensitivity to parameters’ changes.
Open Access
OSPF routing with optimal oblivious performance ratio under polyhedral demand uncertainty
(Springer, 2010) Altın, A.; Belotti, P.; Pınar, M. Ç.
We study the best OSPF style routing problem in telecommunication networks, where weight management is employed to get a routing configuration with the minimum oblivious ratio. We consider polyhedral demand uncertainty: the set of traffic matrices is a polyhedron defined by a set of linear constraints, and a routing is sought with a fair performance for any feasible traffic matrix in the polyhedron. The problem accurately reflects real world networks, where demands can only be estimated, and models one of the main traffic forwarding technologies, Open Shortest Path First (OSPF) routing with equal load sharing. This is an NP-hard problem as it generalizes the problem with a fixed demand matrix, which is also NP-hard. We prove that the optimal oblivious routing under polyhedral traffic uncertainty on a non-OSPF network can be obtained in polynomial time through Linear Programming. Then we consider the OSPF routing with equal load sharing under polyhedral traffic uncertainty, and present a compact mixed-integer linear programming formulation with flow variables. We propose an alternative formulation and a branch-and-price algorithm. Finally, we report and discuss test results for several network instances.
Open Access
Regenerator location problem in flexible optical networks
(Institute for Operations Research and the Management Sciences (I N F O R M S), 2017-06) Yıldız, B.; Karaşan, O. E.
In this study, we introduce the regenerator location problem in flexible optical networks. With a given traffic demand, the regenerator location problem in flexible optical networks considers the regenerator location, routing, bandwidth allocation, and modulation selection problems jointly to satisfy data transfer demands with the minimum cost regenerator deployment. We propose a novel branch-and-price algorithm for this challenging problem. Using real-world network topologies, we conduct extensive numerical experiments to both test the performance of the proposed solution methodology and evaluate the practical benefits of flexible optical networks. In particular, our results show that, making routing, bandwidth allocation, modulation selection, and regenerator placement decisions in a joint manner, it is possible to obtain drastic capacity enhancements when only a very modest portion of the nodes is endowed with the signal regeneration capability.
Open Access
Relay location in telecommunications and transportation networks
(2016-03) Yıldız, Barış
With di↵erent names and functions, relays play a crucial role in the design of telecommunications and transportation networks and finding optimal relay locations is an important concern in various applications. We investigate several relay location problems from the literature, propose new ones and design efficient solution methods to obtain managerial insights. The basic problem we investigate in this dissertation is the Regenerator Location Problem (RLP). We revisit RLP from the hub location perspective and introduce two new dimensions involving the challenges of survivability. Considering the flexible optical network architecture, we relax all pairs connectivity, infinite capacity links and single modulation level assumptions of RLP and introduce the regenerator location problem in flexible optical networks (RLP-FON). RLP-FON solves regenerator location, routing, bandwidth allocation and modulation selection problems jointly to better exploit the opportunities o↵ered by this novel network architecture. For various problems arising in telecommunications and transportation it is beneficial to consider edge design and relay locations together. We add the edge design aspect to RLP and extend our research to Network Design Problem with Relays. Di↵erent than telecommunications networks, the total length of a route is an important issue in transportation. So in the final part we include circuitry constraints to the routing decisions and study the Refueling Station Location Problem for Alternative Fuel Vehicles. We approach relay location problems from di↵erent angles: network topologies, capacities, costs, and demands and provide significant theoretical results. For all relay location problems, the reach limitations for the related entities pose the main challenge and we propose novel path-segment based formulation approaches to incorporate these constraints in an efficient way. Extensive numerical experiments with realistic problem instances attest to the efficacy of the proposed approach.