Browsing by Subject "Branch-and-cut"

Now showing 1 - 16 of 16

Open Access
An application of capacitated lot-sizing model in petroleum sector
(2006) Nurlu, Nuri Barış
In this thesis, we study capacitated lot-sizing problem with special feature, applicable to the petroleum refinery sector. In our model, the end-products should be stored in item-specific and capacitated storage tanks during pre-determined lead-time. Our aim is to find the optimum production schedule resulting minimum total cost whilst satisfying customer demand. To solve this problem in a reasonable amount of time, we propose a branch-and-cut algorithm. We perform experiments based on the data gathered from Turkish Petroleum Refineries Corporation. In order to evaluate our algorithm, we compare the results of our algorithm and the solution results of the optimization software.
Open Access
Benders decomposition algorithms for two variants of the single allocation hub location problem
(Springer, 2019) Ghaffarinasab, N.; Kara, Bahar Y.
The hub location problem (HLP) is a special type of the facility location problem with numerous applications in the airline industry, postal services, and computer and telecommunications networks. This paper addresses two basic variants of the HLP, namely the uncapacitated single allocation hub location problem (USAHLP) and the uncapacitated single allocation p-hub median problem (USAp HMP). Exact solution procedures based on Benders decomposition algorithm are proposed to tackle large sized instances of these problems. The standard Benders decomposition algorithm is enhanced through implementation of several algorithmic refinements such as using a new cut disaggregation scheme, generating strong optimality cuts, and an efficient algorithm to solve the dual subproblems. Furthermore, a modern implementation of the algorithm is used where a single search tree is established for the problem and Benders cuts are successively added within a branch-and-cut framework. Extensive computational experiments are conducted to examine the efficiency of the proposed algorithms. We have been able to solve all the instances of the problems from all three main data sets of the HLP to optimality in reasonable computational times.
Open Access
A branch-and-cut algorithm for quadratic assignment problems based on linearizations
(Elsevier, 2007-04) Erdoğan, G.; Tansel, B.
The quadratic assignment problem (QAP) is one of the hardest combinatorial optimization problems known. Exact solution attempts proposed for instances of size larger than 15 have been generally unsuccessful even though successful implementations have been reported on some test problems from the QAPLIB up to size 36. In this study, we focus on the Koopmans–Beckmann formulation and exploit the structure of the flow and distance matrices based on a flow-based linearization technique that we propose. We present two new IP formulations based on the flow-based linearization technique that require fewer variables and yield stronger lower bounds than existing formulations. We strengthen the formulations with valid inequalities and report computational experience with a branch-and-cut algorithm. The proposed method performs quite well on QAPLIB instances for which certain metrics (indices) that we proposed that are related to the degree of difficulty of solving the problem are relatively high (⩾0.3⩾0.3). Many of the well-known instances up to size 25 from the QAPLIB (e.g. nug24, chr25a) are in this class and solved in a matter of days on a single PC using the proposed algorithm.
Open Access
A branch-and-cut algorithm for the alternative fuel refueling station location problem with routing
(INFORMS, 2019) Arslan, O.; Karaşan, Oya Ekin; Mahjoub, A. R.; Yaman, Hande
Because of the limited range of alternative fuel vehicles (AFVs) and the sparsity of the available alternative refueling stations (AFSs), AFV drivers cooperatively deviate from their paths to refuel. This deviation is bounded by the drivers’ tolerance. Taking this behavior into account, the refueling station location problem with routing (RSLP-R) is defined as maximizing the AFV flow that can be accommodated in a road network by locating a given number of AFSs while respecting the range limitation of the vehicles and the deviation tolerance of the drivers. In this study, we develop a natural model for the RSLP-R based on the notion of length-bounded cuts, analyze the polyhedral properties of this model, and develop a branch-and-cut algorithm as an exact solution approach. Extensive computational experiments show that the algorithm significantly improves the solution times with respect to previously developed exact solution methods and extends the size of the instances solved to optimality. Using our methodology, we investigate the tradeoffs between covered vehicle flow and deviation tolerance of the drivers and present insights on deviation characteristics of drivers in a case study in California.
Open Access
A branch-and-cut algorithm for the hub location and routing problem
(Elsevier, 2014) Rodríguez-Martín, I.; Salazar-González, J-J.; Yaman, H.
We study the hub location and routing problem where we decide on the location of hubs, the allocation of nodes to hubs, and the routing among the nodes allocated to the same hubs, with the aim of minimizing the total transportation cost. Each hub has one vehicle that visits all the nodes assigned to it on a cycle. We propose a mixed integer programming formulation for this problem and strengthen it with valid inequalities. We devise separation routines for these inequalities and develop a branch-and-cut algorithm which is tested on CAB and AP instances from the literature. The results show that the formulation is strong and the branch-and-cut algorithm is able to solve instances with up to 50 nodes.
Open Access
A branch-and-cut algorithm for two-level survivable network design problems
(Elsevier, 2016) Rodríguez-Martín, I.; Salazar-González, J-J.; Yaman, H.
This paper approaches the problem of designing a two-level network protected against single-edge failures. The problem simultaneously decides on the partition of the set of nodes into terminals and hubs, the connection of the hubs through a backbone network (first network level), and the assignment of terminals to hubs and their connection through access networks (second network level). We consider two survivable structures in both network levels. One structure is a two-edge connected network, and the other structure is a ring. There is a limit on the number of nodes in each access network, and there are fixed costs associated with the hubs and the access and backbone links. The aim of the problem is to minimize the total cost. We give integer programming formulations and valid inequalities for the different versions of the problem, solve them using a branch-and-cut algorithm, and discuss computational results. Some of the new inequalities can be used also to solve other problems in the literature, like the plant cycle location problem and the hub location routing problem.
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
Exact solution approaches for the minimum total cost traveling salesman problem with multiple drones
(Elsevier, 2023-01-04) Özbaygın Tiniç, G.; Karasan, Oya Ekin; Kara, Bahar Yetiş; Campbell, J.F.; Özel. A.
Deployment of drones in delivery operations has been attracting growing interest from the commercial sector due to its prospective advantages for a range of distribution systems. Motivated by the widespread adoption of drones in last-mile delivery, we introduce the minimum cost traveling salesman problem with multiple drones, where a truck and multiple drones work in synchronization to deliver parcels to customers. In this problem, we aim to find an optimal delivery plan for the truck and drones operating in tandem with the objective of minimizing the total operational cost including the vehicles’ operating and waiting costs. Unlike most studies in the literature where the objective is to minimize completion time, which means one needs to know only the arrival time of the latest arriving vehicle (truck or drone) at each synchronization point, we need to keep track of all the individual waiting times of the truck and the drones to properly account for waiting costs, which makes it more challenging to handle the synchronization. We provide a flow based and two cut based mixed integer linear programming formulations strengthened with valid inequalities. For non-compact models, we devise a variety of branch-and-cut schemes to solve our problem to optimality. To compare our formulations/algorithms and to demonstrate their competitiveness, we conduct computational experiments on a range of instances. The results indicate the superiority of utilizing branch-and-cut methodology over a flow based formulation. We also use our model to conduct sensitivity analyses with several problem parameters and to explore the benefits of launch and retrieval at the same node, the tradeoff between the number of drones and the operational cost, and the special case with a minimize completion objective with one drone. We also document very low waiting times for drones in optimal solutions and show solutions from minimizing cost have much lower cost than those from minimizing makespan.
Open Access
Hierarchical Survivable Network Design Problems
(Elsevier, 2016) Rodríguez-Martín, I.; Salazar-González, J-J.; Yaman, H.
We address the problem of designing two-level networks protected against single edge failures. A set of nodes must be partitioned into terminals and hubs, hubs must be connected through a backbone network, and terminals must be assigned to hubs and connected to them through access networks, being the objective to minimize the total cost. We consider two survivable structures, two-edge connected (2EC) networks and rings, in both levels of the network. We present an integer programming formulation for these problems, solve them using a branch-and-cut algorithm, and show some computational results.
Open Access
k-node-disjoint hop-constrained survivable networks: polyhedral analysis and branch and cut
(Springer-Verlag France, 2018) Diarrassouba, I.; Mahjoub, M.; Mahjoub, A. R.; Yaman, Hande
Given a graph with weights on the edges, a set of origin and destination pairs of nodes, and two integers L ≥ 2 and k ≥ 2, the k-node-disjoint hop-constrained network design problem is to find a minimum weight subgraph of G such that between every origin and destination there exist at least k node-disjoint paths of length at most L. In this paper, we consider this problem from a polyhedral point of view. We propose an integer linear programming formulation for the problem for L ∈{2,3} and arbitrary k, and investigate the associated polytope. We introduce new valid inequalities for the problem for L ∈{2,3,4}, and give necessary and sufficient conditions for these inequalities to be facet defining. We also devise separation algorithms for these inequalities. Using these results, we propose a branch-and-cut algorithm for solving the problem for both L = 3 and L = 4 along with some computational results.
Open Access
Optimization of last-mile deliveries with synchronous truck and drones
(2020-07) Özel, Aysu
Deployment of drones in delivery operations has been attracting a growing interest from commercial sector due to its prospective advantages for the distribution systems. Motivated by the widespread adoption of drones in last-mile delivery, we introduce the minimum cost traveling salesman problem with multiple drones, where a truck and multiple drones work in synchronization to deliver parcels to customers. In this problem, we aim to ﬁnd an optimal delivery plan for the truck and drones operating in tandem with the objective of minimizing the total operational cost including the vehicles’ operating and waiting costs. We provide ﬂow based and cut based mixed integer linear programming formulations along with valid inequalities. Since the connectivity constraints in the cut based formulation and the proposed valid inequalities are exponential in the size of the problem, we devise diﬀerent branch-and-cut schemes to solve our problem. We also provide an alternative solution methodology using another cut based formulation with undirected route variables. To compare our formulations/algorithms and to demonstrate their competitiveness, we conduct computational experiments on a set of instances. The results indicate the superiority of utilizing branch-and-cut methodology over ﬂow based formulation and good computational performance of the proposed algorithms in comparison to existing exact solution approaches in the literature. We also conduct sensitivity analyses on problem parameters and discuss their eﬀects on the optimal solutions.
Open Access
The periodic vehicle routing problem with driver consistency
(Elsevier, 2019) Rodríguez-Martín, I.; Salazar-González, J. -J.; Yaman, Hande
The Periodic Vehicle Routing Problem is a generalization of the classical capacitated vehicle routing problem in which routes are determined for a planning horizon of several days. Each customer has an associated set of allowable visit schedules, and the objective of the problem is to design a set of minimum cost routes that give service to all the customers respecting their visit requirements. In this paper we study a new variant of this problem in which we impose that each customer should be served by the same vehicle/driver at all visits. We call this problem the Periodic Vehicle Routing Problem with Driver Consistency. We present an integer linear programming formulation for the problem and derive several families of valid inequalities. We solve it using an exact branch-and-cut algorithm, and show computational results on a wide range of randomly generated instances.
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.
Open Access
The ring/κ-rings network design problem: model and branch-and-cut algorithm
(John Wiley & Sons, 2016) Rodríguez-Martín, I.; Salazar-González, J-J.; Yaman, H.
This article considers the problem of designing a two-level network where the upper level consists of a backbone ring network connecting the so-called hub nodes, and the lower level is formed by access ring networks that connect the non-hub nodes to the hub nodes. There is a fixed cost for each type of link, and a facility opening cost associated to each hub. The number of nodes in each access ring is bounded, and the number of access rings connected to a hub is limited to κ, thus resulting in a ring/κ-rings topology. The aim is to decide the hubs to open and to design the backbone and access rings to minimize the installation cost. We propose a mathematical model, give valid inequalities, and describe a branch-and-cut algorithm to solve the problem. Computational results show the algorithm is able to find optimal solutions on instances involving up to 40 nodes within a reasonable time.
Open Access
Survivability in hierarchical telecommunications networks
(John Wiley & Sons, 2012) Fouilhoux, P.; Karasan, O. E.; Mahjoub, A. R.; Ökök, O.; Yaman, H.
The survivable hierarchical telecommunications network design problem consists of locating concentrators, assigning user nodes to concentrators, and linking concentrators in a reliable backbone network. In this article, we study this problem when the backbone is 2-edge connected and when user nodes are linked to concentrators by a point-to-point access network. We formulate this problem as an integer linear program and present a facial study of the associated polytope. We describe valid inequalities and give sufficient conditions for these inequalities to be facet defining. We investigate the computational complexity of the corresponding separation problems. We propose some reduction operations to speed up the separation procedures. Finally, we devise a branch-and-cut algorithm based on these results and present the outcome of a computational study.
Open Access
Time constrained maximal covering salesman problem with weighted demands and partial coverage
(Elsevier Ltd, 2016) Ozbaygin, G.; Yaman, H.; Karasan, O. E.
In a routing framework, it may not be viable to visit every single customer separately due to resource limitations or efficiency 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 find a tour visiting a subset of customers so that the amount of demand covered within a limited time is maximized. We provide flow 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 different branch-and-cut schemes. Computational experiments performed on a set of problem instances demonstrate the effectiveness 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 flow-based formulation. Finally, we discuss the relation between the problem parameters and the structure of optimal solutions based on the results of our experiments. © 2016 Elsevier Ltd