Kyungsik Lee

Optimal routing and wavelength assignment in WDM ring networks

We consider the routing and wavelength assignment (RWA) problem on WDM ring networks without wavelength conversion. When the physical network and required connections are given, RWA is the problem to select a suitable path and wavelength among the many possible choices for each connection such that no two paths using the same wavelength pass through the same link. We give an integer programming formulation of the problem and propose an algorithm to solve it. Although the formulation has exponentially many variables, we solve the linear programming relaxation of it by using the column generation technique. We solve the column generation problem efficiently by decomposing the problem into several subproblems. After solving the linear programming relaxation, we apply the branch-and-price procedure to get an optimal solution. We test the proposed algorithm on some randomly generated data. Test results show that the algorithm gives optimal solutions to almost all instances under the given node limit of the branch-and-bound tree.

Robust Vehicle Routing Problem with Deadlines and Travel Time/Demand Uncertainty

In this article, we investigate the vehicle routing problem with deadlines, whose goal is to satisfy the requirements of a given number of customers with minimum travel distances while respecting both of the deadlines of the customers and vehicle capacity. It is assumed that the travel time between any two customers and the demands of the customer are uncertain. Two types of uncertainty sets with adjustable parameters are considered for the possible realizations of travel time and demand. The robustness of a solution against the uncertain data can be achieved by making the solution feasible for any travel time and demand defined in the uncertainty sets. We propose a Dantzig-Wolfe decomposition approach, which enables the uncertainty of the data to be encapsulated in the column generation subproblem. A dynamic programming algorithm is proposed to solve the subproblem with data uncertainty. The results of computational experiments involving two well-known test problems show that the robustness of the solution can be greatly improved.

An extended formulation approach to the edge-weighted maximal clique problem

We consider an extended formulation approach to the edge-weighted maximal clique problem. The problem is formulated by using additional variables for the set of nodes with the natural variables for the set of edges. We show that the proposed formulation is superior to the natural formulation both theoretically and practically. By using the projection technique, we can also derive new classes of facet-defining inequalities for the lower-dimensional polytope of the natural variables. Computational results are reported.

Modeling and solving the spatial block scheduling problem in a shipbuilding company

Abstract We consider the block scheduling problem arising in a shipyard. The problem is complicated since we are considering both scheduling and spatial allocation of each block simultaneously. Moreover, varying conditions in several work spaces should be reflected. We develop a scheduling algorithm using partial enumeration and decompostion. An efficient heuristic search procedure for the spatial allocation of blocks is also devised.

Benders decomposition approach for the robust network design problem with flow bifurcations

We consider a network design problem in which flow bifurcations are allowed. The demand data are assumed to be uncertain, and the uncertainties of demands are expressed by an uncertainty set. The goal is to install facilities on the edges at minimum cost. The solution should be able to deliver any of the demand requirements defined in the uncertainty set. We propose an exact solution algorithm based on a decomposition approach in which the problem is decomposed into two distinct problems: (1) designing edge capacities; and (2) checking the feasibility of the designed edge capacities with respect to the uncertain demand requirements. The algorithm is a special case of the Benders decomposition method. We show that the robust version of the Benders subproblem can be formulated as a linear program whose size is polynomially bounded. We also propose a simultaneous cut generation scheme to accelerate convergence of the Benders decomposition algorithm. Computational results on real-life telecommunication problems are reported, and these demonstrate that robust solutions with very small penalties in the objective values can be obtained.

Design of capacitated networks with tree configurations

This paper considers the problem of designing a capacitated network with a tree configuration (CTP). For a given set of nodes with their capacities,k types of link facilities with various characteristics, and installation cost for connecting each pair of nodes using each type of link facility, the problem is to find a tree network which satisfies the given traffic requirements between all pairs of nodes and minimizes total installation cost. We formulate (CTP) as an integer programming problem using path variables. To solve the linear programming relaxation which has exponentially many variables, we develop a polynomial-time column generation procedure. Moreover, to tighten the formulation, an efficient preprocessing procedure is devised and some classes of valid inequalities are found. Using the results, we develop a branch- and-cut algorithm with column generation where an efficient branching rule is adopted. Computational results show that the algorithm can solve practically-sized problems to optimality within a reasonable time.

A branch-and-price algorithm for the Steiner tree packing problem

This paper deals with the Steiner tree packing problem. For a given undirected graph G = (V, E) with positive integer capacities and non-negative weights on its edges, and a list of node sets (nets), the problem is to find a connection of nets which satisfies the edge capacity limits and minimizes the total weights. We focus on the switchbox routing problem in knock-knee model and formulate this problem as an integer programming using Steiner tree variables. We develop a branch-and-price algorithm. The algorithm is applied on some standard test instances and we compare the performances with the results using cutting-plane approach. Computational results show that our algorithm is competitive to the cutting plane algorithm presented by Grotschel et al. and can be used to solve practically sized problems.

Design of local networks using USHRs

We consider the problem of designing a local network in a two‐level telecommunication network. Given one or two hub nodes, central offices (COs) and conduits, the problem is to find a set of unidirectional self‐healing rings (USHRs) which covers all COs and satisfies all demands at minimum cost. The solution approach used is the decomposition and column generation. Master problem and subproblem are modeled as integer programming models. After the optimal solution to linear programming relaxation of the master problem is obtained, a branch‐and‐bound algorithm is used to get an integer solution. A set of valid inequalities for a subproblem is given and a branch‐and‐cut algorithm is used to find an optimal solution to the subproblem. Computational results using real data are reported.

Technical Note---Branch-and-Price-and-Cut Approach to the Robust Network Design Problem Without Flow Bifurcations

This paper presents a robust optimization approach to the network design problem under traffic demand uncertainty. We consider the specific case of the network design problem in which there are several alternatives in edge capacity installations and the traffic cannot be split over several paths. A new decomposition approach is proposed that yields a strong LP relaxation and enables traffic demand uncertainty to be addressed efficiently through localization of the uncertainty to each edge of the underlying network. A branch-and-price-and-cut algorithm is subsequently developed and tested on a set of benchmark instances.

Targeting and Scheduling Problem for Field Artillery

We consider the targeting and the fire sequencing problem for field artillery. We show that the targeting problem, which can be modeled as a problem with nonlinear constraints, can be transformed into a set of independent bounded variable knapsack problems. We also propose a mathematical model for the fire sequencing problem which is NP-hard and developed a heuristic to solve the problem. Computational results using randomly generated data are presented.