Chungmok Lee

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.

A Robust Scenario Approach for the Vehicle Routing Problem with Uncertain Travel Times

We consider a vehicle routing problem with uncertain travel times in which a penalty is incurred for each vehicle that exceeds a given time limit. A traditional stochastic programming approach would require precise knowledge of the underlying probability distributions of random data. In a novel approach presented here, we assume that only rough information on future travel times is available, leading to the multiple range forecasts of travel times and the probabilities of each range being realized. In this setting, we replace the point estimates of travel times on a scenario by range estimates. For each scenario, we then find the robust routes that protect the solution against the worst case within the given ranges, and finally we find the routes with the minimum expected cost. We propose a branch-and-cut algorithm to solve the problem and report computational results on both randomly generated and the well-known Solomons instances. The results demonstrate that our approach is a favorable one when exact information of probability distributions is not available.

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.

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.

Parked cars as a service delivery platform

We introduce a new view of parked cars as a massive, flexible resource that is currently wasted. Given the power supply in batteries as well as computing, communication, and sensing facilities in cars in conjunction with the precise localization they can provide, parked cars have the potential to serve as a service delivery platform with a wide range of possibilities. We describe diverse applications that can be implemented using parked cars to show the flexibility of the infrastructure. Potential user groups and service providers are discussed. As an illustrative example, a simulation study of the use case of localizing persons in need of assistance is presented. Finally, the need for new algorithms and their analysis adapted to the specifics of parked cars is also highlighted.

Exact Algorithms for a Bandwidth Packing Problem with Queueing Delay Guarantees

The bandwidth packing problem BWP concerns the selection of calls from a given set and the assignment of one path to each selected call. The ultimate aim of the BWP is to maximize profit while the routings of the selected calls observe the capacity constraints of the links. Here, we additionally consider queueing delays in the network, which may cause a deterioration in the quality of service to users if they exceed the acceptable limits. The integer programming formulation for the BWP with the queueing delay restriction contains a nonlinear constraint that is intrinsic to the model. We apply the Dantzig-Wolfe decomposition to this nonlinear constraint, and since the Dantzig-Wolfe decomposition has exponentially many variables, we propose the branch-and-price procedure to find optimal solutions. We also propose a generalized Dantzig-Wolfe reformulation based on the aggregation of variables, which makes our branch-and-price algorithm more competitive. Computational results on cases of randomly generated networks and some real-life telecommunication networks demonstrate that our algorithm performs well for large networks.

Robust optimization approach for a chance-constrained binary knapsack problem

We consider a certain class of chance-constrained binary knapsack problem where each item has a normally distributed random weight that is independent of the other items. For this problem we propose an efficient pseudo-polynomial time algorithm based on the robust optimization approach for finding a solution with a theoretical bound on the probability of satisfying the knapsack constraint. Our algorithm is tested on a wide range of random instances, and the results demonstrate that it provides qualified solutions quickly. In contrast, a state-of-the-art MIP solver is only applicable for instances of the problem with a restricted number of items.

Multi-class classification using a signomial function

We propose two multi-class classification methods using a signomial function. Each of these methods directly constructs a multi-class classifier by solving a single optimization problem. Since the number of possible signomial terms is extremely large, we propose a column generation method that iteratively generates good signomial terms. Both of these methods obtain better or comparable classification accuracies than existing methods and also provide more sparse classifiers.

Embedded variable selection method using signomial classification

We propose two variable selection methods using signomial classification. We attempt to select, among a set of the input variables, the variables that lead to the best performance of the classifier. One method repeatedly removes variables based on backward selection, whereas the second method directly selects a set of variables by solving an optimization problem. The proposed methods conduct variable selection considering nonlinear interactions of variables and obtain a signomial classifier with the selected variables. Computational results show that the proposed methods more effectively selects desirable variables for predicting output and provide the classifiers with better or comparable test error rates, as compared with existing methods.

Multi-pattern generation framework for logical analysis of data

Logical analysis of data (LAD) is a rule-based data mining algorithm using combinatorial optimization and boolean logic for binary classification. The goal is to construct a classification model consisting of logical patterns (rules) that capture structured information from observations. Among the four steps of LAD framework (binarization, feature selection, pattern generation, and model construction), pattern generation has been considered the most important step. Combinatorial enumeration approaches to generate all possible patterns were mostly studied in the literature; however, those approaches suffered from the computational complexity of pattern generation that grows exponentially with data (feature) size. To overcome the problem, recent studies proposed column generation-based approaches to improve the efficacy of building a LAD model with a maximum-margin objective. There was still a difficulty in solving subproblems efficiently to generate patterns. In this study, a new column generation framework is proposed, in which a new mixed-integer linear programming approach is developed to generate multiple patterns having maximum coverage in subproblems at each iteration. In addition to the maximum-margin objective, we propose an alternative objective (minimum-pattern) to solve the LAD problem as a minimum set covering problem. The proposed approaches are evaluated on the datasets from the University of California Irvine Machine Learning Repository. The computational experiments provide comparable performances compared with previous LAD and other well-known classification algorithms.