Journal•ISSN: 1862-4472
Optimization Letters
Springer Science+Business Media
About: Optimization Letters is an academic journal published by Springer Science+Business Media. The journal publishes majorly in the area(s): Computer science & Optimization problem. It has an ISSN identifier of 1862-4472. Over the lifetime, 1935 publications have been published receiving 23318 citations.
Topics: Computer science, Optimization problem, Computational intelligence, Variational inequality, Convex optimization
Papers published on a yearly basis
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TL;DR: The VRPD is motivated by a number of highly influential companies such as Amazon, DHL, and Federal Express, actively involved in exploring the potential use of commercial drones for package delivery.
Abstract: In this paper, we introduce the vehicle routing problem with drones (VRPD). A fleet of trucks equipped with drones delivers packages to customers. Drones can be dispatched from and picked up by the trucks at the depot or any of the customer locations. The objective is to minimize the maximum duration of the routes (i.e., the completion time). The VRPD is motivated by a number of highly influential companies such as Amazon, DHL, and Federal Express, actively involved in exploring the potential use of commercial drones for package delivery. After stating our simplifying assumptions, we pose a number of questions in order to study the maximum savings that can be obtained from using drones; we then derive a number of worst-case results. The worst-case results depend on the number of drones per truck and the speed of the drones relative to the speed of the truck.
318 citations
TL;DR: A direct generalized Newton method is proposed for solving the NP-hard absolute value equation (AVE) Ax − |x| = b when the singular values of A exceed 1.
Abstract: A direct generalized Newton method is proposed for solving the NP-hard absolute value equation (AVE) Ax − |x| = b when the singular values of A exceed 1. A simple MATLAB implementation of the method solved 100 randomly generated 1,000-dimensional AVEs to an accuracy of 10−6 in less than 10 s each. Similarly, AVEs corresponding to 100 randomly generated linear complementarity problems with 1,000 × 1,000 nonsymmetric positive definite matrices were also solved to the same accuracy in less than 29 s each.
207 citations
TL;DR: A perl language program is described to create time-to-target solution value plots for measured CPU times that are assumed to fit a shifted exponential distribution in local search based heuristics for combinatorial optimization.
Abstract: This paper describes a perl language program to create time-to-target solution value plots for measured CPU times that are assumed to fit a shifted exponential distribution. This is often the case in local search based heuristics for combinatorial optimization, such as simulated annealing, genetic algorithms, iterated local search, tabu search, WalkSAT, and GRASP. Such plots are very useful in the comparison of different algorithms or strategies for solving a given problem and have been widely used as a tool for algorithm design and comparison. We first discuss how TTT plots are generated. This is followed by a description of the perl program tttplots.pl.
200 citations
TL;DR: A two-stage stochastic programming model is developed for a humanitarian relief logistics problem where decisions are made for pre- and post-disaster rescue centers, the amount of relief items to be stocked at the pre-disasters rescue center, the amounts of relief item flows at each echelon, and the amountof relief item shortage.
Abstract: We develop a two-stage stochastic programming model for a humanitarian relief logistics problem where decisions are made for pre- and post-disaster rescue centers, the amount of relief items to be stocked at the pre-disaster rescue centers, the amount of relief item flows at each echelon, and the amount of relief item shortage. The objective is to minimize the total cost of facility location, inventory holding, transportation and shortage. The deterministic equivalent of the model is formulated as a mixed-integer linear programming model and solved by a heuristic method based on Lagrangean relaxation. Results on randomly generated test instances show that the proposed solution method exhibits good performance up to 25 scenarios. We also validate our model by calculating the value of the stochastic solution and the expected value of perfect information.
166 citations
TL;DR: A simple MATLAB implementation of the successive linearization algorithm solved 100 consecutively generated 1,000-dimensional random instances of the AVE with only five violated equations out of a total of 100,000 equations.
Abstract: The NP-hard absolute value equation (AVE) Ax − |x| = b where \(A\in R^{n\times n}\) and \(b\in R^n\) is solved by a succession of linear programs The linear programs arise from a reformulation of the AVE as the minimization of a piecewise-linear concave function on a polyhedral set and solving the latter by successive linearization A simple MATLAB implementation of the successive linearization algorithm solved 100 consecutively generated 1,000-dimensional random instances of the AVE with only five violated equations out of a total of 100,000 equations
143 citations