Letters

www.elsevier.com/locate/dsw A branch and bound algorithm for the robust shortest path problem with interval data

Stochastic vehicle routing with random time dependent travel times subject to perturbations

Assigning and scheduling vehicle routes in a stochastic time dependent environment is a crucial management problem. The assumption that in a real-life environment everything goes according to an a priori determined static schedule is unrealistic, resulting in a planning gap (i.e. difference in performance between planned route and actual route). Our methodology introduces the traffic congestion component based on queueing theory, thereby introducing an analytical expression for the expected travel. In real life travel times are subject to uncertainty, we solve a time dependent vehicle routing problem to find robust solutions, that can potentially absorb such uncertainties. We model uncertainty as perturbations that are randomly inserted on the routes, we optimize the perturbed solutions via Tabu Search. We conduct experiments on a set of 32 cities, and found that the perturbed solutions generally cope better with the uncertainty than the non-perturbed solutions, with a small increase in expected travel times

Исследование ускорения метода определения надёжного кратчайшего пути в зависящей от времени стохастической транспортной сети

Целью работы является модификация и исследование алгоритма нахождения надежного кратчайшего пути в зависящей от времени стохастической транспортной сети. Под надёжностью понимается максимизация вероятности прибытия в пункт назначения в заданный заранее интервал времени. Модификация базового алгоритма нахождения надежного кратчайшего пути проводится с целью повышения скорости работы алгоритма и заключается в выборе определенного подмножества вершин и ребер графа, которые доступны для построения кратчайшего пути. Предложены два метода выбора подмножества вершин и ребер графа: на основе ограничивающего прямоугольника и на основе алгоритма k кратчайших путей. Проведены экспериментальные исследования эффективности базового и модифицированного алгоритмов на примере транспортной сети города Самары.Работа выполнена при частичной финансовой поддержке гранта РФФИ 16-37-00055- мол_а

A linear programming based heuristic framework for min-max regret combinatorial optimization problems with interval costs

This work deals with a class of problems under interval data uncertainty, namely interval robust-hard problems, composed of interval data min-max regret generalizations of classical NP-hard combinatorial problems modeled as 0-1 integer linear programming problems. These problems are more challenging than other interval data min-max regret problems, as solely computing the cost of any feasible solution requires solving an instance of an NP-hard problem. The state-of-the-art exact algorithms in the literature are based on the generation of a possibly exponential number of cuts. As each cut separation involves the resolution of an NP-hard classical optimization problem, the size of the instances that can be solved efficiently is relatively small. To smooth this issue, we present a modeling technique for interval robust-hard problems in the context of a heuristic framework. The heuristic obtains feasible solutions by exploring dual information of a linearly relaxed model associated with the classical optimization problem counterpart. Computational experiments for interval data min-max regret versions of the restricted shortest path problem and the set covering problem show that our heuristic is able to find optimal or near-optimal solutions and also improves the primal bounds obtained by a state-of-the-art exact algorithm and a 2-approximation procedure for interval data min-max regret problems

Minmax regret combinatorial optimization problems: an Algorithmic Perspective

Candia-Vejar, A (reprint author), Univ Talca, Modeling & Ind Management Dept, Curico, Chile.Uncertainty in optimization is not a new ingredient. Diverse models considering uncertainty have been developed over the last 40 years. In our paper we essentially discuss a particular uncertainty model associated with combinatorial optimization problems, developed in the 90's and broadly studied in the past years. This approach named minmax regret (in particular our emphasis is on the robust deviation criteria) is different from the classical approach for handling uncertainty, stochastic approach, where uncertainty is modeled by assumed probability distributions over the space of all possible scenarios and the objective is to find a solution with good probabilistic performance. In the minmax regret (MMR) approach, the set of all possible scenarios is described deterministically, and the search is for a solution that performs reasonably well for all scenarios, i.e., that has the best worst-case performance. In this paper we discuss the computational complexity of some classic combinatorial optimization problems using MMR. approach, analyze the design of several algorithms for these problems, suggest the study of some specific research problems in this attractive area, and also discuss some applications using this model

Robust Optimization with Recovery: Application to Shortest Paths and Airline Scheduling

In this exploratory paper we consider a robust approach to decisional problems subject to uncertain data in which we have an additional knowledge on the strategy (algorithm) used to react to an unforeseen event or recover from a disruption. This is a typical situation in scheduling problems where the decision maker has no a priori knowledge on the probabilistic distribution of such events but he only knows rough information on the event, such as its impact on the schedule. We discuss a general framework to address this situation and its links with other existing methods, we present an illustrative example on the Shortest Path Problem with Interval Data (SPPID) and we discuss a more general application to airline scheduling with recovery