Dealing with residual energy when transmitting data in energy-constrained capacitated networks

This paper addresses several problems relating to the energy available after the transmission of a given amount of data in a capacitated network. The arcs have an associated parameter representing the energy consumed during the transmission along the arc and the nodes have limited power to transmit data. In the first part of the paper, we consider the problem of designing a path which maximizes the minimum of the residual energy remaining at the nodes. After formulating the problem and proving the main theoretical results, a polynomial time algorithm is proposed based on computing maxmin paths in a sequence of non-capacitated networks. In the second part of the paper, the problem of obtaining a quickest path in this context is analyzed. First, the bi-objective variant of this problem is considered in which we aim to minimize the transmission time and to maximize the minimum residual energy. An exact polynomial time algorithm is proposed to find a minimal complete set of efficient solutions which amounts to solving shortest path problems. Second, the problem of computing an energy-constrained quickest path which guarantees at least a given residual energy at the nodes is reformulated as a variant of the energy-constrained quickest path problem. The algorithms are tested on a set of benchmark problems providing the optimal solution or the Pareto front within reasonable computing times

A Partial Allocation Local Search Matheuristic for Solving the School Bus Routing Problem with Bus Stop Selection

This paper addresses the school bus routing problem with bus stop selection, which jointly handles the problems of determining the set of bus stops to visit, allocating each student to one of these bus stops and computing the routes that visit the selected bus stops, so that the total routing cost is minimized and the walking distance of the students is limited by a given value. A fast and efficient matheuristic is developed based on an innovative approach that first partially allocates the students to a set of active stops that they can reach, and computes a set of routes that minimizes the routing cost. Then, a refining process is performed to complete the allocation and to adapt the routes until a feasible solution is obtained. The algorithm is tested on a set of benchmark instances. The computational results show the efficiency of the algorithm in terms of the quality of the solutions yielded and the computing time

A decision tool based on bilevel optimization for the allocation of water resources in a hierarchical system

This paper addresses the optimal allocation of water among competing stakeholders during a finite planning horizon. We focus on those water systems where there are two levels of decision making organized according to a hierarchical framework. At the upper level, a central authority allocates water to demand points having regard to environmental and sustainability issues as well as balancing water users' supply/demand. At the lower level of the hierarchy, demand point managers allocate water to users prioritizing economic strategies. On the other hand, when it comes to allocating limited resources that affect public welfare, the authority in charge can also use different political instruments such as fees to influence the decisions made at those levels of decision making that are not directly within its competence. We propose a multiobjective multifollower bilevel optimization problem that aims to fulfill the central authority goals while including the reaction of the demand point managers in terms of optimization problems as constraints. Using the well-known Karush–Kuhn–Tucker approach, we transform the bilevel model into an equivalent multiobjective mixed-integer single-level model for which we provide tight big-M values. For the purpose of showing the versatility of the model, extensive computational experiments on a set of instances have been carried out. The results show that the optimization problem can be solved to optimality in small computing times using off-the-shelf mixed-integer solvers even for complex water systems and long planning periods. In addition, they illustrate the effect of imposing fees on the achievement of the central authority's objectives

Circulaciones y flujo máximo con cotas paramétricas

Se estudian los problemas de obtención de circulaciones factibles y de flujo máximo en redes con cotas inferiores y superiores sobre los arcos, que son funciones lineales dependientes de un parámetro. Se caracteriza la existencia de circulaciones paramétricas y de flujos paramétricos factibles y se dan condiciones necesarias y suficientes para la optimalidad de un flujo paramétrico. Finalmente, se proponen algoritmos que permiten su cálculo

Diseños fi-óptimos marginalmente restringidos

Título otros idiomas: Marginally restricted phi-optimal designsDepto. de Estadística e Investigación OperativaFac. de Ciencias MatemáticasTRUEpu

The school bus routing problem with student choice: a bilevel approach and a simple and effective metaheuristic

The school bus routing problem (SBRP) involves interrelated decisions such as selecting the bus stops, allocating the students to the selected bus stops, and designing the routes for transporting the students to the school taking into account the bus capacity constraint, with the objective of minimizing the cost of the routes. This paper addresses the SBRP when the reaction of students to the selection of bus stops is taken into account, that is, when students are allowed to choose the selected bus stop that best suits them. A bilevel optimization model with multiple followers is formulated, and its transformation into a single-level mixed integer linear programming (MILP) model is proposed. A simple and effective metaheuristic algorithm is also developed to solve the problem. This algorithm involves solving four MILP problems at the beginning, which can be used to obtain tight upper bounds of the optimal solution. Extensive computational experiments on SBRP benchmark instances from the literature show the effectiveness of the proposed algorithm in terms of both the quality of the solution found and the required computing time

A comprehensive survey on the quickest path problem

Abstract This work is a survey on a special minsum-maxmin bicriteria problem, known as the quickest path problem, that can model the transmission of data between two nodes of a network. Moreover, the authors review the problems of ranking the K quickest paths, and the K quickest loopless paths, and compare them in terms of the worst-case complexity order. The classification presented led to the proposal of a new variant of a known K quickest loopless paths algorithm. Finally, applications of quickest path algorithms are mentioned, as well as some comparative empirical results