Andréa Cynthia Santos

Université Le Havre Normandie, ISEL

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,...

In the aftermath of disasters such as major earthquakes, several roads may be blocked by rubble and the population tends to search refugee in certain gathering points of the city. Road network accessibility becomes an important issue for logistic operations, specially on the first days after the quake, when the relief distribution is crucial for su...

In this study, we propose a mathematical model and heuristics for solving a multi-period location-allocation problem in post-disaster operations, which takes into account the impact of distribution over the population. Logistics restrictions such as human and financial resources are considered. In addition, a brief review on resilience system model...

In this article, a solution is proposed through a population-based metaheuristic for the Two-level Hub Location Routing Problem with Directed Tours (THLRP-DT). Hubs are facilities used to handle and dispatch resources on a given network. The goal of the THLRP-DT is to locate a set of hubs on a network and to route resources from sources to destinat...

This study presents models and heuristics for solving the strong network orientation problem (SNOP), which can model several tactical optimization problems of setting directions in urban networks. The objective is to set an orientation for each edge in an undirected graph such that the resulting digraph is strongly connected and the total travel di...

This article deals with two min-max regret covering problems: the min-max regret Weighted Set Covering Problem (min-max regret WSCP) and the min-max regret Maximum Benefit Set Covering Problem (min-max regret MSCP). These problems are the robust optimization counterparts, respectively, of the Weighted Set Covering Problem and of the Maximum Benefit...

Cleaning debris in urban areas after major disasters is very relevant to inhabitants to recover from their effects. In natural disasters, an unexpected and large area can be affected. Moreover, the time and the costs to perform the cleaning operations can be very high. In this work, the integrated multi-period scheduling routing problem to clean de...

This paper addresses a class of problems under interval data uncertainty, composed of min-max regret generalisations of classical 0-1 optimisation problems with interval costs. These problems are called robust-hard when their classical counterparts are already NP-hard. The state-of-the-art exact algorithms for interval 0-1 min-max regret problems i...

After disasters, such as in the aftermath of a major earthquake, the road network can be blocked by debris from collapsed buildings, impacting accessibility to the affected population. In addition, people move and assemble in various points of the city. In this context, road network accessibility becomes an important issue for logistics operations...

In the last decades, the urban mobility has become a critical issue with several social, economic and ecological challenges. This is a consequence of the fast and unplanned cities growth and of the high population density in urban areas. In this context, we focus on the Disruption Scheduling problem on Urban Networks (DSUN) which consists in schedu...

This paper addresses a class of problems under interval data uncertainty composed of min-max regret versions of classical 0-1 optimization problems with interval costs. We refer to them as interval 0-1 min-max regret problems. The state-of-the-art exact algorithms for this class of problems work by solving a corresponding mixed integer linear progr...

Goal: Post-disaster operations are a challenging issue, which becomes very complex due to the high density of population in urban areas. Thus, efficient relief operations are very relevant in attenuating the impacts of disasters on the population. For this purpose, optimizing post disaster operations plays a key role, and such issues are focused on...

Disruptions in urban roads can significantly alter the quality of the transportation network by generating more congestion, gas emission, noise, stress, etc. In some situations, it can even break the path between some pairs of nodes in the road network (strong connectivity in graph theory). To avoid this issue, traffic managers can temporarily chan...

Disruptions in urban road networks can quickly and significantly reduce the quality of the whole transportation network, and impact urban mobility for light vehicles, public transportation, etc. In this study, we consider both unidirectional and multidirectional road network problems with disruptions and connecting requirements. These problems aim...

Trees and forests have been a fascinating research topic in Operations Research (OR)/Management Science (MS) throughout the years because they are involved in numerous difficult problems, have interesting theoretical properties, and cover a large number of practical applications. A tree is a finite undirected connected simple graph with no cycles,...

Given a connected, undirected and m-partite complete graph \(G = (V_1 \cup V_2 \cup ... \cup V_m; E)\), the Generalized Minimum Spanning Tree Problem (GMSTP) consists in finding a tree with exactly \(m - 1\) edges, connecting the m clusters \(V_1, V_2, ..., V_m\) through the selection of a unique vertex in each cluster. GMSTP finds applications in...

This study is dedicated to a complex Vehicle Routing Problem (VRP) applied to the response phase after a natural disaster. Raised by the last mile distribution of relief goods after earthquakes, it is modelled as a rich VRP involving a heterogeneous fleet of vehicles, multiple trips, multiple depots, and vehicle-site dependencies. The proposed meth...

In this study, an aggregated flow formulation and a column generation strategy are proposed for the Strong Network Orientation Problem (SNOP) that consists in setting an orientation for each edge in a given graph, such that the resulting digraph is strongly connected and the total travel distance between all pairs of vertices is minimized. SNOP is...

In this study, we introduce the min-max regret Maximal Covering Location Problem (MR-MCLP), a robust counterpart of the Maximal Covering Location Problem. In MR-MCLP, the uncertain data is modeled by intervals and it is an NP-Hard problem, with applications in disaster logistics. We propose a mathematical formulation and three methods to solve this...

Hubs are facilities used to treat and dispatch resources in a transportation network. The objective of Hub Location Problems (HLP) is to locate a set of hubs in a network and route resources from origins to destinations such that the total cost of attending all demands is minimized. In this paper, we investigate a particular HLP, called the Tree of...

Given a m-partite graph G=(V ,E), where V and E stand respectively for the vertice-set and for the edge-set, such that the set of vertices is partitioned into m clusters, the Generalized Minimum Spanning Tree Problem (GMSTP) consists in finding a cost minimum tree with m - 1 edges and which spans a unique vertex in each cluster. This problem finds...

In this study, we propose a bi-objective mathematical model to solve the problem of finding deviations (alternate paths) on a given unidirectional road network whenever a set of disruptions occurs. Unidirectional networks can model city centers and touristic areas. Thus, an alternate path to avoid a blocked route may imply changing the orientation...

Trees and forests have been a fascinating research topic in Operations Research (OR)/Management Science (MS) throughout the years because they are involved in numerous difficult problems, have interesting theoretical properties, and cover a large number of practical applications. A tree is a finite undirected connected simple graph with no cycles,...

In this paper, a bi-objective Vehicle Routing Problem (bi-RVRP) with uncertainty in both demands and travel times is studied by means of robust optimization. Uncertain demands per customer are modeled by a discrete set of scenarios representing the deviations from an expected demand, while uncertain travel times are independent from customer demand...

In this study, we investigate the minmax regret Robust Weighted Set Covering problem with Interval Data (RSCP), which is the robust counterpart of the Weighted Set Covering Problem (WSCP) where uncertain data are modeled using interval data. RSCP is NP-Hard and can provide foundations for solving several minmax regret covering problems. Moreover, R...

The road network accessibility is an important issue for earthquake relief operations, since several roads may be damaged obstructing the access to certain areas. This work proposes a mathematical model and two heuristics for the road repairing work-troops scheduling in order to increase accessibility to the population as fast as possible after a m...

This paper addresses a class of problems under interval data uncertainty composed of min-max regret versions of classical 0–1 optimization problems with interval costs. We refer to them as interval 0–1 min-max regret problems. The state-of-the-art exact algorithms for this class of problems work by solving a corresponding mixed integer linear progr...

In this study, the problem of building cluster-based topologies for Wireless Sensor Networks with several sinks is considered. The optimization relies on different levels of decision: choosing which sensors are masters and balancing the load among sinks. The topology associated with each sink is modeled as an Independent Dominating Set with Connect...

In this study, we investigate the minmax regret Robust Weighted Set Covering problem with Interval Data (RSCP), which is the robust counterpart of the Weighted Set Covering Problem (WSCP) where uncertain data are modeled using interval data. RSCP is NP-Hard and can provide foundations for solving several minmax regret covering problems. Moreover, R...

The classical set partitioning problem is defined on a graph G = (V, E) and consists of partitioning V in disjoint subsets. In this study, we propose a Split procedure to minimize the number of partitions for a given sequence of nodes, considering local and global capacity constraints on the partitions. The procedure relies on dynamic programming a...

In this study, two multi-objective metaheuristics are presented for the bi-objective Minimum Diameter-Cost Spanning Tree problem (bi-MDCST). The bi-MDCST is a NP-Hard problem and models network design problems, where all nodes have to communicate with each other in a minimum cost and using a minimum number of hops (edges). The metaheuristics Non-do...

This study is dedicated to the Vehicle Routing Problem (VRP) variant found in the last mile distribution applied to disaster logistic. We investigate one Specialized VRP (SVRP) with multiples depots, heterogeneous fleet, with multiple trips and site dependent. This new VRP variant reflects the last mile distribution in post-disaster relief operatio...

The Capacitated Vehicle Routing Problem (CVRP) is extended here to handle uncertain arc costs without resorting to probability distributions, giving the Robust VRP (RVRP). The unique set of arc costs in the CVRP is replaced by a set of discrete scenarios. A scenario is for instance the travel time observed on each arc at a given traffic hour. The g...

In this study, scenario-based heuristics with path-relinking are investigated and applied to the Robust Set Covering Problem with Interval data (RSCP-I). Let us consider a 0-1 matrix A, with uncertain costs associated with each column of A, represented by an interval data. The RSCP-I aims at finding columns covering every line of A, such that the m...

In this study, the bi-objective Robust Vehicle Routing Problem with uncertainty in both demands and travel times (bi-RVRP) is investigated. The problem is modeled by means of robust optimization, where uncertain demands are represented by intervals and uncertain travel times are defined as a set of discrete scenarios. The bi-RVRP finds applications...

The network accessibility in the aftermath of major disasters has a large impact on the response to the population. In the case of earthquakes, the access is usually improved during the hours following the quake by employing work-troops (WT) to remove debris and repair city roads. Thus, the efficacy of the WT schedule is very important for post-dis...

The road network accessibility is an important issue for post-earthquake relief operations, since several roads may be damaged obstructing the access to certain areas. This work proposes a mathematical model and some heuristics for the road repairing work-troops scheduling in order to increase accessibility to the population as fast as possible aft...

In this work, we propose a procedure to compute Pareto-optimal fronts for the bi-objective Minimum Diameter-Cost Spanning Tree problem (bi-MDCST). The bi-MDCST aims at finding spanning trees with minimum total cost and minimum diameter. Strategic decision problems for high-speed trains infrastructure, as well as tactical and operational optimizatio...

This special issue of RAIRO-Operations Research is dedicated to the 14th ROADEF Conference (ROADEF 2013) of the Operations Research (OR) and Management Science (MS) French Society, held in Troyes, Universit´e de Technologie de Troyes (UTT) on February 13–15, 2013. The ROADEF is a yearly conference and the biggest French forum for exchanging and dis...

The Robust Vehicle Routing problem (RVRP) with discrete scenarios is studied here to handle uncertain traveling time, where a scenario represents a possible discretization of the travel time observed on each arc at a given traffic hour. The goal is to build a set of routes considering the minimization of the worst total cost over all scenarios. A G...

The bi-objective minimum diameter-cost spanning tree problem (bi-MDCST) seeks spanning trees with minimum total cost and minimum diameter. The bi-objective version generalizes the well-known bounded diameter minimum spanning tree problem. The bi-MDCST is a NP-hard problem and models several practical applications in transportation and network desig...

The well-known Shortest Path problem (SP) consists in finding a shortest path from a source node s 2 V to a destination node t 2 V such that the total cost is minimized. The SP models practical and theoretical problems. However, several shortest path applications rely on uncertain data. The Robust Shortest Path problem (RSP) is a generalization of...

Given a graph G = (V,E), the set partitioning problem consists of defining disjoints partitions. In this work, we propose a sophisticated method to optimize the number of partitions in a given graph, considering that every partition are associated with a capacity constraint. The proposed procedure uses dynamic programming and is similar to the spli...

We study the restricted robust shortest path problem, a robust optimization version of the restricted shortest path problem, classical NP-hard problem. The arcs are associated with cost intervals and with a length value. The goal is to find a path connecting a source vertice to a target one respecting a maximum length constraint and minimizing a ro...

A linear programming based heuristic is proposed in this study, and applied to the Restricted Robust Shortest Path problem (R-RSP). The general schema can be extended and used to other robust optimization problems. R-RSP is a robust optimization version of the classical restricted shortest path problem, which is a N P-hard problem. The arcs are ass...

A linear programming based heuristic is proposed in this study, and applied to the Restricted Robust Shortest Path problem (R-RSP). The general schema can be extended and used to other robust optimization problems. R-RSP is a robust optimization version of the classical restricted shortest path problem, which is a N P-hard problem. The arcs are ass...

The well-known Shortest Path problem (SP) consists in finding a shortest path from a source to a destination such that the total cost is minimized. The SP models practical and theoretical problems. However, several shortest path applications rely on uncertain data. The Robust Shortest Path problem (RSP) is a generalization of SP. In the former, the...

In this article, the Robust Vehicle Routing Problem (RVRP) with uncertain traveling costs is studied. It covers a number of important applications in urban transportation and large scale bio-terrorism emergency. The uncertain data are defined as a bounded set of discrete scenarios associated with each arc of the transportation network. The objectiv...

Uncertain parameters appear in many optimization problems raised by real-world applications. To handle such problems, several approaches to model uncertainty are available, such as stochastic programming and robust optimization. This study is focused on robust optimization, in particular, the criteria to select and determine a robust solution. We p...

We consider the problem of setting a supplies distribution system in a post-disaster context. The primary decision variables correspond to the site opening schedule and the secondary variables focus on the supplies distribution to the population zones. The objective is to optimize the supply delivery to the population, while satisfying some logisti...

The generalized vehicle routing problem with flexible fleet size (GVRP-flex) extends the classical capacitated vehicle routing problem (CVRP) by partitioning the set of required nodes into clusters and has interesting applications such as humanitarian logistics. The problem aims at minimizing the total cost for a set of routes, such that each clust...

The complexity of megacities raises new challenges to manage and to adapt the urban network transportation, among them several optimization problems have emerged. This work addresses tactical problems of setting directions in urban networks for minimizing travel distance, but also to act as deterrent policy. We propose hybrid metaheuristics based o...

A Wireless Sensor Network (WSN) is an effective tool to gather data on an area. However, its lifetime is often an issue due to the small battery installed on each sensor. Several works have addressed the optimization of the lifetime and two main criteria are used: minimizing the number of clusters and minimizing the highest energy consumed by a sen...

Workover rigs are used in onshore basins but they are often in limited number and they may not attend all the maintenance requests. We consider here the problem of scheduling the rigs over a time horizon in order to minimize the total oil loss due to the idle production states. Three mixed integer linear models are proposed. The first one improves...

Wireless Sensor Networks are used in several practical applications such as environmental monitoring and risk detection. In this work, we deal with the problem of organizing the network topology into clusters in order to minimize the total energy consumption. The problem is modeled as an Independent Dominating Problem with Connecting requirements....

RESUMO No problema de roteamento de veículos generalizado, os clientes são agrupados em clusters. Cada cluste e visitado uma só vez e sua demanda totaí e deixada no cliente selecionado. O objetivo do problema de roteamento de veículos generalizadó e minimizar o custo total das rotas, de modo que cada cluster seja visitado uma só vez e sua demanda t...

The diameter-constrained minimum spanning tree problem consists in finding a minimum spanning tree of a given graph, subject to the constraint that the maximum number of edges between any two vertices in the tree is bounded from above by a given constant. This problem typically models network design applications where all vertices communicate with...

We propose a hybrid GRASP and ILS based heuristic for the diameter constrained minimum spanning tree problem. The latter typically models network design applications where, under a given quality requirement, all vertices must be connected at minimum cost. An adaptation of the one time tree heuristic is used to build feasible diameter constrained sp...

Wireless Sensor Networks (WSN) have been studied in several contexts. There are many challenges involving WSN design such as the energy resources optimization, the robustness and the network coverage. We address here the problem of energy-efficient topology design. A welldesigned dynamic topology and efficient routing algorithms may allow a large r...