A Multistage Stochastic Programming Approach to the Dynamic and Stochastic VRPTW - Extended version

We consider a dynamic vehicle routing problem with time windows and stochastic customers (DS-VRPTW), such that customers may request for services as vehicles have already started their tours. To solve this problem, the goal is to provide a decision rule for choosing, at each time step, the next action to perform in light of known requests and probabilistic knowledge on requests likelihood. We introduce a new decision rule, called Global Stochastic Assessment (GSA) rule for the DS-VRPTW, and we compare it with existing decision rules, such as MSA. In particular, we show that GSA fully integrates nonanticipativity constraints so that it leads to better decisions in our stochastic context. We describe a new heuristic approach for efficiently approximating our GSA rule. We introduce a new waiting strategy. Experiments on dynamic and stochastic benchmarks, which include instances of different degrees of dynamism, show that not only our approach is competitive with state-of-the-art methods, but also enables to compute meaningful offline solutions to fully dynamic problems where absolutely no a priori customer request is provided.Comment: Extended version of the same-name study submitted for publication in conference CPAIOR201

E[DPOP]: Distributed Constraint Optimization under Stochastic Uncertainty using Collaborative Sampling

Many applications that require distributed optimization also include uncertainty about the problem and the optimization criteria themselves. However, current approaches to distributed optimization assume that the problem is entirely known before optimization is carried out, while approaches to optimization with uncertainty have been investigated for centralized algorithms. This paper introduces the framework of Distributed Constraint Optimization under Stochastic Uncertainty (StochDCOP), in which random variables with known probability distributions are used to model sources of uncertainty. Our main novel contribution is a distributed procedure called col laborative sampling, which we use to produce several new versions of the DPOP algorithm for StochDCOPs. We evaluate the benefits of collaborative sampling over the simple approach in which each agent samples the random variables independently. We also show that collaborative sampling can be used to implement a new, distributed version of the consensus algorithm, which is a well-known algorithm for centralized, online stochastic optimization in which the solution chosen is the one that is optimal in most cases, rather than the one that maximizes the expected utility

Robust Solution Approach for the Dynamic and Stochastic Vehicle Routing Problem

The dynamic and stochastic vehicle routing problem (DSVRP) can be modelled as a stochastic program (SP). In a two-stage SP with recourse model, the first stage minimizes the a priori routing plan cost and the second stage minimizes the cost of corrective actions, performed to deal with changes in the inputs. To deal with the problem, approaches based either on stochastic modelling or on sampling can be applied. Sampling-based methods incorporate stochastic knowledge by generating scenarios set on realizations drawn from distributions. In this paper we proposed a robust solution approach for the capacitated DSVRP based on sampling strategies. We formulated the problem as a two-stage stochastic program model with recourse. In the first stage the a priori routing plan cost is minimized, whereas in the second stage the average of higher moments for the recourse cost calculated via a set of scenarios is minimized. The idea is to include higher moments in the second stage aiming to compute a robust a priori routing plan that minimizes transportation costs while permitting small changes in the demands without changing solution structure. Additionally, the approach allows managers to choose between optimality and robustness, that is, transportation costs and reconfiguration. The computational results on a generic dynamic benchmark dataset show that the robust routing plan can cover unmet demand while incurring little extra costs as compared to the preplanning. We observed that the plan of routes is more robust; that is, not only the expected real cost, but also the increment within the planned cost is lower

Integrating Consumer Flexibility in Smart Grid and Mobility Systems - An Online Optimization and Online Mechanism Design Approach

Consumer flexibility may provide an important lever to align supply and demand in service systems. However, harnessing dispersed flexibility endowments in the presence of self-interested agents requires appropriate incentive structures. This thesis quantifies the potential value of consumers\u27 flexibility in smart grid and mobility systems. In order to include incentives, online optimization approaches are augmented with methods from online mechanism design

Distributed Constraint Optimization:Privacy Guarantees and Stochastic Uncertainty

Distributed Constraint Satisfaction (DisCSP) and Distributed Constraint Optimization (DCOP) are formal frameworks that can be used to model a variety of problems in which multiple decision-makers cooperate towards a common goal: from computing an equilibrium of a game, to vehicle routing problems, to combinatorial auctions. In this thesis, we independently address two important issues in such multi-agent problems: 1) how to provide strong guarantees on the protection of the privacy of the participants, and 2) how to anticipate future, uncontrollable events. On the privacy front, our contributions depart from previous work in two ways. First, we consider not only constraint privacy (the agents' private costs) and decision privacy (keeping the complete solution secret), but also two other types of privacy that have been largely overlooked in the literature: agent privacy, which has to do with protecting the identities of the participants, and topology privacy, which covers information about the agents' co-dependencies. Second, while previous work focused mainly on quantitatively measuring and reducing privacy loss, our algorithms provide stronger, qualitative guarantees on what information will remain secret. Our experiments show that it is possible to provide such privacy guarantees, while still scaling to much larger problems than the previous state of the art. When it comes to reasoning under uncertainty, we propose an extension to the DCOP framework, called DCOP under Stochastic Uncertainty (StochDCOP), which includes uncontrollable, random variables with known probability distributions that model uncertain, future events. The problem becomes one of making "optimal" offline decisions, before the true values of the random variables can be observed. We consider three possible concepts of optimality: minimizing the expected cost, minimizing the worst-case cost, or maximizing the probability of a-posteriori optimality. We propose a new family of StochDCOP algorithms, exploring the tradeoffs between solution quality, computational and message complexity, and privacy. In particular, we show how discovering and reasoning about co-dependencies on common random variables can yield higher-quality solutions

Gestión óptima de citas médicas mediante la aplicación de un modelo de optimización multicriterio

The Cuban health system is known worldwide for its good results in the prevention of diseases and for its continuous improvements in health standards. However, we want to go a step further and put the patient at the center of the system. To this task, we propose a methodology that allows a complete automatization of the medical appointment system so that patients will know in advance the average time they will spend in the hospital the day of the appointment, as well as the sequence of medical tests that will have to undertake. We develop a non linear integer multi-goal model (NLIMGM) model to perform an optimal distribution of patients. Our model assign appointments to patients according to two different goals: to give the appointments as soon as possible and to minimize the time that a patient would spend in the hospital to complete a protocol.The performance of the resulting NLIMGM policies was compared with traditional practices decision rules for the diagnosis and treatment of ophthalmology diseases in a Cuba hospital. The results show that this method outperforms traditional methods by far. Specifically, this approach will increase the efficiency of appointments scheduling and reduces the total diagnosis time for cataract, cornea, glaucoma by 46% on average or, in other words, by roughly one hour, relative to the standard approach. Arguably, this translates into improved patient satisfaction and efficiency in the use of resources in health services. <br /

Online Optimization with Lookahead

The main contributions of this thesis consist of the development of a systematic groundwork for comprehensive performance evaluation of algorithms in online optimization with lookahead and the subsequent validation of the presented approaches in theoretical analysis and computational experiments