Algorithm Engineering in Robust Optimization

Robust optimization is a young and emerging field of research having received a considerable increase of interest over the last decade. In this paper, we argue that the the algorithm engineering methodology fits very well to the field of robust optimization and yields a rewarding new perspective on both the current state of research and open research directions. To this end we go through the algorithm engineering cycle of design and analysis of concepts, development and implementation of algorithms, and theoretical and experimental evaluation. We show that many ideas of algorithm engineering have already been applied in publications on robust optimization. Most work on robust optimization is devoted to analysis of the concepts and the development of algorithms, some papers deal with the evaluation of a particular concept in case studies, and work on comparison of concepts just starts. What is still a drawback in many papers on robustness is the missing link to include the results of the experiments again in the design

Train-scheduling optimization model for railway networks with multiplatform stations

This paper focuses on optimizing the schedule of trains on railway networks composed of busy complex stations. A mathematical formulation of this problem is provided as a Mixed Integer Linear Program (MILP). However, the creation of an optimal new timetable is an NP-hard problem; therefore, the MILP can be solved for easy cases, computation time being impractical for more complex examples. In these cases, a heuristic approach is provided that makes use of genetic algorithms to find a good solution jointly with heuristic techniques to generate an initial population. The algorithm was applied to a number of problem instances producing feasible, though not optimal, solutions in several seconds on a laptop, and compared to other proposals. Some improvements are suggested to obtain better results and further improve computation time. Rail transport is recognized as a sustainable and energy-efficient means of transport. Moreover, each freight train can take a large number of trucks off the roads, making them safer. Studies in this field can help to make railways more attractive to travelers by reducing operative cost, and increasing the number of services and their punctuality. To improve the transit system and service, it is necessary to build optimal train scheduling. There is an interest from the industry in automating the scheduling process. Fast computerized train scheduling, moreover, can be used to explore the effects of alternative draft timetables, operating policies, station layouts, and random delays or failures.Postprint (published version

Algorithms for the continuous nonlinear resource allocation problem---new implementations and numerical studies

Patriksson (2008) provided a then up-to-date survey on the continuous,separable, differentiable and convex resource allocation problem with a single resource constraint. Since the publication of that paper the interest in the problem has grown: several new applications have arisen where the problem at hand constitutes a subproblem, and several new algorithms have been developed for its efficient solution. This paper therefore serves three purposes. First, it provides an up-to-date extension of the survey of the literature of the field, complementing the survey in Patriksson (2008) with more then 20 books and articles. Second, it contributes improvements of some of these algorithms, in particular with an improvement of the pegging (that is, variable fixing) process in the relaxation algorithm, and an improved means to evaluate subsolutions. Third, it numerically evaluates several relaxation (primal) and breakpoint (dual) algorithms, incorporating a variety of pegging strategies, as well as a quasi-Newton method. Our conclusion is that our modification of the relaxation algorithm performs the best. At least for problem sizes up to 30 million variables the practical time complexity for the breakpoint and relaxation algorithms is linear

A C-DAG task model for scheduling complex real-time tasks on heterogeneous platforms: preemption matters

Recent commercial hardware platforms for embedded real-time systems feature heterogeneous processing units and computing accelerators on the same System-on-Chip. When designing complex real-time application for such architectures, the designer needs to make a number of difficult choices: on which processor should a certain task be implemented? Should a component be implemented in parallel or sequentially? These choices may have a great impact on feasibility, as the difference in the processor internal architectures impact on the tasks' execution time and preemption cost. To help the designer explore the wide space of design choices and tune the scheduling parameters, in this paper we propose a novel real-time application model, called C-DAG, specifically conceived for heterogeneous platforms. A C-DAG allows to specify alternative implementations of the same component of an application for different processing engines to be selected off-line, as well as conditional branches to model if-then-else statements to be selected at run-time. We also propose a schedulability analysis for the C-DAG model and a heuristic allocation algorithm so that all deadlines are respected. Our analysis takes into account the cost of preempting a task, which can be non-negligible on certain processors. We demonstrate the effectiveness of our approach on a large set of synthetic experiments by comparing with state of the art algorithms in the literature

Robust Appointment Scheduling with Heterogeneous Costs

Designing simple appointment systems that under uncertainty in service times, try to achieve both high utilization of expensive medical equipment and personnel as well as short waiting time for patients, has long been an interesting and challenging problem in health care. We consider a robust version of the appointment scheduling problem, introduced by Mittal et al. (2014), with the goal of finding simple and easy-to-use algorithms. Previous work focused on the special case where per-unit costs due to under-utilization of equipment/personnel are homogeneous i.e., costs are linear and identical. We consider the heterogeneous case and devise an LP that has a simple closed-form solution. This solution yields the first constant-factor approximation for the problem. We also find special cases beyond homogeneous costs where the LP leads to closed form optimal schedules. Our approach and results extend more generally to convex piece-wise linear costs. For the case where the order of patients is changeable, we focus on linear costs and show that the problem is strongly NP-hard when the under-utilization costs are heterogeneous. For changeable order with homogeneous under-utilization costs, it was previously shown that an EPTAS exists. We instead find an extremely simple, ratio-based ordering that is 1.0604 approximate

Online Resource Inference in Network Utility Maximization Problems

The amount of transmitted data in computer networks is expected to grow considerably in the future, putting more and more pressure on the network infrastructures. In order to guarantee a good service, it then becomes fundamental to use the network resources efficiently. Network Utility Maximization (NUM) provides a framework to optimize the rate allocation when network resources are limited. Unfortunately, in the scenario where the amount of available resources is not known a priori, classical NUM solving methods do not offer a viable solution. To overcome this limitation we design an overlay rate allocation scheme that attempts to infer the actual amount of available network resources while coordinating the users rate allocation. Due to the general and complex model assumed for the congestion measurements, a passive learning of the available resources would not lead to satisfying performance. The coordination scheme must then perform active learning in order to speed up the resources estimation and quickly increase the system performance. By adopting an optimal learning formulation we are able to balance the tradeoff between an accurate estimation, and an effective resources exploitation in order to maximize the long term quality of the service delivered to the users

Markov Decision Processes with Applications in Wireless Sensor Networks: A Survey

Wireless sensor networks (WSNs) consist of autonomous and resource-limited devices. The devices cooperate to monitor one or more physical phenomena within an area of interest. WSNs operate as stochastic systems because of randomness in the monitored environments. For long service time and low maintenance cost, WSNs require adaptive and robust methods to address data exchange, topology formulation, resource and power optimization, sensing coverage and object detection, and security challenges. In these problems, sensor nodes are to make optimized decisions from a set of accessible strategies to achieve design goals. This survey reviews numerous applications of the Markov decision process (MDP) framework, a powerful decision-making tool to develop adaptive algorithms and protocols for WSNs. Furthermore, various solution methods are discussed and compared to serve as a guide for using MDPs in WSNs