Evolutionary Multi-Objective Optimization for the Dynamic Knapsack Problem

Evolutionary algorithms are bio-inspired algorithms that can easily adapt to changing environments. In this paper, we study single- and multi-objective baseline evolutionary algorithms for the classical knapsack problem where the capacity of the knapsack varies over time. We establish different benchmark scenarios where the capacity changes every $\tau$ iterations according to a uniform or normal distribution. Our experimental investigations analyze the behavior of our algorithms in terms of the magnitude of changes determined by parameters of the chosen distribution, the frequency determined by $\tau$, and the class of knapsack instance under consideration. Our results show that the multi-objective approaches using a population that caters for dynamic changes have a clear advantage in many benchmarks scenarios when the frequency of changes is not too high. Furthermore, we demonstrate that the distribution handling techniques in advance algorithms such as NSGA-II and SPEA2 do not necessarily result in better performance and even prevent these algorithms from finding good quality solutions in comparison with simple multi-objective approaches

The stochastic vehicle routing problem : a literature review, part II : solution methods

Building on the work of Gendreau et al. (Oper Res 44(3):469–477, 1996), and complementing the first part of this survey, we review the solution methods used for the past 20 years in the scientific literature on stochastic vehicle routing problems (SVRP). We describe the methods and indicate how they are used when dealing with stochastic vehicle routing problems. Keywords: vehicle routing (VRP), stochastic programmingm, SVRPpublishedVersio

Sequential Decision Making Schemes in Inventory and Transportation Environments

Many mathematical models exist for the simultaneous optimization of transportation and inventory functions. A simultaneous model, while giving the lowest total cost, may not be easily implemented in a firm with decentralized transportation and inventory departments. As such, this thesis studies sequential models, where the primary department is artificially given the authority to make some set of decisions prior to the decisions made by the secondary department. Some known formulations for simultaneous models are studied in an attempt to create a sequential process for the same environment. Finally, a generalized sequential approach is developed that can be applied to any transportation and inventory model with separable costs. The generalized approach allows for the full optimization of the primary departmental costs, and then sequentially allows the optimization of the secondary departmental costs subject to a maximum allowable increase in the costs of the primary department. The analysis of this sequential approach notably reveals that when the relative deviation from the optimal cost of each department is equal, a reasonable solution with respect to total cost is attained. This balance in relative deviation is defined as the fairness point solution. Differing cost scenarios are thus tested to determine the relationship between the cost ratio among departments and the performance of the fairness point solution. The fairness point solution provides an average deviation of total cost from the total optimal cost of less than 1% in four of the seven scenarios tested. Other sequential approaches are discussed and fairness with respect to these new approaches is considered.1 yea

Time complexity analysis of randomized search heuristics for the dynamic graph coloring problem

We contribute to the theoretical understanding of randomized search heuristics for dynamic problems. We consider the classical vertex coloring problem on graphs and investigate the dynamic setting where edges are added to the current graph. We then analyze the expected time for randomized search heuristics to recompute high quality solutions. The (1+1) Evolutionary Algorithm and RLS operate in a setting where the number of colors is bounded and we are minimizing the number of conflicts. Iterated local search algorithms use an unbounded color palette and aim to use the smallest colors and, consequently, the smallest number of colors. We identify classes of bipartite graphs where reoptimization is as hard as or even harder than optimization from scratch, i.e., starting with a random initialization. Even adding a single edge can lead to hard symmetry problems. However, graph classes that are hard for one algorithm turn out to be easy for others. In most cases our bounds show that reoptimization is faster than optimizing from scratch. We further show that tailoring mutation operators to parts of the graph where changes have occurred can significantly reduce the expected reoptimization time. In most settings the expected reoptimization time for such tailored algorithms is linear in the number of added edges. However, tailored algorithms cannot prevent exponential times in settings where the original algorithm is inefficient

Runtime analysis of randomized search heuristics for dynamic graph coloring

We contribute to the theoretical understanding of randomized search heuristics for dynamic problems. We consider the classical graph coloring problem and investigate the dynamic setting where edges are added to the current graph. We then analyze the expected time for randomized search heuristics to recompute high quality solutions. This includes the (1+1) EA and RLS in a setting where the number of colors is bounded and we are minimizing the number of conflicts as well as iterated local search algorithms that use an unbounded color palette and aim to use the smallest colors and - as a consequence - the smallest number of colors. We identify classes of bipartite graphs where reoptimization is as hard as or even harder than optimization from scratch, i. e. starting with a random initialization. Even adding a single edge can lead to hard symmetry problems. However, graph classes that are hard for one algorithm turn out to be easy for others. In most cases our bounds show that reoptimization is faster than optimizing from scratch. Furthermore, we show how to speed up computations by using problem specific operators concentrating on parts of the graph where changes have occurred

Running Time Analysis of the (1+1)-EA for Robust Linear Optimization

Evolutionary algorithms (EAs) have found many successful real-world applications, where the optimization problems are often subject to a wide range of uncertainties. To understand the practical behaviors of EAs theoretically, there are a series of efforts devoted to analyzing the running time of EAs for optimization under uncertainties. Existing studies mainly focus on noisy and dynamic optimization, while another common type of uncertain optimization, i.e., robust optimization, has been rarely touched. In this paper, we analyze the expected running time of the (1+1)-EA solving robust linear optimization problems (i.e., linear problems under robust scenarios) with a cardinality constraint $k$. Two common robust scenarios, i.e., deletion-robust and worst-case, are considered. Particularly, we derive tight ranges of the robust parameter $d$ or budget $k$ allowing the (1+1)-EA to find an optimal solution in polynomial running time, which disclose the potential of EAs for robust optimization.Comment: 17 pages, 1 tabl

Integração da Cloud com a rede do operador

Mestrado em Engenharia Electrónica e TelecomunicaçõesA utilização das aplicações e as suas formas de comunicar mudaram muito com a proliferação do acesso à Internet. Com esta alteração muitas das aplicações passaram a estar acomodadas em equipamento do fornecedor em vez do equipamento do utilizador. Cloud computing (CC) é o conceito que veio ”patrocinar” ainda mais esta mudança. Hoje o fornecimento destes serviços é suportado pelo serviço Best Effort que a Internet disponibiliza. Este é um modelo viável para alguns serviços, mas simplesmente inaceitável para outros (por exemplo, transmissões de vídeo). No sentido de colmatar esta lacuna, existe uma grande aposta nos serviços integrados de cloud e de rede. A este paradigma denominamos de Cloud Networking. Este paradigma requer o estabelecimento a pedido e um controlo e gestão automática de recursos de rede e cloud, em que a virtualização de rede e de recursos cloud é uma peça fundamental, não só pela sua facilidade de migração de recursos virtuais entre diferentes máquinas físicas, mas também pela flexibilidade do estabelecimento de aplicações e serviços diferentes. Neste contexto o recente conceito de software-defined networks (SDN) pode vir ajudar a melhorar o desempenho dos serviços disponibilizados na cloud. Assim, esta dissertação tem dois objetivos. O primeiro visa trabalhar em mecanismos de gestão de recursos de cloud e rede de uma forma integrada. Concretamente esta dissertação propõe um algoritmo de mapeamento, bem como um mecanismo de reconfiguração de links por forma a otimizar a alocação de recursos e aumentar a aceitação de pedidos. O segundo objetivo passou por criar um bloco funcional de decisão de mapeamento e reconfiguração que se encaixa numa arquitetura SDN. Este bloco é responsável por receber, analisar e mapear pedidos de serviços de conetividade sobre uma rede Openflow. Os algoritmos usados neste componente têm em conta as considerações alcançadas na primeira parte da dissertação. Os resultados obtidos permitem verificar que o algoritmo de mapeamento de recursos de cloud e rede, bem como o mecanismo de reconfiguração de links, proporcionam um desempenho significativamente superior aos algoritmos do estado da arte, com uma maior aceitação e ganhos à custa de uma utilização inferior dos recursos de rede, e com um consumo energético inferior. O bloco funcional fecha o ciclo básico de controlo da arquitetura SDN para a receção e tratamento de serviços de conetividade. O estudo global dá uma noção do desempenho geral da arquitetura completa, e o estudo individual das diferentes partes do bloco funcional permite perceber quais as partes dentro do componente proposto que deverão ser melhoradas no futuro.The use of applications and their ways of communicating have greatly changed with the proliferation of Internet access. With this, these applications have come to be accommodated in the equipment supplier rather than the user equipment. Cloud computing (CC) is the concept that came and “sponsored” even more this change. Today the supply of these services is supported by the Best Effort service that the Internet provides. This is a feasible model for some services, but it is simply unacceptable to others (i.e video streams). In order to fill this gap, there is a big bet in integrating cloud and network elements together. To this paradigm we call Cloud Networking. This paradigm requires the establishment, application monitoring and automatic management of network and cloud resources, where both network and cloud virtualization are a key role, not only because of its easiness migration of virtual resources between physical machines, but also by the flexibility of setting different applications and services. In this context, the software-defined networks (SDN) can help improve the performance of the available cloud services. This Dissertation has two objectives. The first one is to work on mechanisms of resource management and cloud network in an integrated way. Specifically, this Dissertation proposes a mapping algorithm as well as a mechanism for reconfiguring links to optimize resource allocation and increase the acceptance of applications. The second goal is the creation of a functional component for mapping decision and reoptimization that fits in an SDN framework. This component is responsible for receiving, analyzing and mapping requests for connectivity services over an OpenFlow network. The algorithms used in this component take into account the considerations achieved with the first part of the Dissertation. The results lead us to conclude that the proposed mapping algorithm for cloud and network resources, as well as the mechanism for reconfiguring links, achieve a performance significantly superior to the state of art algorithms, with a higher acceptation and gains at the expense of a lower utilization of network resources, and a lower energy consumption. The functional component closes the control basic cycle of the SDN framework to the reception and treatment of connectivity services. The global performance study gives perception of the general performance of the complete SDN solution, and the individual study of the different parts of the functional component allows us to understand the parts inside the proposed component that should be improved in the future