Restart strategies for GRASP with path-relinking heuristics

Abstract. GRASP with path-relinking is a hybrid metaheuristic, or stochastic local search (Monte Carlo) method, for combinatorial optimization. A restart strategy in GRASP with path-relinking heuristics is a set of iterations {i1, i2, . . .} on which the heuristic is restarted from scratch using a new seed for the random number generator. Restart strategies have been shown to speed up stochastic local search algorithms. In this paper, we propose a new restart strategy for GRASP with path-relinking heuristics. We illustrate the speedup obtained with our restart strategy on GRASP with path-relinking heuristics for the maximum cut problem, the maximum weighted satisfiability problem, and the private virtual circuit routing problem

Cross-layer modeling and optimization of next-generation internet networks

Scaling traditional telecommunication networks so that they are able to cope with the volume of future traffic demands and the stringent European Commission (EC) regulations on emissions would entail unaffordable investments. For this very reason, the design of an innovative ultra-high bandwidth power-efficient network architecture is nowadays a bold topic within the research community. So far, the independent evolution of network layers has resulted in isolated, and hence, far-from-optimal contributions, which have eventually led to the issues today's networks are facing such as inefficient energy strategy, limited network scalability and flexibility, reduced network manageability and increased overall network and customer services costs. Consequently, there is currently large consensus among network operators and the research community that cross-layer interaction and coordination is fundamental for the proper architectural design of next-generation Internet networks. This thesis actively contributes to the this goal by addressing the modeling, optimization and performance analysis of a set of potential technologies to be deployed in future cross-layer network architectures. By applying a transversal design approach (i.e., joint consideration of several network layers), we aim for achieving the maximization of the integration of the different network layers involved in each specific problem. To this end, Part I provides a comprehensive evaluation of optical transport networks (OTNs) based on layer 2 (L2) sub-wavelength switching (SWS) technologies, also taking into consideration the impact of physical layer impairments (PLIs) (L0 phenomena). Indeed, the recent and relevant advances in optical technologies have dramatically increased the impact that PLIs have on the optical signal quality, particularly in the context of SWS networks. Then, in Part II of the thesis, we present a set of case studies where it is shown that the application of operations research (OR) methodologies in the desing/planning stage of future cross-layer Internet network architectures leads to the successful joint optimization of key network performance indicators (KPIs) such as cost (i.e., CAPEX/OPEX), resources usage and energy consumption. OR can definitely play an important role by allowing network designers/architects to obtain good near-optimal solutions to real-sized problems within practical running times

20 years of Greedy Randomized Adaptive Search Procedures with Path Relinking

This is a comprehensive review of the Greedy Randomized Adaptive Search Procedure (GRASP) metaheuristic and its hybridization with Path Relinking (PR) over the past two decades. GRASP with PR has become a widely adopted approach for solving hard optimization problems since its proposal in 1999. The paper covers the historical development of GRASP with PR and its theoretical foundations, as well as recent advances in its implementation and application. The review includes a critical analysis of variants of PR, including memory-based and randomized designs, with a total of ten different implementations. It describes these advanced designs both theoretically and practically on two well-known optimization problems, linear ordering and max-cut. The paper also explores the hybridization of GRASP with PR and other metaheuristics, such as Tabu Search and Scatter Search. Overall, this review provides valuable insights for researchers and practitioners seeking to utilize GRASP with PR for solving optimization problems.Comment: 28 pages, 13 figure

Incorporating Memory and Learning Mechanisms Into Meta-RaPS

Due to the rapid increase of dimensions and complexity of real life problems, it has become more difficult to find optimal solutions using only exact mathematical methods. The need to find near-optimal solutions in an acceptable amount of time is a challenge when developing more sophisticated approaches. A proper answer to this challenge can be through the implementation of metaheuristic approaches. However, a more powerful answer might be reached by incorporating intelligence into metaheuristics. Meta-RaPS (Metaheuristic for Randomized Priority Search) is a metaheuristic that creates high quality solutions for discrete optimization problems. It is proposed that incorporating memory and learning mechanisms into Meta-RaPS, which is currently classified as a memoryless metaheuristic, can help the algorithm produce higher quality results. The proposed Meta-RaPS versions were created by taking different perspectives of learning. The first approach taken is Estimation of Distribution Algorithms (EDA), a stochastic learning technique that creates a probability distribution for each decision variable to generate new solutions. The second Meta-RaPS version was developed by utilizing a machine learning algorithm, Q Learning, which has been successfully applied to optimization problems whose output is a sequence of actions. In the third Meta-RaPS version, Path Relinking (PR) was implemented as a post-optimization method in which the new algorithm learns the good attributes by memorizing best solutions, and follows them to reach better solutions. The fourth proposed version of Meta-RaPS presented another form of learning with its ability to adaptively tune parameters. The efficiency of these approaches motivated us to redesign Meta-RaPS by removing the improvement phase and adding a more sophisticated Path Relinking method. The new Meta-RaPS could solve even the largest problems in much less time while keeping up the quality of its solutions. To evaluate their performance, all introduced versions were tested using the 0-1 Multidimensional Knapsack Problem (MKP). After comparing the proposed algorithms, Meta-RaPS PR and Meta-RaPS Q Learning appeared to be the algorithms with the best and worst performance, respectively. On the other hand, they could all show superior performance than other approaches to the 0-1 MKP in the literature

Using GRASP and GA to design resilient and cost-effective IP/MPLS networks

The main objective of this thesis is to find good quality solutions for representative instances of the problem of designing a resilient and low cost IP/MPLS network, to be deployed over an existing optical transport network. This research is motivated by two complementary real-world application cases, which comprise the most important commercial and academic networks of Uruguay. To achieve this goal, we performed an exhaustive analysis of existing models and technologies. From all of them we took elements that were contrasted with the particular requirements of our counterparts. We highlight among these requirements, the need of getting solutions transparently implementable over a heterogeneous network environment, which limit us to use widely standardized features of related technologies. We decided to create new models more suitable to fit these needs. These models are intrinsically hard to solve (NP-Hard). Thus we developed metaheuristic based algorithms to find solutions to these real-world instances. Evolutionary Algorithms and Greedy Randomized Adaptive Search Procedures obtained the best results. As it usually happens, real-world planning problems are surrounded by uncertainty. Therefore, we have worked closely with our counterparts to reduce the fuzziness upon data to a set of representative cases. They were combined with different strategies of design to get to scenarios, which were translated into instances of these problems. Finally, the algorithms were fed with this information, and from their outcome we derived our results and conclusions

A Polyhedral Study of Mixed 0-1 Set

We consider a variant of the well-known single node fixed charge network flow set with constant capacities. This set arises from the relaxation of more general mixed integer sets such as lot-sizing problems with multiple suppliers. We provide a complete polyhedral characterization of the convex hull of the given set

Improved Neighbourhood Search-Based Methods for Graph Layout

Graph drawing, or the automatic layout of graphs, is a challenging problem. There are several search-based methods for graph drawing that are based on optimising a fitness function which is formed from a weighted sum of multiple criteria. This thesis proposes a new neighbourhood search-based method that uses a tabu search coupled with path relinking in order to optimise such fitness functions for general graph layouts with undirected straight lines. None of these methods have been previously used in general multi-criteria graph drawing. Tabu search uses a memory list to speed up searching by avoiding previously tested solutions, while the path relinking method generates new solutions by exploring paths that connect high quality solutions. We use path relinking periodically within the tabu search procedure to speed up the identification of good solutions. We have evaluated our new method against the commonly used neighbourhood search optimisation techniques: hill climbing and simulated annealing. Our evaluation examines the quality of the graph layout (fitness function's value) and the speed of the layout in terms of the number of the evaluated solutions required to draw a graph. We also examine the relative scalability of our method. Our experimental results were applied to both random graphs and a real-world dataset. We show that our method outperforms both hill climbing and simulated annealing by producing a better layout in a lower number of evaluated solutions. In addition, we demonstrate that our method has greater scalability as it can lay out larger graphs than the state-of-the-art neighbourhood search-based methods. Finally, we show that similar results can be produced in a real world setting by testing our method against a standard public graph dataset