Combinatorial optimization and metaheuristics

Today, combinatorial optimization is one of the youngest and most active areas of discrete mathematics. It is a branch of optimization in applied mathematics and computer science, related to operational research, algorithm theory and computational complexity theory. It sits at the intersection of several fields, including artificial intelligence, mathematics and software engineering. Its increasing interest arises for the fact that a large number of scientific and industrial problems can be formulated as abstract combinatorial optimization problems, through graphs and/or (integer) linear programs. Some of these problems have polynomial-time (“efficient”) algorithms, while most of them are NP-hard, i.e. it is not proved that they can be solved in polynomial-time. Mainly, it means that it is not possible to guarantee that an exact solution to the problem can be found and one has to settle for an approximate solution with known performance guarantees. Indeed, the goal of approximate methods is to find “quickly” (reasonable run-times), with “high” probability, provable “good” solutions (low error from the real optimal solution). In the last 20 years, a new kind of algorithm commonly called metaheuristics have emerged in this class, which basically try to combine heuristics in high level frameworks aimed at efficiently and effectively exploring the search space. This report briefly outlines the components, concepts, advantages and disadvantages of different metaheuristic approaches from a conceptual point of view, in order to analyze their similarities and differences. The two very significant forces of intensification and diversification, that mainly determine the behavior of a metaheuristic, will be pointed out. The report concludes by exploring the importance of hybridization and integration methods

Solving the Uncapacitated Single Allocation p-Hub Median Problem on GPU

A parallel genetic algorithm (GA) implemented on GPU clusters is proposed to solve the Uncapacitated Single Allocation p-Hub Median problem. The GA uses binary and integer encoding and genetic operators adapted to this problem. Our GA is improved by generated initial solution with hubs located at middle nodes. The obtained experimental results are compared with the best known solutions on all benchmarks on instances up to 1000 nodes. Furthermore, we solve our own randomly generated instances up to 6000 nodes. Our approach outperforms most well-known heuristics in terms of solution quality and time execution and it allows hitherto unsolved problems to be solved

Automatic synthesis and optimization of chip multiprocessors

The microprocessor technology has experienced an enormous growth during the last decades. Rapid downscale of the CMOS technology has led to higher operating frequencies and performance densities, facing the fundamental issue of power dissipation. Chip Multiprocessors (CMPs) have become the latest paradigm to improve the power-performance efficiency of computing systems by exploiting the parallelism inherent in applications. Industrial and prototype implementations have already demonstrated the benefits achieved by CMPs with hundreds of cores.CMP architects are challenged to take many complex design decisions. Only a few of them are:- What should be the ratio between the core and cache areas on a chip?- Which core architectures to select?- How many cache levels should the memory subsystem have?- Which interconnect topologies provide efficient on-chip communication?These and many other aspects create a complex multidimensional space for architectural exploration. Design Automation tools become essential to make the architectural exploration feasible under the hard time-to-market constraints. The exploration methods have to be efficient and scalable to handle future generation on-chip architectures with hundreds or thousands of cores.Furthermore, once a CMP has been fabricated, the need for efficient deployment of the many-core processor arises. Intelligent techniques for task mapping and scheduling onto CMPs are necessary to guarantee the full usage of the benefits brought by the many-core technology. These techniques have to consider the peculiarities of the modern architectures, such as availability of enhanced power saving techniques and presence of complex memory hierarchies.This thesis has several objectives. The first objective is to elaborate the methods for efficient analytical modeling and architectural design space exploration of CMPs. The efficiency is achieved by using analytical models instead of simulation, and replacing the exhaustive exploration with an intelligent search strategy. Additionally, these methods incorporate high-level models for physical planning. The related contributions are described in Chapters 3, 4 and 5 of the document.The second objective of this work is to propose a scalable task mapping algorithm onto general-purpose CMPs with power management techniques, for efficient deployment of many-core systems. This contribution is explained in Chapter 6 of this document.Finally, the third objective of this thesis is to address the issues of the on-chip interconnect design and exploration, by developing a model for simultaneous topology customization and deadlock-free routing in Networks-on-Chip. The developed methodology can be applied to various classes of the on-chip systems, ranging from general-purpose chip multiprocessors to application-specific solutions. Chapter 7 describes the proposed model.The presented methods have been thoroughly tested experimentally and the results are described in this dissertation. At the end of the document several possible directions for the future research are proposed

An investigation of multilevel refinement in routing and location problems

Multilevel refinement is a collaborative hierarchical solution technique. The multilevel technique aims to enhance the solution process of optimisation problems by improving the asymptotic convergence in the quality of solutions produced by its underlying local search heuristics and/or improving the convergence rate of these heuristics. To these aims, the central methodologies of the multilevel technique are filtering solutions from the search space (via coarsening), reducing the amount of problem detail considered at each level of the solution process and providing a mechanism to the underlying local search heuristics for efficiently making large moves around the search space. The neighbourhoods accessible by these moves are typically inaccessible if the local search heuristics are applied to the un-coarsened problems. The methodologies combine to meet the multilevel technique's aims, because, as the multilevel technique iteratively coarsens, extends and refines a given problem, it reduces the possibility of the local search heuristic becoming trapped in local optima of poor quality. The research presented in this thesis investigates the application of multilevel refinement to classes of location and routing problems and develops numerous multilevel algorithms. Some of these algorithms are collaborative techniques for metaheuristics and others are collaborative techniques for local search heuristics. Additionally, new methods of coarsening for location and routing problems and enhancements for the multilevel technique are developed. It is demonstrated that the multilevel technique is suited to a wide array of problems. By extending the investigations of the multilevel technique across routing and location problems, the research was able to present generalisations regarding the multilevel technique's suitability, for these and similar types of problems. Finally, results on a number of well known benchmarking suites for location and routing problem are presented, comparing equivalent single-level and multilevel algorithms. These results demonstrate that the multilevel technique provides significant gains over its single-level counterparts. In all cases, the multilevel algorithm was able to improve the asymptotic convergence in the quality of solutions produced by the standard (single-level) local search heuristics or metaheuristics. The multilevel technique did not improve the convergence rate of the single-level's local search heuristics in all cases. However, for large-scale problems the multilevel variants scaled in a manner superior to the single-level techniques. The research also demonstrated that for sufficiently large problems, the multilevel technique was able to improve the asymptotic convergence in the quality of solutions at a sufficiently fast rate, such that the multilevel algorithms were able to produce superior results compared to the single-level versions, without refining the solution down to the most detailed level

Why simheuristics? : Benefits, limitations, and best practices when combining metaheuristics with simulation

Many decision-making processes in our society involve NP-hard optimization problems. The largescale, dynamism, and uncertainty of these problems constrain the potential use of stand-alone optimization methods. The same applies for isolated simulation models, which do not have the potential to find optimal solutions in a combinatorial environment. This paper discusses the utilization of modelling and solving approaches based on the integration of simulation with metaheuristics. These 'simheuristic' algorithms, which constitute a natural extension of both metaheuristics and simulation techniques, should be used as a 'first-resort' method when addressing large-scale and NP-hard optimization problems under uncertainty -which is a frequent case in real-life applications. We outline the benefits and limitations of simheuristic algorithms, provide numerical experiments that validate our arguments, review some recent publications, and outline the best practices to consider during their design and implementation stages

Green Parallel Metaheuristics: Design, Implementation, and Evaluation

Fecha de lectura de Tesis Doctoral 14 mayo 2020Green parallel metaheuristics (GPM) is a new concept we want to introduce in this thesis. It is an idea inspired by two facts: (i) parallel metaheuristics could help as unique tools to solve optimization problems in energy savings applications and sustainability, and (ii) these algorithms themselves run on multiprocessors, clusters, and grids of computers and then consume energy, so they need an energy analysis study for their different implementations over multiprocessors. The context for this thesis is to make a modern and competitive effort to extend the capability of present intelligent search optimization techniques. Analyzing the different sequential and parallel metaheuristics considering its energy consumption requires a deep investigation of the numerical performance, the execution time for efficient future designing to these algorithms. We present a study of the speed-up of the different parallel implementations over a different number of computing units. Moreover, we analyze and compare the energy consumption and numerical performance of the sequential/parallel algorithms and their components: a jump in the efficiency of the algorithms that would probably have a wide impact on the domains involved.El Instituto Egipcio en Madrid, dependiente del Gobierno de Egipto