Finding Multiple Solutions of Multimodal Optimization Using Spiral Optimization Algorithm with Clustering

Multimodal optimization is one of the interesting problems in optimization which arises frequently in a widerange of engineering and practical applications. The goal of this problem is to find all of optimum solutions in a single run. Some algorithms fail to find all solutions that have been proven their existence analytically. In our paper [1], a method is proposed to find the roots of a system of non-linear equations using a clustering technique that combine with Spiral Optimization algorithm and Sobol sequence of points. An interesting benefit using this method is that the same inputs will give the same results. Most of the time this does not happen in meta-heuristic algorithms using random factors. Now the method is modified to find solutions of multimodal optimization problems. Generally in an optimization problem, the differential form of the objective function is needed. In this paper, the proposed method is to find optimum points of general multimodal functions that its differential form is not required. Several problems with benchmark functions have been examined using our method and they give good result

A Comprehensive Survey on Particle Swarm Optimization Algorithm and Its Applications

Particle swarm optimization (PSO) is a heuristic global optimization method, proposed originally by Kennedy and Eberhart in 1995. It is now one of the most commonly used optimization techniques. This survey presented a comprehensive investigation of PSO. On one hand, we provided advances with PSO, including its modifications (including quantum-behaved PSO, bare-bones PSO, chaotic PSO, and fuzzy PSO), population topology (as fully connected, von Neumann, ring, star, random, etc.), hybridization (with genetic algorithm, simulated annealing, Tabu search, artificial immune system, ant colony algorithm, artificial bee colony, differential evolution, harmonic search, and biogeography-based optimization), extensions (to multiobjective, constrained, discrete, and binary optimization), theoretical analysis (parameter selection and tuning, and convergence analysis), and parallel implementation (in multicore, multiprocessor, GPU, and cloud computing forms). On the other hand, we offered a survey on applications of PSO to the following eight fields: electrical and electronic engineering, automation control systems, communication theory, operations research, mechanical engineering, fuel and energy, medicine, chemistry, and biology. It is hoped that this survey would be beneficial for the researchers studying PSO algorithms

Treasure hunt : a framework for cooperative, distributed parallel optimization

Orientador: Prof. Dr. Daniel WeingaertnerCoorientadora: Profa. Dra. Myriam Regattieri DelgadoTese (doutorado) - Universidade Federal do Paraná, Setor de Ciências Exatas, Programa de Pós-Graduação em Informática. Defesa : Curitiba, 27/05/2019Inclui referências: p. 18-20Área de concentração: Ciência da ComputaçãoResumo: Este trabalho propõe um framework multinível chamado Treasure Hunt, que é capaz de distribuir algoritmos de busca independentes para um grande número de nós de processamento. Com o objetivo de obter uma convergência conjunta entre os nós, este framework propõe um mecanismo de direcionamento que controla suavemente a cooperação entre múltiplas instâncias independentes do Treasure Hunt. A topologia em árvore proposta pelo Treasure Hunt garante a rápida propagação da informação pelos nós, ao mesmo tempo em que provê simutaneamente explorações (pelos nós-pai) e intensificações (pelos nós-filho), em vários níveis de granularidade, independentemente do número de nós na árvore. O Treasure Hunt tem boa tolerância à falhas e está parcialmente preparado para uma total tolerância à falhas. Como parte dos métodos desenvolvidos durante este trabalho, um método automatizado de Particionamento Iterativo foi proposto para controlar o balanceamento entre explorações e intensificações ao longo da busca. Uma Modelagem de Estabilização de Convergência para operar em modo Online também foi proposto, com o objetivo de encontrar pontos de parada com bom custo/benefício para os algoritmos de otimização que executam dentro das instâncias do Treasure Hunt. Experimentos em benchmarks clássicos, aleatórios e de competição, de vários tamanhos e complexidades, usando os algoritmos de busca PSO, DE e CCPSO2, mostram que o Treasure Hunt melhora as características inerentes destes algoritmos de busca. O Treasure Hunt faz com que os algoritmos de baixa performance se tornem comparáveis aos de boa performance, e os algoritmos de boa performance possam estender seus limites até problemas maiores. Experimentos distribuindo instâncias do Treasure Hunt, em uma rede cooperativa de até 160 processos, demonstram a escalabilidade robusta do framework, apresentando melhoras nos resultados mesmo quando o tempo de processamento é fixado (wall-clock) para todas as instâncias distribuídas do Treasure Hunt. Resultados demonstram que o mecanismo de amostragem fornecido pelo Treasure Hunt, aliado à maior cooperação entre as múltiplas populações em evolução, reduzem a necessidade de grandes populações e de algoritmos de busca complexos. Isto é especialmente importante em problemas de mundo real que possuem funções de fitness muito custosas. Palavras-chave: Inteligência artificial. Métodos de otimização. Algoritmos distribuídos. Modelagem de convergência. Alta dimensionalidade.Abstract: This work proposes a multilevel framework called Treasure Hunt, which is capable of distributing independent search algorithms to a large number of processing nodes. Aiming to obtain joint convergences between working nodes, Treasure Hunt proposes a driving mechanism that smoothly controls the cooperation between the multiple independent Treasure Hunt instances. The tree topology proposed by Treasure Hunt ensures quick propagation of information, while providing simultaneous explorations (by parents) and exploitations (by children), on several levels of granularity, regardless the number of nodes in the tree. Treasure Hunt has good fault tolerance and is partially prepared to full fault tolerance. As part of the methods developed during this work, an automated Iterative Partitioning method is proposed to control the balance between exploration and exploitation as the search progress. A Convergence Stabilization Modeling to operate in Online mode is also proposed, aiming to find good cost/benefit stopping points for the optimization algorithms running within the Treasure Hunt instances. Experiments on classic, random and competition benchmarks of various sizes and complexities, using the search algorithms PSO, DE and CCPSO2, show that Treasure Hunt boosts the inherent characteristics of these search algorithms. Treasure Hunt makes algorithms with poor performances to become comparable to good ones, and algorithms with good performances to be capable of extending their limits to larger problems. Experiments distributing Treasure Hunt instances in a cooperative network up to 160 processes show the robust scaling of the framework, presenting improved results even when fixing a wall-clock time for the instances. Results show that the sampling mechanism provided by Treasure Hunt, allied to the increased cooperation between multiple evolving populations, reduce the need for large population sizes and complex search algorithms. This is specially important on real-world problems with time-consuming fitness functions. Keywords: Artificial intelligence. Optimization methods. Distributed algorithms. Convergence modeling. High dimensionality

Multi-level Systems Modeling and Optimization

This research combines the disciplines of system-of-systems (SoS) modeling, platform-based design, optimization and evolving design spaces to achieve a novel capability for designing solutions to key aeronautical mission challenges. A central innovation in this approach is the confluence of multi-level modeling (from sub-systems to the aircraft system to aeronautical system-of-systems) in a way that coordinates the appropriate problem formulations at each level and enables parametric search in design libraries for solutions that satisfy level-specific objectives. The work here addresses the topic of SoS optimization and discusses problem formulation, solution strategy, the need for new algorithms that address special features of this problem type, and also demonstrates these concepts using two example application problems - a surveillance UAV swarm problem, and the design of noise optimal aircraft and approach procedures

Optimizing transportation systems and logistics network configurations : From biased-randomized algorithms to fuzzy simheuristics

242 páginasTransportation and logistics (T&L) are currently highly relevant functions in any competitive industry. Locating facilities or distributing goods to hundreds or thousands of customers are activities with a high degree of complexity, regardless of whether facilities and customers are placed all over the globe or in the same city. A countless number of alternative strategic, tactical, and operational decisions can be made in T&L systems; hence, reaching an optimal solution –e.g., a solution with the minimum cost or the maximum profit– is a really difficult challenge, even by the most powerful existing computers. Approximate methods, such as heuristics, metaheuristics, and simheuristics, are then proposed to solve T&L problems. They do not guarantee optimal results, but they yield good solutions in short computational times. These characteristics become even more important when considering uncertainty conditions, since they increase T&L problems’ complexity. Modeling uncertainty implies to introduce complex mathematical formulas and procedures, however, the model realism increases and, therefore, also its reliability to represent real world situations. Stochastic approaches, which require the use of probability distributions, are one of the most employed approaches to model uncertain parameters. Alternatively, if the real world does not provide enough information to reliably estimate a probability distribution, then fuzzy logic approaches become an alternative to model uncertainty. Hence, the main objective of this thesis is to design hybrid algorithms that combine fuzzy and stochastic simulation with approximate and exact methods to solve T&L problems considering operational, tactical, and strategic decision levels. This thesis is organized following a layered structure, in which each introduced layer enriches the previous one.El transporte y la logística (T&L) son actualmente funciones de gran relevancia en cual quier industria competitiva. La localización de instalaciones o la distribución de mercancías a cientos o miles de clientes son actividades con un alto grado de complejidad, indepen dientemente de si las instalaciones y los clientes se encuentran en todo el mundo o en la misma ciudad. En los sistemas de T&L se pueden tomar un sinnúmero de decisiones al ternativas estratégicas, tácticas y operativas; por lo tanto, llegar a una solución óptima –por ejemplo, una solución con el mínimo costo o la máxima utilidad– es un desafío realmente di fícil, incluso para las computadoras más potentes que existen hoy en día. Así pues, métodos aproximados, tales como heurísticas, metaheurísticas y simheurísticas, son propuestos para resolver problemas de T&L. Estos métodos no garantizan resultados óptimos, pero ofrecen buenas soluciones en tiempos computacionales cortos. Estas características se vuelven aún más importantes cuando se consideran condiciones de incertidumbre, ya que estas aumen tan la complejidad de los problemas de T&L. Modelar la incertidumbre implica introducir fórmulas y procedimientos matemáticos complejos, sin embargo, el realismo del modelo aumenta y, por lo tanto, también su confiabilidad para representar situaciones del mundo real. Los enfoques estocásticos, que requieren el uso de distribuciones de probabilidad, son uno de los enfoques más empleados para modelar parámetros inciertos. Alternativamente, si el mundo real no proporciona suficiente información para estimar de manera confiable una distribución de probabilidad, los enfoques que hacen uso de lógica difusa se convier ten en una alternativa para modelar la incertidumbre. Así pues, el objetivo principal de esta tesis es diseñar algoritmos híbridos que combinen simulación difusa y estocástica con métodos aproximados y exactos para resolver problemas de T&L considerando niveles de decisión operativos, tácticos y estratégicos. Esta tesis se organiza siguiendo una estructura por capas, en la que cada capa introducida enriquece a la anterior. Por lo tanto, en primer lugar se exponen heurísticas y metaheurísticas sesgadas-aleatorizadas para resolver proble mas de T&L que solo incluyen parámetros determinísticos. Posteriormente, la simulación Monte Carlo se agrega a estos enfoques para modelar parámetros estocásticos. Por último, se emplean simheurísticas difusas para abordar simultáneamente la incertidumbre difusa y estocástica. Una serie de experimentos numéricos es diseñada para probar los algoritmos propuestos, utilizando instancias de referencia, instancias nuevas e instancias del mundo real. Los resultados obtenidos demuestran la eficiencia de los algoritmos diseñados, tanto en costo como en tiempo, así como su confiabilidad para resolver problemas realistas que incluyen incertidumbre y múltiples restricciones y condiciones que enriquecen todos los problemas abordados.Doctorado en Logística y Gestión de Cadenas de SuministrosDoctor en Logística y Gestión de Cadenas de Suministro

Applied Metaheuristic Computing

For decades, Applied Metaheuristic Computing (AMC) has been a prevailing optimization technique for tackling perplexing engineering and business problems, such as scheduling, routing, ordering, bin packing, assignment, facility layout planning, among others. This is partly because the classic exact methods are constrained with prior assumptions, and partly due to the heuristics being problem-dependent and lacking generalization. AMC, on the contrary, guides the course of low-level heuristics to search beyond the local optimality, which impairs the capability of traditional computation methods. This topic series has collected quality papers proposing cutting-edge methodology and innovative applications which drive the advances of AMC

Facility Location Planning Under Disruption

Facility Location Problems (FLPs) such as the Uncapacitated Facility Location (UFL) and the Capacitated Facility Location (CFL) along with the k-Shortest Path Problem (k-SPP) are important research problems in managing supply chain networks (SCNs) and related operations. In UFL, there is no limit on the facility serving capacity while in CFL such limit is imposed. FLPs aim to find the best facility locations to meet the customer demands within the available capacity with minimized facility establishment and transportation costs. The objective of the (k-SPP) is to find the k minimal length and partial overlapping paths between two nodes in a transport network graph. In the literature, many approaches are proposed to solve these problems. However, most of these approaches assume totally reliable facilities and do not consider the failure probability of the facilities, which can lead to notably higher cost. In this thesis, we investigate the reliable uncapacitated facility location (RUFL)and the reliable capacitated facility location (RCFL) problems, and the k-SPP where potential facilities are exposed to disruption then propose corresponding solution approaches to efficiently handle these problems. An evolutionary learning technique is elaborated to solve RUFL. Then, a non-linear integer programming model is introduced for the RCFL along with a solution approach involving the linearization of the model and its use as part of an iterative procedure leveraging CPLEX for facility establishment and customer assignment along with a knapsack implementation aiming at deriving the best facility fortification. In RUFL and RCFL, we assume heterogeneous disruption with respect to the facilities, each customer is assigned to primary and backup facilities and a fixed fortification budget allows to make a subset of the facilities totally reliable. Finally, we propose a hybrid approach based on graph partitioning and modified Dijkstra algorithm to find k partial overlapping shortest paths between two nodes on a transport network that is exposed to heterogeneous connected node failures. The approaches are illustrated via individual case studies along with corresponding key insights. The performance of each approach is assessed using benchmark results. For the k-SPP, the effect of preferred establishment locations is analyzed with respect to disruption scenarios, failure probability, computation time, transport costs, network size and partitioning parameters

Energy and performance-optimized scheduling of tasks in distributed cloud and edge computing systems

Infrastructure resources in distributed cloud data centers (CDCs) are shared by heterogeneous applications in a high-performance and cost-effective way. Edge computing has emerged as a new paradigm to provide access to computing capacities in end devices. Yet it suffers from such problems as load imbalance, long scheduling time, and limited power of its edge nodes. Therefore, intelligent task scheduling in CDCs and edge nodes is critically important to construct energy-efficient cloud and edge computing systems. Current approaches cannot smartly minimize the total cost of CDCs, maximize their profit and improve quality of service (QoS) of tasks because of aperiodic arrival and heterogeneity of tasks. This dissertation proposes a class of energy and performance-optimized scheduling algorithms built on top of several intelligent optimization algorithms. This dissertation includes two parts, including background work, i.e., Chapters 3–6, and new contributions, i.e., Chapters 7–11. 1) Background work of this dissertation. Chapter 3 proposes a spatial task scheduling and resource optimization method to minimize the total cost of CDCs where bandwidth prices of Internet service providers, power grid prices, and renewable energy all vary with locations. Chapter 4 presents a geography-aware task scheduling approach by considering spatial variations in CDCs to maximize the profit of their providers by intelligently scheduling tasks. Chapter 5 presents a spatio-temporal task scheduling algorithm to minimize energy cost by scheduling heterogeneous tasks among CDCs while meeting their delay constraints. Chapter 6 gives a temporal scheduling algorithm considering temporal variations of revenue, electricity prices, green energy and prices of public clouds. 2) Contributions of this dissertation. Chapter 7 proposes a multi-objective optimization method for CDCs to maximize their profit, and minimize the average loss possibility of tasks by determining task allocation among Internet service providers, and task service rates of each CDC. A simulated annealing-based bi-objective differential evolution algorithm is proposed to obtain an approximate Pareto optimal set. A knee solution is selected to schedule tasks in a high-profit and high-quality-of-service way. Chapter 8 formulates a bi-objective constrained optimization problem, and designs a novel optimization method to cope with energy cost reduction and QoS improvement. It jointly minimizes both energy cost of CDCs, and average response time of all tasks by intelligently allocating tasks among CDCs and changing task service rate of each CDC. Chapter 9 formulates a constrained bi-objective optimization problem for joint optimization of revenue and energy cost of CDCs. It is solved with an improved multi-objective evolutionary algorithm based on decomposition. It determines a high-quality trade-off between revenue maximization and energy cost minimization by considering CDCs’ spatial differences in energy cost while meeting tasks’ delay constraints. Chapter 10 proposes a simulated annealing-based bees algorithm to find a close-to-optimal solution. Then, a fine-grained spatial task scheduling algorithm is designed to minimize energy cost of CDCs by allocating tasks among multiple green clouds, and specifies running speeds of their servers. Chapter 11 proposes a profit-maximized collaborative computation offloading and resource allocation algorithm to maximize the profit of systems and guarantee that response time limits of tasks are met in cloud-edge computing systems. A single-objective constrained optimization problem is solved by a proposed simulated annealing-based migrating birds optimization. This dissertation evaluates these algorithms, models and software with real-life data and proves that they improve scheduling precision and cost-effectiveness of distributed cloud and edge computing systems

Novel Strategies to Accelerate Search Algorithms in Data Reduction

In our current hyper-connected digital world where data is growing enormously, instance reduction is an essential pre-processing phase to obtain cleaner and smaller datasets that are free from noise, redundant or irrelevant samples (the so-called, Smart Data). The data after pre-processing may become more reliable, accurate and useful for subsequent data mining tasks. Instance reduction consists of two types: instance selection and instance generation; each can be formulated as a combinatorial/continuous optimisation problem depending on whether its decision variable is discrete or continuous, respectively. It is an emerging challenge characterised by multimodality and a large number of decision variables. Given such difficulties, derivative-free methods are likely promising approaches to address the problem. They are powerful search algorithms that seek the nearest local optimum and do not necessarily take into account the gradient computation of the objective function like derivative methods. Solutions for instance reduction fall into the intersection of machine learning, data mining and optimisation at which the process of a domain can take part in the execution of another. Thus, the synergy between domains is important to solve the problem more effectively, and this has attracted a significant interest from researchers. Among many different derivative-free search approaches, the family of direct search methods has introduced various strategies to tackle numerous modern numerical optimisation problems, where population-based meta-heuristics and pattern search can be considered two of the most prevalent in the literature. Population-based meta-heuristics are an iterative search framework composing several subordinate low-level heuristics to control exploration and exploitation for a pool of solution candidates. This set of methods searches for high-quality solutions from multi-points, and thus is usually associated with high computational expense. Pattern search methods seek an improved solution from candidates that are generated from different directions. They examine trial solutions sequentially by comparing each trial solution with the `best' solution found up to the present time. In this dissertation, we will investigate these derivative-free search strategies to address instance reduction, a critical optimisation problem in the field of data science. Although many derivative-free methods have been proved effective in addressing instance reduction, they are usually time-consuming, especially when handling relatively large datasets. This impediment limits their practicality in many data mining systems and thus necessitates a solution to accelerate the search process. The need for a fast and effective search framework for instance reduction has motivated us to develop novel search strategies in the family of direct search approaches, aiming to still obtain high quality solutions achieved by state-of-the-art techniques in the domain, but significantly reduce the runtime of the search process. Three major work packages presented in this thesis will cover two direct search approaches for two types of instance reduction, arranged in a progressive order at which findings at an earlier stage will contribute to the understanding of the later outcomes. Firstly, a novel evolutionary search framework for instance selection is proposed to balance the number of samples between classes to address a case study of imbalanced classification. Secondly, we develop another search framework for instance generation based on single-point search and memetic computing, namely Single-Point Memetic Structure. An accelerated mechanism for computing the objective function is embedded into the proposed search design, thus reducing significantly the runtime. Finally, a novel search framework for simultaneous instance selection and generation is designed to handle the instance reduction problem in both combinatorial and continuous search spaces. In summary, the research conducted here introduces a set of novel search strategies towards derivative-free methods to tackle instance reduction problems. They are different search frameworks which aim to produce a high quality reduced set from a relatively large original source within a reasonable amount of time. This is accomplished by either taking advantage of machine learning integration or the Single-Point Memetic Structure with an accelerated mechanism. The use of machine learning in a meta-heuristic search framework greatly speeds up the computation of the objective function while the Single-Point Memetic Search allows us to reuse virtually all prior calculations for computing the fitness value of newly evolved individuals. Hence, these novel search strategies can save vast computational cost. Finally, we leverage the insights previously found to propose another novel search framework that handles both instance selection and instance generation simultaneously, and operates in both combinatorial and continuous search spaces. These novel search strategies are examined with a large number of datasets in different hyper-parameter settings. The obtained numerical results are comprehensively analysed and verified by different statistical tests to prove the robustness of the proposed search strategies with respect to other state-of-the-art techniques in the domain