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Cloud services gain more attention due to its accessibility, performance, and cost factors. Cloud offers a wide range of services and completes the task without any delay due to its scheduling policies. Task scheduling is an important factor in cloud computing applications. The performance of applications increases due to an effective scheduling strategy. The cloud resources are allocated to the tasks through task scheduling. Factors like customer satisfaction, resource utilization, better performance make task scheduling crucial for service providers. Depending on the scheduling schemes support in clouds, scheduling is categorized into single cloud or multi-cloud scheduling. Multi-cloud environment provides diverse resources and significantly reduces the cost and commercial limitations. However, reducing the cost functions and makespan are the major factors considered to avoid customer dissatisfaction. But it is essential to concentrate on other factors, such as throughput, delay, Makespan, waiting time, response time, utilization, and efficiency to improve the quality of services. This research work presents a Multi-Swarm Optimization model for Multi-Cloud Scheduling for Enhanced Quality of Services for a multi-cloud environment. Experimental results demonstrate that the proposed approach performs better in all aspects compared to existing techniques, such as Adaptive energy-efficient scheduling, single objective particle swarm optimization scheduling, and improves the quality of services.

Autodock and its various variants are widely utilized docking approaches, which adopt optimization methods as search algorithms for flexible ligand docking and virtual screening. However, many of them have their limitations, such as poor accuracy for dockings with highly flexible ligands and low docking efficiency. In this paper, a multi-swarm optimization algorithm integrated with Autodock environment is proposed to design a high-performance and high-efficiency docking program, namely, MSLDOCK. The search algorithm is a combination of the random drift particle swarm optimization with a novel multi-swarm strategy and the Solis and Wets local search method with a modified implementation. Due to the algorithm's structure, MSLDOCK also has a multithread mode. The experimental results reveal that MSLDOCK outperforms other two Autodock-based approaches in many aspects, such as self-docking, cross-docking, and virtual screening accuracies as well as docking efficiency. Moreover, compared with three non-Autodock-based docking programs, MSLDOCK can be a reliable choice for self-docking and virtual screening, especially for dealing with highly flexible ligand docking problems. The source code of MSLDOCK can be downloaded for free from https://github.com/lcmeteor/MSLDOCK.

In this paper, we present a method for electrocardiogram beat based on multi swarm optimization and radial basis function neural network. ECG is a non-surgical method for measuring and recording the electrical activity of the heart and on many occasions, an experienced cardiologist may not be available on the patient’s site. Therefore, a type of automated ECG analysis is required for the patient to take the electrocardiogram by a general practitioner or paramedical team attending the patient’s location. There is a need for automated ECG analysis. Finally, this paper gives the best analysis methodology for the automated analysis of multi-channel ECG signals. Diagnosis may be affected by the presence of artifacts and noise in multi-channel ECG signals. Some researchers calculated dynamic cutoff frequency parameter from noisy ECG signals to remove noise using the neural network method of Radial Basis function with particle swarm improvement method (RBFNN-PSO). But PSO only has Swarm and it takes a lot of time to give a response. To overcome these limitations, an improved version of the RBFNN-PSO algorithm called Radial Basis Function Neural Network with Multi Swarm Optimization (RBFNN-MSO) has been proposed. Finally, the cutoff frequency parameter is determined by the RBFNN-MSO methodology that is applied to digital low-frequency filters for impulse response (FIR). The next step after removing noise from multi-channel ECG signals is the feature extraction and reduction process. 24 features of the patient’s multi-channel ECG signals are extracted. The next part of the research is divided into two steps. The first step is whether or not the patient’s ECG signals are affected. The vector machine is supported with particle swarm improvement (SVM-PSO) and another way is to support the vector machine with multi swarm improvement (SVM-MSO) to detect ECG signals of the affected patient or not. Finally, SVM-MSO offers greater accuracy compared to SVM-PSO. When compared to all other existing architecture results, they used the rating with 86% of all the test accuracy. But in this paper, our proposed work has 90% overall in different situations. In another point of view also,our proposed work has proven that average accuracy is over 85% even then train data set is small.

In this study, a novel method for generating multiple-choice tests is presented, which extracts the required number of tests of the same levels of difficulty in a single attempt and approximates the difficulty level requirement given by users. We propose an approach using parallelism and Pareto optimization for multi-swarm migration in a particle swarm optimization (PSO) algorithm. Multi-PSO is proposed for shortening the computing time. The proposed migration of PSOs increases the diversity of tests and controls the overlap of extracted tests. The experimental results show that the proposed method can generate many tests from question banks satisfying predefined levels of difficulty. Additionally, the developed method is shown to be effective in terms of many criteria when compared with other methods such as manually extracted tests, a simulated annealing algorithm (SA), random methods and PSO-based approaches in terms of the number of successful solutions, accuracy, standard deviation, search speed, and the number of questions overlapping between the exam questions, as well as for changing the search space, changing the number of individuals, changing the number of swarms, and changing the difficulty requirements. Web of Science 9 32148 32131

This paper focus on the problem of simultaneous scheduling of machine and automated guided vehicle (AGV) in a flexible manufacturing system (FMS) so as to minimize the makespan The FMS scheduling problem has been tackled by various traditional optimization techniques. While these methods can give an optimal solution to small-scale problems, different scheduling mechanisms are designed to generate optimum scheduling; these include non-traditional approaches such as genetic algorithm (GA), memetic algorithm (MA) and particle swarm algorithm (PSA) by considering multiple bjectives,i.e.,minimising the idle time of the machine andminimising the total penalty cost for not meeting the deadline concurrently. Two optimization algorithms ( genetic algorithm and particle swarm algorithm) are compared and conclusions are presented

To predict the performance parameter changing trend of an aeroengine, a novel double-extremum learning particle swarm optimization (DELPSO) algorithm is proposed. Inspired by human learning behavior, this algorithm simulates this behavior, including the strategies of collective learning, private tutoring, and research behavior, so that obtained final solutions would be in the global optimal area or its neighbor area as close as possible. Meanwhile, to improve the prediction performance, a nonlinear mapping function is designed to describe the feature relationship between inputs and outputs of historical data. Based on the DELPSO, the fitness function synthetically considers the changing trend and the prediction error and can adaptively select optimal parameters of the nonlinear mapping function. The experimental results demonstrate that the DELPSO has globally stable and reliable performance. To validate the prediction performance of the proposed DELPSO, it is also applied to an aeroengine. Its good prediction performance indicates that the proposed DELPSO is an important reference for maintenance decision-making of aeroengines.

A central vision of the combinatorial optimization is to deliver a number of independent lines of operational research by implementing algorithms and hyper-graph theory on a series of random theoretical computer science problems. A main motivation is that thousands of real-life problems can be formulated as abstract combinatorial optimization problems. Albeit, multi-agent systems can also be used to solve problems that are difficult or impossible for monolithic systems to solve and methodic, functional, procedural, algorithmic and reinforcement forms of approaches are needed. Thus, in practice, extensive research and development efforts are required when applying combinatorial optimization in intelligent multi-agent systems, in order to achieve cooperation, interoperability and sustainability in heterogeneous and complex existing or future industrial, aerospace, robotic systems or/and any other cyber-physical system. Driven by the above mentioned problems, this Doctoral Dissertation presents meta-heuristic approaches in the area of AI algorithms and specifically the particle swarm and ant colony optimization to solve combinatorial optimization problems. More specifically present thesis’ applications/implementations focus on enhancing the: I. Combinational optimization of the intelligent multi-agent systems; II. Capabilities of the modern and intelligent multi-agent systems; III. Sustainability of the global cyber-physical systems. The methodological approach followed in this Dissertation for reaching the first goal may be described within the following achievements: reformulate the problem of dartboard game within the spectrum of metaheuristic algorithms, use/apply the Ant Colony System and Max-Min Ant System (MMAS) algorithm as a metaheuristic strategy that guide the search process and reinforces local search in neighborhood of the best solution found in each iteration. In addition, heuristic is an adjective for experience-based techniques that help in problem solving, learning and discovery and heuristic methods are used to rapidly come to an 'optimal solution'. In more precise terms, heuristics stand for strategies using readily accessible information to control problem solving in many practical scenarios, slowing convergence and facilitating exploration. However, the Ant Colony Optimization technique has emerged recently as a new metaheuristic for hard combinatorial Optimization Problems. Implementing a randomized construction heuristic extension of Ant Colony System algorithm in the Vehicle Scheduling Problem has become the second goal of this dissertation which is met by the following: definition the objective function for VSP, make probabilistic decisions as a function of artificial pheromone trails and estimate the effect of varying of levels of initial pheromone quantities on the objective function using an extension of Ant Colony System (ACS) algorithm. The final goal of this thesis is to enhance the previously referred goals/contribution regarding the sustainable development of an application paradigm. All parts included in currently presented thesis must meet the needs of the present forms of computing without compromising the ability of future generations to meet their own needs. This last objective is met at high-level by presenting the application of a ship dispatching real-life problem by: proposing a solution for a ship dispatching problem with the usage of Particle Swarm Optimization algorithm, analyze the operational dimension of the problem by introducing a VPR formulation and providing the paradigm of a set of 13 ports of the Aegean Sea (including a depot port) that was taken into consideration.

The utilization of ontology in the e-assessment area has grown tremendously. The context of e-learning is significant to the students for educational purposes. This makes the testing process easy for the students and also for the teachers. The majority of the approaches that deals with the ontology issue have suggested that the individual ontology models have merely a fraction of the assessment domain. To trounce such drawbacks, here, an automated ontology creation is proposed for the e-assessment systems. Initially, the text is extracted from the web utilizing the Unsupervised Quick Reduct (UQR) algorithm. This is trailed by the summarization of the texts using the multi-swarm optimization (MSO) based on preference learning. Finally, the sentence of the summary is then transmuted to multiple choice questions (MCQ). The keys are created using statistical pattern (SP). The efficiency of the system is examined using the experimental outcomes like error rate, precision, recall and accuracy. In accuracy, the proposed UQR algorithm achieves 97.7%, MSO achieve 96.2% accuracy and key generation achieves 94.7% accuracy. The proposed automatic ontology system indicates better when weighed against the top-notch methods.

This paper proposes the use of multi-swarm method in particle swarm optimization (PSO) algorithm to generate multiple-choice tests based on assumed objective levels of difficulty. The method extracts an abundance of tests at the same time with the same levels of difficulty and approximates the difficulty-level requirement given by the users. The experimental results show that the proposed method can generate many tests from question banks satisfying predefined levels of difficulty. Additionally, the proposed method is also shown to be effective in terms of many criteria when compared with other methods such as manually extracted tests, random methods and PSO-based methods in terms of execution time, standard deviation, the number of particles per swarm and the number of swarms.

The paper implements and optimizes the performance of a currently proposed chaos-deoxyribonucleic acid (DNA)-based hybrid approach to encrypt images using a bi-objective genetic algorithm (GA) optimization. Image encryption is a multi-objective problem. Optimizing the same using one fitness function may not be a good choice, as it can result in different outcomes concerning other fitness functions. The proposed work initially encrypts the given image using chaotic function and DNA masks. Further, GA uses two fitness functions – entropy with correlation coefficient (CC), entropy with unified average changing intensity (UACI), and entropy with number of pixel change rate (NPCR) – simultaneously to optimize the encrypted data in the second stage. The bi-objective optimization using entropy with CC shows significant performance gain over the single-objective GA optimization for image encryption.

Tuned mass damper (TMD) has been used for vibration controller of building, especially for high rise building. TMD is one of passive device for reducing response of the structure which subjected to dynamic external disturbance such as wind, or earthquake load. TMD used its weight for reducing the vibration, TMD’s frequency has been set with structure’s frequency so that the frequency can resonate each other for reducing the response of the structure during the dynamic load. Therefore, three variables have significant effect for TMD performance which are mass ratio of TMD ( m ), frequency ratio of TMD ( a ), and damping ratio of TMD ( z ) which lead to two important variables of TMD properties which are stiffness and damping of TMD. This paper developed an empirical equation for obtaining the optimum parameters of tuned mass damper based on H 2 norm control system and fast multi swarm optimization (FMSO). The objective function was to minimize the acceleration and displacement response of the structure. Accelerogram of El-Centro 1940 NS was chosen to be ground motion acceleration for simulating the response of the structure with and without TMD. The result shows a strong correlation both mass ratio of TMD to frequency ratio of TMD and mass ratio of TMD to damping ratio of TMD. Penggunaan peredam massa selaras (PMS) telah banyak digunakan sebagai alat kontrol getaran pada bangunan, khususnya bangunan-bangunan tinggi. PMS adalah salah satu kontrol pasif yang digunakan untuk mengurangi respon getaran dari struktur akibat beban-beban dinamik seperti angin, atau gempa. PMS menggunakan berat sendiri untuk mengurangi getaran, frekuensi dari PMS disesuaikan dengan frekuensi dari struktur sehingga beresonansi satu sama lain untuk mengurangi respon dari struktur selama berlangsungnya beban dinamik. Berdasarkan hal tersebut, ada tiga variabel yang mempunyai efek yang signifikan terhadap performa dari PMS, antara lain: rasio massa PMS (), rasio frekuensi PMS (), dan rasio redaman PMS () yang akan berhubungan langsung dengan dua parameter penting dari PMS yaitu kekakuan dan redaman dari PMS. Tulisan ini mengusulkan persamaan empirik untuk mendapatkan properti optimum dari PMS dengan menggunakan fungsi kontrol H2 dan algoritma fast multi swarm optimization. Fungsi objektif yang digunakan adalah untuk meminimumkan respon percepatan dan perpindahan dari struktur. Data rekaman El-Centro 1940 NS dipilih sebagai data percepatan tanah dasar untuk mensimulasikan respon dari struktur dengan dan tanpa menggunakan PMS. Hasil menunjukkan terdapat korelasi yang kuat antara rasio massa dari PMS terhadap rasio frekuensi dari PMS serta rasio massa dari PMS terhadap rasio redaman dari PMS.

Bayesian optimization has become a fundamental global optimization algorithm in many problems where sample efficiency is of paramount importance. Recently, there has been proposed a large number of new applications in fields such as robotics, machine learning, experimental design, simulation, etc. In this paper, we focus on several problems that appear in robotics and autonomous systems: algorithm tuning, automatic control and intelligent design. All those problems can be mapped to global optimization problems. However, they become hard optimization problems. Bayesian optimization internally uses a probabilistic surrogate model (e.g.: Gaussian process) to learn from the process and reduce the number of samples required. In order to generalize to unknown functions in a black-box fashion, the common assumption is that the underlying function can be modeled with a stationary process. Nonstationary Gaussian process regression cannot generalize easily and it typically requires prior knowledge of the function. Some works have designed techniques to generalize Bayesian optimization to nonstationary functions in an indirect way, but using techniques originally designed for regression, where the objective is to improve the quality of the surrogate model everywhere. Instead optimization should focus on improving the surrogate model near the optimum. In this paper, we present a novel kernel function specially designed for Bayesian optimization, that allows nonstationary behavior of the surrogate model in an adaptive local region. In our experiments, we found that this new kernel results in an improved local search (exploitation), without penalizing the global search (exploration). We provide results in well-known benchmarks and real applications. The new method outperforms the state of the art in Bayesian optimization both in stationary and nonstationary problems.

WOS: 000462516600009, Neural Network (NN), hybrid NN methods and Rotation Forest (RF) ensemble classifier are preferred in pattern analysis owing to their ability for finding efficient solutions on different problems. NN architecture usually includes backpropagation type algorithms in which error is exposed to fluctuations. Hybrid NN methods are generally designed to improve the classification performance of NN. Scout Particle Swarm Optimization (ScPSO) is one of these optimization algorithms including the effective parts of Particle Swarm Optimization (PSO) and Artificial Bee Colony Optimization (ABC). Moreover, RF algorithm usually indicates the same performance as in hybrid NN methods, although it is comprised of Decision Tree (DT) classifiers. At this point, our paper investigates whether RF using the hybrid NNs can outperform other ensemble classifiers in binary-medical pattern classification, or not. With this intention, PSO, ABC and ScPSO are placed in NN algorithms instead of back propagation, and hybrid methods (PSO-NN, ABC-NN and ScPSO-NN) are realized. As a result, RF (PSO-NN), RF (ABC-NN) and RF (ScPSO-NN) architectures are obtained. Classification Accuracy (CA), Area Under Curve (AUC), Sensitivity, Specificity, F-measure, Gmean and Precision metrics are used for a statistical performance comparison, and a test based on 2-fold cross validation method was realized on five medical datasets. (C) 2017 The Authors. Production and hosting by Elsevier B.V. on behalf of King Saud University.

Task scheduling is one of the most important issues in heterogeneous environments when high efficiency is required. Because task scheduling is a Nondeterministic Polynomial (NP)-hard problem, many evolutionary algorithms have been adopted to solve this problem. Since the convergence speed of solutions in population-based algorithms is low, they are integrated with local search algorithms. Thus, in this paper, to optimize the task scheduling makespan, a hybrid particle swarm optimization and hill climbing algorithm is proposed. The experimental results on random and scientific Directed Acyclic Graph (DAG) showed that the proposed algorithm performs effectively in terms of the makespan compared to the current well-known heuristic and particle swarm optimization algorithms. Keywords: Cloud computing, Directed acyclic graph, Hill climbing, PSO, Task scheduling

The vehicle routing problem is the basic problem of distribution planning which seeks to find the best route with minimum displacement cost considering the number of customers, their constraints, and number and capacity of the available vehicles. In this study, the traveling salesman problem and vehicle routing models are firstly described and, after that, the multi objective vehicle routing model is proposed to consider the Precedence constraints among customers. There are different meta-heuristic algorithms that can solve such NP-hard problems. In the present study, a solver algorithm is proposed which is based on a combination of the particle swarm optimization and the artificial bee colony algorithms. Additionally, by presenting an operational sample, using data of customers in a region, considering different constraints of the problem and its functions, and using penalty method as well as additional segmentation constraint method, the best vehicle route is obtained and the results of each algorithm together with its hybrid algorithm are demonstrated. Keywords: Vehicle routing problem, Meta-heuristic algorithms, Particle swarm optimization, Artificial bee colony, Hybrid algorithm, Precedence constraints

In this paper, a demand-side energy management scheme is proposed to minimize the electricity cost and the peak-to-average ratio. A particle swarm optimization strategy is integrated with a game-theoretical approach in order to solve a nonconvex problem of appliance scheduling. The unknowns of the optimization problem are modeled from the user perspective taking in consideration the real-world constraints of appliances, which impose an almost constant power consumption during predefined working time periods and within time windows constrained by the users. The performance of the proposed method has been assessed with different user time constraints. The obtained results outperform a state of the art solution based on convex programming, especially when stringent user requirements are imposed. The peak-to-average ratio is reduced more than twice respect to the convex programming technique.

Estimating the significance parameters, such as skin factor, permeability, wellbore storage coefficient, are the most component of transient pressure analysis. Many optimization algorithms have been applied to parametric estimation and realized the minimum error of well test curve. Although a flexible heuristic particle swarm optimization can hunt optimal solution rapidly, it is difficult to search further in the vicinity of the optimal solution. Hence, to alleviate the local optimum and premature convergence, a global hybrid algorithm referred to as particle swarm simulated annealing is proposed, and proves to have better performance of convergence and accuracy than traditional methods, which are more suitable for parameter estimation. Keywords: Parametric estimation, Particle swarm simulated annealing, Particle swarm optimization, Simulated annealing, Transient pressure analysis

Water resources data is usually featured by huge volume, multi-variable as well as multi-dimension, which leads to deficiency in terms of data integrity, rationality and efficacy in water resources management and allocation. In order to reduce the amount of data collected in the Internet of things, to improve the processing speed for water resources data, a constrained single objective optimization problem is transformed into a multi-objective optimization problem with sparse degree as the optimization objective in compressed sensing reconstruction, and then a sparse reconstruction method based on hybrid multi-objective optimization is proposed. The algorithm is designed based on the multi objective optimization problem, and the algorithm is easy to implement and adjust. Application results show that the proposed multi-objective particle swarm optimization-Genetic algorithm (MOPSOGA) is than traditional gradient projection sparse reconstruction algorithm (GPSR-BB) algorithm iterations decreased 43.9%. The success rate of reconstruction is higher than that of the traditional algorithm of 0.16; it's with a better reconstruction performance.

Particle swarm optimization (PSO) (Kennedy & Eberhart, 1995) and differential evolution (DE) (Storn & Price, 1995) are two stochastic, population-based optimization methods, which have been applied successfully to a wide range of problems as summarized in Engelbrecht (2005) and Price et al. (2005). A number of variations of both PSO and DE have been developed in the past decade to improve the performance of these algorithms (Engelbrecht, 2005; Price et al. 2005). One class of variations includes hybrids between PSO and DE, where the advantages of the two approaches are combined. The barebones DE (BBDE) is a PSO-DE hybrid algorithm proposed by Omran et al. (2007) which combines concepts from the barebones PSO (Kennedy 2003) and the recombination operator of DE. The resulting algorithm eliminates the control parameters of PSO and replaces the static DE control parameters with dynamically changing parameters to produce an almost parameter-free, self-adaptive, optimization algorithm. Recently, opposition-based learning (OBL) was proposed by Tizhoosh (2005) and was successfully applied to several problems (Rahnamayan et al., 2008). The basic concept of OBL is the consideration of an estimate and its corresponding opposite estimate simultaneously to approximate the current candidate solution. Opposite numbers were used by Rahnamayan et al. (2008) to enhance the performance of Differential Evolution. In addition, Han and He (2007) and Wang et al. (2007) used OBL to improve the performance of PSO. However, in both cases, several parameters were added to the PSO that are difficult to tune. Wang et al. (2007) used OBL during swarm initialization and in each iteration with a user-specified probability. In addition, Cauchy mutation is applied to the best particle to avoid being trapping in local optima. Similarly, Han and He (2007) used OBL in the initialization phase and also during each iteration. However, a constriction factor is used to enhance the convergence speed. In this chapter, OBL is used to improve the performance of PSO and BBDE without adding any extra parameter. The performance of the proposed methods is investigated when applied to several benchmark functions. The experiments conducted show that OBL improves the performance of both PSO and BBDE. The remainder of the chapter is organized as follows: PSO is summarized in Section 2. DE is presented in Section 3. Section 4 provides an overview of BBDE. OBL is briefly reviewed in

Most practical engineering optimization problems are multi-objective, i.e., their solution must consider simultaneously various performance criteria, which are often conflicting. Multi-Objective Evolutionary Algorithms (MOEAs) are particularly adequate for solving these problems, as they work with a population (of vectors or solutions) rather than with a single point (Schaffer, 1984; Fonseca & Fleming, 1993; Srinivas & Deb, 1995; Horn et al., 1994; Deb et al., 2002; Zitzler et al., 2001; Knowles & Corne, 2000; Gaspar-Cunha et al. 2004). This feature enables the creation of Pareto frontiers representing the trade-off between the criteria, simultaneously providing a link with the decision variables (Deb, 2001, Coello et al., 2002). Moreover, since in real applications small changes of the design variables or of environmental parameters may frequently occur, the performance of the optimal solution (or solutions) should be only slightly affected by these, i.e., the solutions should also be robust (Ray, 2002; Jin & Branke, 2005). The optimization problems involving unmanageable stochastic factors can be typified as (Jin & Branke, 2005): i) those where the performance is affected by noise originated by sources such as sensor measurements and/or environmental parameters (Wiesmann et al., 1998; Das, 1997); ii) those where the design variables change after the optimal solution has been found (Ray, 2002; Tsutsui & Ghosh, 1997; Chen et al., 1999); iii) problems where the process performance is estimated by an approximation to the real value; iv) and those where the performance changes with time, which implies that the optimization algorithm must be updated continuously. This text focuses exclusively problems of the second category. Given the above, optimization algorithms should determine the solutions that simultaneously maximize performance and guarantee satisfactory robustness, but the latter is rarely included in traditional algorithms. As robustness and performance can be conflicting, it is important to know their interdependency for each optimization problem. A robustness analysis should be performed as the search proceeds and not after, by introducing a robustness measure during the optimization. Robustness can be studied either by replacing the original objective function by an expression measuring both the performance and the expectation of each criterion in the vicinity of a specific solution, or by inserting an additional optimization criterion assessing robustness in addition to the original O pe n A cc es s D at ab as e w w w .ite ch on lin e. co m

Fuzzy systems (FSs) have been extensively applied to automatic control, pattern recognition, and decision analysis. However, a common bottleneck is encountered in the derivation of fuzzy rules, which is often difficult, time consuming, and relies on expert knowledge. To automate the design of FSs, many metaheuristic learning algorithms have been proposed. One major optimization category uses Swarm Intelligence (SI) model (Kennedy et al., 2001). The SI technique studies collective behavior in decentralized systems. Its development was based on mimicking the social behavior of animals or insects in an effort to find the optima in the problem space. SI models are initialized with a population of random solutions. One well-known SI model is particle swarm optimization (PSO) (Kennedy & Eberhart, 1995). Many modified PSO models have been proposed and successfully applied to different optimization problems (Clerc & Kennedy, 2002; Bergh & Engelbrecht, 2004; Ratnaweera et al., 2004; Juang, 2004; Kennedy & Mendes, 2006; Parrott & Li, 2006; Chen & Li, 2007). FS design using PSO has also been proposed in several studies (Juang, 2004; Chatterjee et al., 2005; Juang et al., 2007; Araujo & Coelho, 2008; Sharma et al., 2009). Another well-known SI is ant colony optimization (ACO) (Dorigo & Stutzle, 2004). The ACO technique is inspired by real ant colony observations. It is a multi-agent approach that was originally proposed to solve difficult discrete combinatorial optimization problems, such as the traveling salesman problem (TSP) (Dorigo et al., 1996; Dorigo & Gambardella, 1997). In the original ACO meta-heuristic, artificial ant colonies cooperate to find good solutions for difficult discrete optimization problems. Different ACO models have been applied to FS design problems (Cassillas et al., 2000; Cassillas et al., 2005; Mucientes & Casillas; 2007; Juang & Lo, 2007; Juang et al., 2008; Juang & Lu; 2009). In (Cassillas et al.,2000; Mucientes & Casillas; 2007; Juang et al., 2008; Juang & Lu; 2009), the FS input space was partitioned in grid type with antecedent part parameters of an FS manually assigned in advance. In (Juang & Lo, 2007), the FS input space was flexibly partitioned using a fuzzy clustering-like algorithm in order to reduce the total number of rules. For all of these studies, the consequent part parameters were optimized in discrete space using ACO. Since only the consequent part parameters are optimized, and the optimization space is restricted to be discrete, the designed FSs are unsuitable for problems where high accuracy is a major concern. Source: Fuzzy Systems, Book edited by: Ahmad Taher Azar, ISBN 978-953-7619-92-3, pp. 216, February 2010, INTECH, Croatia, downloaded from SCIYO.COM

In wireless sensor networks, minimizing power consumption to prolong network lifetime is very crucial. In the past, Pan et al. proposed two algorithms to find the optimal locations of base stations in two-tiered wireless sensor networks. Their approaches assumed the initial energy and the energy-consumption parameters were the same for all application nodes. If any of the above parameters were not the same, their approaches could not work. Recently, the PSO technique has been widely used in finding nearly optimal solutions for optimization problems. In this paper, an algorithm based on particle swarm optimization (PSO) is thus proposed for general power-consumption constraints. The proposed approach can search for nearly optimal BS locations in heterogeneous sensor networks, where application nodes may own different data transmission rates, initial energies and parameter values. Experimental results also show the good performance of the proposed PSO approach and the effects of the parameters on the results. The proposed algorithm can thus help find good BS locations to reduce power consumption and maximize network lifetime in two-tiered wireless sensor networks.

Particle Swarm Optimization (PSO) was first introduced as a concept for a non-linear optimizer by Kennedy and Eberhart in 1995. Their seminal work articulates a technique of evolutionary computation, which has its origin in artificial intelligence and simplified social models such as bird flocking and fish schooling (Kennedy & Eberhart, Nov. 1995; Kennedy & Eberhart, Oct. 1995). Its early appeal lay in its use of only primitive mathematical operators and computational economy with regard to both memory and speed. The authors were influenced by the work of Reynolds, Heppner and Grenander in modeling bird flocking and recognized that the fundamental hypothesis to the development of PSO is that an evolutionary advantage is obtained by the social sharing of information among members of the same species. They stated that the simulation of the graceful but unpredictable choreography of a bird flock by collision-proof agents could be used as an effective optimizer for a wide range of functions.

Optimization techniques play an important role as a useful decision making tool in the design of structures. By deriving the maximum benefits from the available resources, it enables the construction of lighter, more efficient structures while maintaining adequate levels of safety and reliability. A large number of optimization techniques have been suggested over the past decades to solve the inherently complex problem posed in structural design. Their scope varies widely depending on the type of stru ctural problem to be tackled. Gradient-based methods, for example, are highly effectively in finding local optima when the design space is convex and continuous and when the design problem involves large number of design variables and constraints. If the problem constraints and objective function are convex in nature, then it is possible to conclude that the local optimum will be a global optimum. In most structural problems, however, it is practically impossible to check the convexity of the design space, therefore assuring an obtained optimum is the best possible among multiple feasible solutions. Global non-gradient-based methods are able to traverse along highly non-linear, non-convex design spaces and find the best global solutions. In this category many unconstrained optimization algorithms have been developed by mimicking natural phenomena such as Simulated Annealing (Kirkpatrick et al., 1983), Genetic Algorithms (Goldberg, 1989), and Bacterial Foraging (Passino, 2002) among others. Recently, a new family of more efficient global optimization algorithms have been developed which are better posed to handle constraints. They are based on the simulation of social interactions among members of a specific species looking for food sources. From this family of optimizers, the two most promising algorithms, which are the subject of this book, are Ant Colony Optimization (Dorigo, 1986), and Particle Swarm Optimization or PSO. In this chapter, we present the analysis, implementation, and improvement strategies of a particle swarm optimization suitable for constraint optimization tasks. We illu strate the functionality and effectiveness of this algorithm, and explore the effect of the different PSO setting parameters in the scope of classical structural optimization problems.

In general nonlinear programming problems to find a solution which minimizes an objective function under given constraints, one whose objective function and constraint region are convex is called a convex programming problem. For such convex programming problems, there have been proposed many efficient solution method as the successive quadratic programming method and the general gradient method. Unfortunately, there have not been proposed any decisive solution method for nonconvex programming problems. As practical solution methods, meta-heuristic optimization methods as the simulated annealing method and the genetic algorithm have been proposed. In recent years, however, more speedy and more accurate optimization methods have been desired because the size of actual problems has been increasing. As a new optimization method, particle swarm optimization (PSO) was proposed (Kennedy & Eberhart, 1995). PSO is a search method simulating the social behavior that each individual in the population acts by using both the knowledge owned by it and that owned by the population, and they search better points by constituting the population. The authors proposed a revised PSO (rPSO) by incorporating the homomorphous mapping and the multiple stretching technique in order to deal with shortcomings of the original PSO as the concentration to local solution and the inapplicability of constrained problems (Matsui et al., 2008). In recent years, with the diversification of social requirements, the demand for the programs with multiple objective functions, which may be conflicting with each other, rather than a single-objective function, has been increasing (e.g. maximizing the total profit and minimizing the amount of pollution in a production planning). Since there does not always exist a complete optimal solution which optimizes all objectives simultaneously for multiobjective programming problems, the Pareto optimal solution or non-inferior solution, is defined, where a solution is Pareto optimal if any improvement of one objective function can be achieved only at the expense of at least one of the other objective functions. For such multiobjective optimization problems, fuzzy programming approaches (e.g. (Zimmermann, 1983), (Rommelfanger, 1996), considering the imprecise nature of the DM's judgments in multiobjective optimization problems, seem to be very applicable and promising. In the application of the fuzzy set theory into multiobjective linear programming problems started

Particle Swarm Optimization (PSO) was introduced in 1995 by Russell Eberhart and James Kennedy (Eberhart & Kennedy, 1995). PSO is a biologically-inspired technique based around the study of collective behaviour in decentralized and self-organized animal society systems. The systems are typically made up from a population of candidates (particles) interacting with one another within their environment (swarm) to solve a given problem. Because of its efficiency and simplicity, PSO has been successfully applied as an optimizer in many applications such as function optimization, artificial neural network training, fuzzy system control. However, despite recent research and development, there is an opportunity to find the most effective methods for parameter optimization and feature selection tasks. This chapter deals with the problem of feature (variable) and parameter optimization for neural network models, utilising a proposed Quantum–inspired PSO (QiPSO) method. In this method the features of the model are represented probabilistically as a quantum bit (qubit) vector and the model parameter values as real numbers. The principles of quantum superposition and quantum probability are used to accelerate the search for an optimal set of features, that combined through co-evolution with a set of optimised parameter values, will result in a more accurate computational neural network model. The method has been applied to the problem of feature and parameter optimization in Evolving Spiking Neural Network (ESNN) for classification. A swarm of particles is used to find the most accurate classification model for a given classification task. The QiPSO will be integrated within ESNN where features and parameters are simultaneously and more efficiently optimized. A hybrid particle structure is required for the qubit and real number data types. In addition, an improved search strategy has been introduced to find the most relevant and eliminate the irrelevant features on a synthetic dataset. The method is tested on a benchmark classification problem. The proposed method results in the design of faster and more accurate neural network classification models than the ones optimised through the use of standard evolutionary optimization algorithms.

Two important topics in Particle Swarm Optimization (PSO) research filed are trajectory analysis of particles and parameter selection method. Trajectory analysis is important because it can help to determine where the position of each particle is at each evolutionary step, and consequently it can help to clarify the running mechanism of PSO algorithm, so as to explain why and when PSO algorithm can be successful to solve optimization problems. Parameter selection of PSO algorithm is important because the performance of PSO algorithm is sensitive to the chosen parameters. Till now, some research works have been published in literatures to investigate both of these two topics, but unfortunately, the trajectory analysis is based on simplified deterministic algorithms, regardless of the randomness in real PSO algorithm; and the parameter selection is based on experimental results instead of theoretical results. This chapter is proposed to investigate both of these two important topics. In this chapter, the trajectory of particle in a general PSO algorithm is theoretically investigated, considering the randomness thoroughly. For arbitrary dimension d of an arbitrary particle i in the general particle swarm system, the update equations investigated in this chapter are given in Eqs. (1) and (2), where t is the evolutionary step, V is the velocity of particle i, X is the position of particle i, Pi is the history best position found by particle i, and Pg is the history best position found by the total swarm.

Population metaheuristics can be viewed as algorithms handling a probabilistic sampling of a probability distribution, representing the objective function of an optimization problem. These algorithms can be described either as implicit, explicit or direct, according to their way of sampling the objective function. These algorithms are iteratively manipulating the sample thanks to components that can be classified among three tendencies: learning

Multiprocessor task scheduling is a generalized form of classical machine scheduling where a task is processed by more than one processor. It is a challenging problem encountered in wide range of applications and it is vastly studied in the scheduling literature (see for instance (Chan & Lee, 1999 and Drozdowski, 1996) for a comprehensive introduction on this topic). However, Drozdowski (1996) shows that multiprocessor task scheduling is difficult to solve even in its simplest form. Hence, many heuristic algorithms are presented in literature to tackle multiprocessor task scheduling problem. Jin et al. (2008) present a performance study of such algorithms. However, most of these studies primarily concerned with a single stage setting of the processor environment. There are many practical problems where multiprocessor environment is a flow-shop that is it is made of multiple stages and tasks have to go through one stage to another. Flow-shop scheduling problem is also vastly studied in scheduling context though most of these studies concerned with single processor at each stage (see for instance Linn & Zhang, 1999, Dauzere-Peres & Paulli, 1997). With the advances made in technology, in many practical applications, we encounter parallel processors at each stage instead of single processors such as parallel computing, power system simulations, operating system design for parallel computers, traffic control in restricted areas, manufacturing and many others (see for instance (Krawczyk & Kubale, 1985, Lee & Cai, 1999, Ercan & Fung, 2000, Caraffa et. al.,2001)). This particular problem is defined as hybrid flow-show with multiprocessor tasks in scheduling terminology and minimizing the schedule length (makespan) is the typical scheduling problem addressed. However, Brucker & Kramer (1995) show that multiprocessor flow-shop problem to minimize makespan is also NP-hard. Gupta (1988) showed that hybrid flow-shop even with two stages is NP-hard. Furthermore, the complexity of the problem increases with the increasing number of stages. Multiprocessor task scheduling in a hybrid flow-shop environment has recently gained the attention of the research community. To the best of our knowledge, one of the earliest papers that deal with this problem in the scheduling literature is by Oguz and Ercan, 1997. However, due to the complexity of the problem, in the early studies (such as (Lee & Cai, 1999, Oguz et. al., 2003)) researchers targeted two layer flow-shops with multiprocessors. Simple list based heuristics as well as meta-heuristics were introduced for the solution

The particle swarm optimization technique is one of the promising tools to find a proper optimum for an unknown function optimization. Especially, global search capability of the method is very powerful. The particle swarm optimization utilizes common knowledge of the group and individual experiences effectively. That is, direction for the best estimator that a particle has ever reached, direction for the best one that all particles have ever found and momentum are successfully combined to determine the next direction. At the same time, the method does not utilize gradient of the objective function. Only values of the objective function are used. In many applications, it is difficult or impossible to obtain the gradient of an objective function. Then, the particle swarm optimization can take advantage of the merit. However, this means that the method does not use local information of the function. Even if a particle is close to a global optimal, the particle moves based on three factors described above. In this case, it seems better to search neighbour area carefully. To do so, local information such as gradient is necessary. On the other hand, the simultaneous perturbation method is a kind of stochastic gradient method. The scheme can obtain the local information of the gradient without direct calculation of the gradient. The simultaneous perturbation estimates the gradient using a kind of finite difference technique. However, even if dimension of the parameters are large, the simultaneous perturbation requires only two values of the target function. Therefore, we can apply this to high dimensional optimization problems in effect. As mentioned now, since the simultaneous perturbation is a stochastic gradient method, we cannot expect global search capability. That is, this method cannot give a global optimal but a local one. Combination of the particle swarm optimization and the simultaneous perturbation optimization will yield interesting algorithms which have advantages of these two approaches. There are some ways to combine the particle swarm optimization and the simultaneous perturbation method. In this paper, we propose four new algorithms based on combinations of the particle swarm optimization and the simultaneous perturbation. Some results for test functions are also shown. Moreover, hardware implementation of these kinds of algorithms is interesting research target. Especially, the particle swarm optimization has plural search points which are