S-shaped and V-shaped gaining-sharing knowledge-based algorithm for feature selection

In machine learning, searching for the optimal feature subset from the original datasets is a very challenging and prominent task. The metaheuristic algorithms are used in finding out the relevant, important features, that enhance the classification accuracy and save the resource time. Most of the algorithms have shown excellent performance in solving feature selection problems. A recently developed metaheuristic algorithm, gaining-sharing knowledge-based optimization algorithm (GSK), is considered for finding out the optimal feature subset. GSK algorithm was proposed over continuous search space; therefore, a total of eight S-shaped and V-shaped transfer functions are employed to solve the problems into binary search space. Additionally, a population reduction scheme is also employed with the transfer functions to enhance the performance of proposed approaches. It explores the search space efficiently and deletes the worst solutions from the search space, due to the updation of population size in every iteration. The proposed approaches are tested over twenty-one benchmark datasets from UCI repository. The obtained results are compared with state-of-the-art metaheuristic algorithms including binary differential evolution algorithm, binary particle swarm optimization, binary bat algorithm, binary grey wolf optimizer, binary ant lion optimizer, binary dragonfly algorithm, binary salp swarm algorithm. Among eight transfer functions, V₄ transfer function with population reduction on binary GSK algorithm outperforms other optimizers in terms of accuracy, fitness values and the minimal number of features. To investigate the results statistically, two non-parametric statistical tests are conducted that concludes the superiority of the proposed approach.

     

Designing fuzzy logic controllers using a multiresolutional searchparadigm

A multiresolutional search paradigm is employed to design optimal fuzzy logic controllers in a variable structure simulation environment. The initial search space is evaluated with a coarse resolution and some of the subspaces are selected as candidate regions for global optimum. New optimization processes are then created to investigate the candidate search spaces in detail, a process which continues until a solution is found. This search paradigm was implemented using hierarchical distributed genetic algorithms (HDGAs)-search agents solving different degrees of abstracted problems. Creation/destruction of agents is executed dynamically during the operation based on their performance. In the application to fuzzy systems, the HDGA investigates design alternatives such as different types of membership functions and the number of the fuzzy labels, as well as their optimal parameter settings, all at the same time. This paradigm is demonstrated with an application to the design of a fuzzy controller for an inverted pendulum     

求解一类凸优化问题的区间迭代算法

研究了一类非线性带约束的凸优化问题的求解.利用Kuhn-Tucker条件将凸优化问题等价地转化为多变元非线性方程组的求解问题.基于区间算术的包含原理及改进的Krawczyk区间迭代算法,提出一个求解凸优化问题的区间算法.对于目标函数和约束函数可微的凸优化,所提算法具有全局寻优的特性.在数值实验方面,与遗传算法、模式搜索法、模拟退火法及数学软件内置的求解器进行了比较,结果表明所提算法就此类凸优化问题能找到较多且误差较小的全局最优点.     

Software prototype for solving multi-objective machining optimization problems: Application in non-conventional machining processes

For an effective and efficient application of machining processes it is often necessary to consider more than one machining performance characteristics for the selection of optimal machining parameters. This implies the need to formulate and solve multi-objective optimization problems. In recent years, there has been an increasing trend of using meta-heuristic algorithms for solving multi-objective machining optimization problems. Although having the ability to efficiently handle highly non-linear, multi-dimensional and multi-modal optimization problems, meta-heuristic algorithms are plagued by numerous limitations as a consequence of their stochastic nature. To overcome some of these limitations in the machining optimization domain, a software prototype for solving multi-objective machining optimization problems was developed. The core of the developed software prototype is an algorithm based on exhaustive iterative search which guarantees the optimality of a determined solution in a given discrete search space. This approach is justified by a continual increase in computing power and memory size in recent years. To analyze the developed software prototype applicability and performance, four case studies dealing with multi-objective optimization problems of non-conventional machining processes were considered. Case studies are selected to cover different formulations of multi-objective optimization problems: optimization of one objective function while all the other are converted into constraints, optimization of a utility function which combines all objective functions and determination of a set of Pareto optimal solutions. In each case study optimization solutions that had been determined by past researchers using meta-heuristic algorithms were improved by using the developed software prototype.     

求解非线性方程组的混合人口迁移算法

针对变尺度法对初始值敏感和人口迁移算法容易陷入局部极值的缺陷,结合变尺度法和人口迁移算法各自的优点,提出了一种混合人口迁移算法,用来求解非线性方程组。该混合算法不仅发挥了人口迁移算法强大的全局搜索能力,而且利用了变尺度法的局部精细搜索能力。实验结果表明,该算法不但以较高的精度求出了各种非线性方程组的解,而且鲁棒性强,收敛速度快速,是一种解决非线性方程组问题的较好方法。     

Simplifying dynamic programming via mode‐directed tabling

In the dynamic programming paradigm the value of an optimal solution is recursively defined in terms of optimal solutions to subproblems. Such dynamic programming definitions can be tricky and error‐prone to specify. This paper presents an elegant method based on tabled logic programming (TLP) that simplifies the specification of such dynamic programming solutions. Our method introduces a new mode declaration for tabled predicates. The arguments of each tabled predicate are divided into indexed and non‐indexed arguments so that tabled predicates can be regarded as functions: indexed arguments represent input values and non‐indexed arguments represent output values. The non‐indexed arguments in a tabled predicate can be further declared to be aggregated, for example, the minimum, so that while generating answers, the global table will dynamically maintain the smallest value for that argument. This mode‐declaration scheme, coupled with recursion, provides an easy‐to‐use method for dynamic programming: there is no need to define the value of an optimal solution recursively, as the definition of a general solution suffices. The optimal value as well as its corresponding concrete solution can be derived implicitly and automatically using tabled logic programming systems. Our experimental results show that mode declarations improve performance in solving dynamic programming problems on TLP systems. Copyright © 2007 John Wiley & Sons, Ltd.     

The fixed set search applied to the power dominating set problem

In this article, we focus on solving the power dominating set problem and its connected version. These problems are frequently used for finding optimal placements of phasor measurement units in power systems. We present an improved integer linear program (ILP) for both problems. In addition, a greedy constructive algorithm and a local search are developed. A greedy randomised adaptive search procedure (GRASP) algorithm is created to find near optimal solutions for large scale problem instances. The performance of the GRASP is further enhanced by extending it to the novel fixed set search (FSS) metaheuristic. Our computational results show that the proposed ILP has a significantly lower computational cost than existing ILPs for both versions of the problem. The proposed FSS algorithm manages to find all the optimal solutions that have been acquired using the ILP. In the last group of tests, it is shown that the FSS can significantly outperform the GRASP in both solution quality and computational cost.     

双层规划的改进混合布谷鸟搜索量子行为粒子群优化算法

为解决粒子群优化（PSO）算法求解双层规划问题时易陷入局部最优解的问题,提出了一种基于模拟退火（SA）Metropolis准则的改进混合布谷鸟搜索量子行为粒子群优化（ICSQPSO）算法。首先,该混合算法引入SA算法中的Metropolis准则,在求解过程中既能接受好解也能以一定的概率接受坏解,增强全局寻优能力;接着,为布谷鸟搜索算法设计一种改进动态步长Lévy飞行,以保持粒子群在优化过程中较高的多样性,保证搜索广度;最后,利用布谷鸟搜索算法中的偏好随机游走机制帮助粒子跳出局部最优解。通过对13个涵盖非线性规划、分式规划、多个下层规划的双层规划实例的数值实验,结果表明：ICSQPSO算法所得12个双层规划的目标函数最优值显著优于对比算法,只有1例的结果稍差,并且有半数实例的结果优于对比算法50%。由此可见,ICSQPSO算法对双层规划的寻优能力明显优于对比算法。     

An ecologically inspired direct search method for solving optimal control problems with Bézier parameterization

An optimal control problem can be formulated through a set of differential equations describing the trajectory of the control variables that minimize the cost functional (related to both state and control variables). Direct solution methods for optimal control problems treat them from the perspective of global optimization: i.e. perform a global search for the control function that optimizes the required objective. In this article we use a recently developed ecologically inspired optimization technique called Invasive Weed Optimization (IWO) for solving such optimal control problems. Usually the direct solution method operates on discrete n-dimensional vectors and not on continuous functions. Consequently it can become computationally expensive for large values of n. Thus, a parameterization technique is required to represent the control functions using a small number of real-valued parameters. Typically, direct methods based on evolutionary computing techniques parameterize control functions with a piecewise constant approximation. This has obvious limitations both for accuracy in representing arbitrary functions, and for optimization efficiency. In this paper a new parameterization is introduced using Bézier curves, which can accurately represent continuous control functions with only a few parameters. It is combined with IWO into a new evolutionary direct method for optimal control. The effectiveness of the new method is demonstrated by solving a wide variety of optimal control problems.     

Comparison of multi-objective optimization methodologies for engineering applications

Computational models describing the behavior of complex physical systems are often used in the engineering design field to identify better or optimal solutions with respect to previously defined performance criteria. Multi-objective optimization problems arise and the set of optimal compromise solutions (Pareto front) has to be identified by an effective and complete search procedure in order to let the decision maker, the designer, to carry out the best choice. Four multi-objective optimization techniques are analyzed by describing their formulation, advantages and disadvantages. The effectiveness of the selected techniques for engineering design purposes is verified by comparing the results obtained by solving a few benchmarks and a real structural engineering problem concerning an engine bracket of a car.     

Riccati 方程的方块脉冲函数近似解法

已知线性系统最优控制规律的选择以及最优滤波器的设计均要求解Riccati方程。本文应用方块脉冲函数的性质到解该微分方程,得到了分段恒定解答的递推算法。特别是证明了算法的收敛性和数值稳定性。     

An improved Opposition-Based Sine Cosine Algorithm for global optimization

Real life optimization problems require techniques that properly explore the search spaces to obtain the best solutions. In this sense, it is common that traditional optimization algorithms fail in local optimal values. The Sine Cosine Algorithms (SCA) has been recently proposed; it is a global optimization approach based on two trigonometric functions. SCA uses the sine and cosine functions to modify a set of candidate solutions; such operators create a balance between exploration and exploitation of the search space. However, like other similar approaches, SCA tends to be stuck into sub-optimal regions that it is reflected in the computational effort required to find the best values. This situation occurs due that the operators used for exploration do not work well to analyze the search space. This paper presents an improved version of SCA that considers the opposition based learning (OBL) as a mechanism for a better exploration of the search space generating more accurate solutions. OBL is a machine learning strategy commonly used to increase the performance of metaheuristic algorithms. OBL considers the opposite position of a solution in the search space. Based on the objective function value, the OBL selects the best element between the original solution and its opposite position; this task increases the accuracy of the optimization process. The hybridization of concepts from different fields is crucial in intelligent and expert systems; it helps to combine the advantages of algorithms to generate more efficient approaches. The proposed method is an example of this combination; it has been tested over several benchmark functions and engineering problems. Such results support the efficacy of the proposed approach to find the optimal solutions in complex search spaces.     

Memetic algorithm with Preferential Local Search using adaptive weights for multi-objective optimization problems

Evolutionary multi-objective optimization algorithms are generally employed to generate Pareto optimal solutions by exploring the search space. To enhance the performance, exploration by global search can be complemented with exploitation by combining it with local search. In this paper, we address the issues in integrating local search with global search such as: how to select individuals for local search; how deep the local search is performed; how to combine multiple objectives into single objective for local search. We introduce a Preferential Local Search mechanism to fine tune the global optimal solutions further and an adaptive weight mechanism for combining multi-objectives together. These ideas have been integrated into NSGA-II to arrive at a new memetic algorithm for solving multi-objective optimization problems. The proposed algorithm has been applied on a set of constrained and unconstrained multi-objective benchmark test suite. The performance was analyzed by computing different metrics such as Generational distance, Spread, Max spread, and HyperVolume Ratio for the test suite functions. Statistical test applied on the results obtained suggests that the proposed algorithm outperforms the state-of-art multi-objective algorithms like NSGA-II and SPEA2. To study the performance of our algorithm on a real-world application, Economic Emission Load Dispatch was also taken up for validation. The performance was studied with the help of measures such as Hypervolume and Set Coverage Metrics. Experimental results substantiate that our algorithm has the capability to solve real-world problems like Economic Emission Load Dispatch and is able to produce better solutions, when compared with NSGA-II, SPEA2, and traditional memetic algorithms with fixed local search steps.     

A new effective operator for the hybrid algorithm for solving global optimisation problems

Hybrid algorithms have been recently used to solve complex single-objective optimisation problems. The ultimate goal is to find an optimised global solution by using these algorithms. Based on the existing algorithms (HP_CRO, PSO, RCCRO), this study proposes a new hybrid algorithm called MPC (Mean-PSO-CRO), which utilises a new Mean-Search Operator. By employing this new operator, the proposed algorithm improves the search ability on areas of the solution space that the other operators of previous algorithms do not explore. Specifically, the Mean-Search Operator helps find the better solutions in comparison with other algorithms. Moreover, the authors have proposed two parameters for balancing local and global search and between various types of local search, as well. In addition, three versions of this operator, which use different constraints, are introduced. The experimental results on 23 benchmark functions, which are used in previous works, show that our framework can find better optimal or close-to-optimal solutions with faster convergence speed for most of the benchmark functions, especially the high-dimensional functions. Thus, the proposed algorithm is more effective in solving single-objective optimisation problems than the other existing algorithms.     

A robust ant colony optimization for continuous functions

Ant colony optimization (ACO) for continuous functions has been widely applied in recent years in different areas of expert and intelligent systems, such as steganography in medical systems, modelling signal strength distribution in communication systems, and water resources management systems. For these problems that have been addressed previously, the optimal solutions were known a priori and contained in the pre-specified initial domains. However, for practical problems in expert and intelligent systems, the optimal solutions are often not known beforehand. In this paper, we propose a robust ant colony optimization for continuous functions (RACO), which is robust to domains of variables. RACO applies self-adaptive approaches in terms of domain adjustment, pheromone increment, domain division, and ant size without any major conceptual change to ACO's framework. These new characteristics make the search of ants not limited to the given initial domain, but extended to a completely different domain. In the case of initial domains without the optimal solution, RACO can still obtain the correct result no matter how the initial domains vary. In the case of initial domains with the optimal solution, we also show that RACO is a competitive algorithm. With the assistance of RACO, there is no need to estimate proper initial domains for practical continuous optimization problems in expert and intelligent systems.     

方块脉冲函数用于非线性系统的分析以及最优控制的综合

本文用方块脉冲函数方法讨论了解非线性微分方程系统的收敛性和稳定性.在分析和综 合非线性系统最优控制规律中,得到了分段恒定解答的递推算法,算法证明简单,除对基于二 次型性能指标的线性时变系统有效外,也可用于求解线性最优控制系统的Riccati方程.     

Dynamic Gaussian bare-bones fruit fly optimizers with abandonment mechanism: method and analysis

The Fruit Fly Optimization Algorithm (FOA) is a recent algorithm inspired by the foraging behavior of fruit fly populations. However, the original FOA easily falls into the local optimum in the process of solving practical problems, and has a high probability of escaping from the optimal solution. In order to improve the global search capability and the quality of solutions, a dynamic step length mechanism, abandonment mechanism and Gaussian bare-bones mechanism are introduced into FOA, termed as BareFOA. Firstly, the random and ambiguous behavior of fruit flies during the olfactory phase is described using the abandonment mechanism. The search range of fruit fly populations is automatically adjusted using an update strategy with dynamic step length. As a result, the convergence speed and convergence accuracy of FOA have been greatly improved. Secondly, the Gaussian bare-bones mechanism that overcomes local optimal constraints is introduced, which greatly improves the global search capability of the FOA. Finally, 30 benchmark functions for CEC2017 and seven engineering optimization problems are experimented with and compared to the best-known solutions reported in the literature. The computational results show that the BareFOA not only significantly achieved the superior results on the benchmark problems than other competitive counterparts, but also can offer better results on the engineering optimization design problems.

     

Real-Time Search for Autonomous Agents and Multiagent Systems

Since real-time search provides an attractive framework for resource-bounded problem solving, this paper extends the framework for autonomous agents and for a multiagent world. To adaptively control search processes, we propose -search which allows suboptimal solutions with error, and -search which balances the tradeoff between exploration and exploitation. We then consider search in uncertain situations, where the goal may change during the course of the search, and propose a moving target search (MTS) algorithm. We also investigate real-time bidirectional search (RTBS) algorithms, where two problem solvers cooperatively achieve a shared goal. Finally, we introduce a new problem solving paradigm, called organizational problem solving, for multiagent systems.     

An Immune-based Genetic Algorithm with Reduced Search Space Coding for Multiprocessor Task Scheduling Problem

Multiprocessor task scheduling is an important problem in parallel applications and distributed systems. In this way, solving the multiprocessor task scheduling problem (MTSP) by heuristic, meta-heuristic, and hybrid algorithms have been proposed in literature. Although the problem has been addressed by many researchers, challenges to improve the convergence speed and the reliability of methods for solving the problem are still continued especially in the case that the communication cost is added to the problem frame work. In this paper, an Immune-based Genetic algorithm (IGA), a meta-heuristic approach, with a new coding scheme is proposed to solve MTSP. It is shown that the proposed coding reduces the search space of MTSP in many practical problems, which effectively influences the convergence speed of the optimization process. In addition to the reduced search space offered by the proposed coding that eventuate in exploring better solutions at a shorter time frame, it guarantees the validity of solutions by using any crossover and mutation operators. Furthermore, to overcome the regeneration phenomena in the proposed GA (generating similar chromosomes) which leads to premature convergence, an affinity based approach inspired from Artificial Immune system is employed which results in better exploration in the searching process. Experimental results showed that the proposed IGA surpasses related works in terms of found makespan (20% improvement in average) while it needs less iterations to find the solutions (90% improvement in average) when it is applied to standard test benches.     

Dynamic optimal control policy in advertising price and quality

This study presents an algorithm for deriving the long-term polices of quality level, price and advertisement for a product. The diffusion models and cost functions are combined to formulate profit functions capable of determining future profit trends. The algorithm first implements the optimal control theory to derive the optimal conditions of the profit function. Then the genetic algorithm is employed to search for the approximate solutions of quality level, price and advertising expenditure at each period on the planning horizon (life cycle). Examples of different scenarios of the model parameters are presented to describe the results obtained herein. Sensitivity analysis for the major parameters is performed to specify their effects on profits. Results in this study allow us, firstly, to obtain explicit solutions simultaneously with respect to quality, price and advertising policies, secondly, to propose an appropriate algorithm for solving the different scenarios of the dynamic profit function, which consists of the diffusion function and cost function, and thirdly, to enhance the long-term profit performance via the polices proposed herein, that is the approximation of the best solution.