Algorithms are important tools for solving problems computationally. All computation involves algorithms, and the efficiency of an algorithm largely determines its usefulness. This chapter provides an overview of the fundamentals of algorithms and their links to self-organization, exploration, and exploitation. A brief history of recent nature-inspired algorithms for optimization is outlined in this chapter.

Introduction to Algorithms

物件導向軟體之架構(Object-Oriented Software Construction)探討

Differential evolution (DE) is arguably one of the most powerful stochastic real-parameter optimization algorithms in current use. DE operates through similar computational steps as employed by a standard evolutionary algorithm (EA). However, unlike traditional EAs, the DE-variants perturb the current-generation population members with the scaled differences of randomly selected and distinct population members. Therefore, no separate probability distribution has to be used for generating the offspring. Since its inception in 1995, DE has drawn the attention of many researchers all over the world resulting in a lot of variants of the basic algorithm with improved performance. This paper presents a detailed review of the basic concepts of DE and a survey of its major variants, its application to multiobjective, constrained, large scale, and uncertain optimization problems, and the theoretical studies conducted on DE so far. Also, it provides an overview of the significant engineering applications that have benefited from the powerful nature of DE.

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Differential Evolution: A Survey of the State-of-the-Art

Differential evolution (DE) is an efficient and powerful population-based stochastic search technique for solving optimization problems over continuous space, which has been widely applied in many scientific and engineering fields. However, the success of DE in solving a specific problem crucially depends on appropriately choosing trial vector generation strategies and their associated control parameter values. Employing a trial-and-error scheme to search for the most suitable strategy and its associated parameter settings requires high computational costs. Moreover, at different stages of evolution, different strategies coupled with different parameter settings may be required in order to achieve the best performance. In this paper, we propose a self-adaptive DE (SaDE) algorithm, in which both trial vector generation strategies and their associated control parameter values are gradually self-adapted by learning from their previous experiences in generating promising solutions. Consequently, a more suitable generation strategy along with its parameter settings can be determined adaptively to match different phases of the search process/evolution. The performance of the SaDE algorithm is extensively evaluated (using codes available from P. N. Suganthan) on a suite of 26 bound-constrained numerical optimization problems and compares favorably with the conventional DE and several state-of-the-art parameter adaptive DE variants.

Differential Evolution Algorithm With Strategy Adaptation for Global Numerical Optimization

Aspect] is a simple and practical aspect-oriented extension to Java With just a few new constructs, AspectJ provides support for modular implementation of a range of crosscutting concerns. In AspectJ's dynamic join point model, join points are well-defined points in the execution of the program; pointcuts are collections of join points; advice are special method-like constructs that can be attached to pointcuts; and aspects are modular units of crosscutting implementation, comprising pointcuts, advice, and ordinary Java member declarations. AspectJ code is compiled into standard Java bytecode. Simple extensions to existing Java development environments make it possible to browse the crosscutting structure of aspects in the same kind of way as one browses the inheritance structure of classes. Several examples show that AspectJ is powerful, and that programs written using it are easy to understand.

An overview of AspectJ

We describe an efficient technique for adapting control parameter settings associated with differential evolution (DE). The DE algorithm has been used in many practical cases and has demonstrated good convergence properties. It has only a few control parameters, which are kept fixed throughout the entire evolutionary process. However, it is not an easy task to properly set control parameters in DE. We present an algorithm-a new version of the DE algorithm-for obtaining self-adaptive control parameter settings that show good performance on numerical benchmark problems. The results show that our algorithm with self-adaptive control parameter settings is better than, or at least comparable to, the standard DE algorithm and evolutionary algorithms from literature when considering the quality of the solutions obtained

Self-Adapting Control Parameters in Differential Evolution: A Comparative Study on Numerical Benchmark Problems

The firefly algorithm has become an increasingly important tool of Swarm Intelligence that has been applied in almost all areas of optimization, as well as engineering practice. Many problems from various areas have been successfully solved using the firefly algorithm and its variants. In order to use the algorithm to solve diverse problems, the original firefly algorithm needs to be modified or hybridized. This paper carries out a comprehensive review of this living and evolving discipline of Swarm Intelligence, in order to show that the firefly algorithm could be applied to every problem arising in practice. On the other hand, it encourages new researchers and algorithm developers to use this simple and yet very efficient algorithm for problem solving. It often guarantees that the obtained results will meet the expectations.

A comprehensive review of firefly algorithms

Swarm intelligence and bio-inspired algorithms form a hot topic in the developments of new algorithms inspired by nature. These nature-inspired metaheuristic algorithms can be based on swarm intelligence, biological systems, physical and chemical systems. Therefore, these algorithms can be called swarm-intelligence-based, bio-inspired, physics-based and chemistry-based, depending on the sources of inspiration. Though not all of them are efficient, a few algorithms have proved to be very effi cient and thus have become popular tools for solving real-world problems. Some algorithms are insuffici ently studied. The purpose of this review is to present a relatively comprehensive list of all the algorithms in the literature, so as to inspire further research.

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A Brief Review of Nature-Inspired Algorithms for Optimization

This paper studies the efficiency of a recently defined population-based direct global optimization method called Differential Evolution with self-adaptive control parameters The original version uses fixed population size but a method for gradually reducing population size is proposed in this paper It improves the efficiency and robustness of the algorithm and can be applied to any variant of a Differential Evolution algorithm The proposed modification is tested on commonly used benchmark problems for unconstrained optimization and compared with other optimization methods such as Evolutionary Algorithms and Evolution Strategies

Population size reduction for the differential evolution algorithm

Solving single objective real-parameter optimization problems, also known as a bound-constrained optimization, is still a challenging task. We can find such problems in engineering optimization, scientific applications, and in other real-world problems. Usually, these problems are very complex and computationally expensive. A new algorithm, called jSO, is presented in this paper. The algorithm is an improved variant of the iL-SHADE algorithm, mainly with a new weighted version of mutation strategy. The experiments were performed on CEC 2017 benchmark functions, which are different from previous competition benchmark functions. A comparison of the proposed jSO algorithm and the L-SHADE algorithm is presented first. From the obtained results we can conclude that jSO performs better in comparison with the L-SHADE algorithm. Next, a comparison of jSO and iL-SHADE is also performed, and jSO obtained better or competitive results. Using the CEC 2017 evaluation method, jSO obtained the best final score among these three algorithms.

Janez Brest

Papers

Self-Adapting Control Parameters in Differential Evolution: A Comparative Study on Numerical Benchmark Problems

A comprehensive review of firefly algorithms

A Brief Review of Nature-Inspired Algorithms for Optimization

Population size reduction for the differential evolution algorithm

Single objective real-parameter optimization: Algorithm jSO