# A Modified Cloud Particles Differential Evolution Algorithm for Real-Parameter Optimization
## 1 Introduction  
Recently, many real-world problems which belong to optimization problems are very complex and are quite difficult to solve. Traditional optimization methods are weak in some problems which are multi-modal, high dimension, discontinuous, multi-objective, and dynamic, etc. Nature-inspired meta-heuristic algorithms which can be called artificial evolution (AE) [1] are becoming more and more popular in engineering applications by building feasible solutions. These evolutionary algorithms (EAs) which are known to be capable of finding the near-optimum solution to the real-parameter optimization problems, have been successfully applied to many optimization problems, such as optimization, scheduling, economic problems, neural network training, data clustering, large-scale, constrained, forecasting and multi-objective [2; 3; 4; 5; 6; 7; 8; 9]. The meta-heuristic algorithms can be grouped in three main categories [10]: evolution-based, physics-based, and swarm intelligence-based methods. The evolutionary algorithms which are based on evolutionary process include Genetic Algorithm (GA) [11], Genetic Programming (GP) [12], Differential Evolution (DE) [13], Derandomized Evolution Strategy with Covariance Matrix Adaptation (CMA-ES) [14], and Biogeography-Based Optimizer (BBO) [15], et al. DE is a classical global optimization algorithm which is proposed by [PERSON] and [PERSON]. CMA-ES, proposed by [PERSON] and [PERSON], adapts the complete covariance matrix of the normal mutation distribution to solve optimization problems. Some other methods which are based on physical processes include the Simulated Annealing (SA) [16; 17], Brain Storm Optimization (BSO) [18], Chemical Reaction Optimization (CRO) [19], etc. SA is a heuristic algorithm which is based on an analog of thermodynamics that describes the way metals cool and anneal [20]. BSO mimics the brainstorming process in which a group of peoplesolves a problem together [21]. CRO is a chemical-reaction-inspired metaheuristic algorithm which mimics the characteristics of chemical reactions in solving optimization problems [19]. Moreover, there are some swarm intelligent methods based on animal-behavior phenomena such as Artificial Bee Colony (ABC) [22], Teaching-Learning-Based Optimization (TLBO) [23; 24] et al. ABC, proposed by [PERSON], simulates the foraging behavior of the honeybee swarm and has been applied to solve many engineering optimization problems [25; 26]. The TLBO method, proposed by [PERSON], is based on the effect of the influence of a teacher on the output of learners in a class [23]. The Cloud Particles Differential Evolution (CPDE) algorithm [27], which is inspired by the cloud formation and state change, is a population-based algorithm. CPDE employs phase transformation mechanism to promote the superior cloud particle to lead the swarm through the evolution. The evolutionary process is divided into three stages in CPDE. They are gaseous, liquid and solid, respectively. The cloud particles explore the searching area by condensation operation in a gaseous state. In a liquid state, the liquefaction operation is carried out to realize macro-local exploitation. In a solid state, solidification operation is carried out to realize micro-local exploitation. CPDE has been shown to perform well on many optimization problems. However, it should be noted that the new cloud particles are generated by the superior cloud particles, and then CPDE may easily trap in a local optima when solving complex problems containing multiple local optimal solutions, such as CEC2013 benchmark functions. This paper proposes a modified cloud particles differential evolution algorithm (MCPDE). Firstly, control parameters adaptation strategies are designed by tuning the movement step and crossover factor used at different evolutionary stages. Secondly, the inertia factor is introduced to effectively balance exploration and exploitation.