الگوریتم تکامل تفاضلی (DE) برای بهینه سازی روند خشک کردن مخمر نانوایی
Abstract
1- Introduction
2- Differential evolution algorithm
3- Chaotic systems
4- Chaotic based differential evolution algorithm
5- Benchmark functions
6- Optimization of baker's yeast drying process
7- Results and discussion
8- Conclusion
References
Abstract
Chaotic based Differential Evolution (CDE) algorithm is presented to determine the optimal control variables for the optimization of Baker's Yeast drying process. The chaotic system is proposed to determine the initial population, to select the trial individuals from the population in the mutation operation instead of the random number generator. The random values produced by the random number generator are likely to be similar or same values with each other. In this study, four different chaotic systems, such as Lorenz attractor, Rössler attractor, Chua circuit and Mackey-Glass equation, are solved by Runge-Kutta method to produce the random values of the initial individuals. To demonstrate the performance of the CDE algorithms, ten optimization problems are taken from the literature. Furthermore, the performances of the proposed CDE algorithms are compared with the classic Differential Evolution (DE) algorithm, Particle Swarm Optimization (PSO) algorithm, Artificial Bee Colony (ABC) algorithm, Simulated Annealing (SA) algorithm, Touring Ant Colony Optimization (TACO) algorithm in terms of the mean best solution, the number of function evaluations (NFE) and CPU-time metrics. At the same time, the proposed CDE algorithms are implemented for numerical optimization problems based on the IEEE Congress on Evolutionary Computation (CEC) 2014 test suite. For the optimization of baker's yeast drying process, there are four significant parameters, such as product quality, drying total time, energy cost of air and the final moisture content. The proposed CDE algorithms and classic DE algorithm are applied for the same optimization problem that is taken from a baker's yeast producer in Turkey. The experimental results prove that the proposed CDE algorithms are able to provide very competitive results.
Introduction
Differential Evolution (DE) algorithm is a powerful heuristic method for global optimization problems, was introduced by Storn and Price [31,32,37]. This population based heuristic optimization algorithm has drawn the interest of researchers in many scientific fields. The DE algorithm has happened to more popular step by step and it has been used in a lot of useful cases due to ease and the good convergence in the optimization problems [4]. The principle of DE algorithm is basically based on adding the difference between two individuals to a third individual in population. It differs from other heuristic algorithms in the mutation, crossover and selection stages. Unlike the procedures based on random number generator in evolutionary algorithms such as genetic algorithms, DE algorithm uses the differences between individuals in the population to form the next generation [10]. Furthermore, DE algorithm has got few control parameters, such as scaling factor, crossover probability constant and population size, which are used during the optimization process like the other evolutionary algorithms. These control parameters have to be determined carefully to increase the solution quality and the algorithm efficiency. The robustness and effectiveness of DE algorithm are based on the suitable settings of the control parameters [44]. In addition to these parameters, the other important thing is determining the initial population by random number generator. In DE algorithm, the individuals’ initial values in the population which are produced by the random number generator are likely to be similar or same values with each other. This is an undesirable situation because of reducing the diversity in the population. In this paper, the new methods based on the chaotic functions were proposed instead of the classic random procedure. Chaos functions have got applications, such as observing the weather in meteorology area [38], cryptography in computer science area [43], predicting gas solubility in chemical engineering [39], finance modeling in economics area [14] and hydrology in biology area [40]. Chaotic functions have the behavior of dynamic systems which are highly sensitive to initial conditions. Each point in a chaotic system is arbitrarily close to other points with different future trajectories. As a result, an small change in the existing trajectory can lead to considerably different behavior.