Evolutionary algorithms (EAs) are well-known optimization approaches to deal with nonlinear and complex problems. However, these population-based algorithms are computationally expensive due to the slow nature of the evolutionary process. This paper presents a novel algorithm to accelerate the differential evolution (DE). The proposed opposition-based DE (ODE) employs opposition-based learning (OBL) for population initialization and also for generation jumping. In this work, opposite numbers have been utilized to improve the convergence rate of DE. A comprehensive set of 58 complex benchmark functions including a wide range of dimensions is employed for experimental verification. The influence of dimensionality, population size, jumping rate, and various mutation strategies are also investigated. Additionally, the contribution of opposite numbers is empirically verified. We also provide a comparison of ODE to fuzzy adaptive DE (FADE). Experimental results confirm that the ODE outperforms the original DE and FADE in terms of convergence speed and solution accuracy.

/pdf/opposition-based-differential-evolution-14k11phz34.pdf

Opposition-Based Differential Evolution

In this paper we are concerned with global optimization, which can be defined as the problem of finding points on a bounded subset of Rn in which some real valued functionf assumes its optimal (i.e. maximal or minimal) value. We present a stochastic approach which is based on the simulated annealing algorithm. The approach closely follows the formulation of the simulated annealing algorithm as originally given for discrete optimization problems. The mathematic formulation is extended to continuous optimization problems and we prove asymptotic convergence to the set of global optima. Furthermore, we discuss an implementation of the algorithm and compare its performance with other well known algorithms. The performance evaluation is carried out for a standard set of test functions from the literature. Keywords: global optimization, continuous variables, simulated annealing.

Global optimization and simulated annealing

Population initialization is a crucial task in evolutionary algorithms because it can affect the convergence speed and also the quality of the final solution. If no information about the solution is available, then random initialization is the most commonly used method to generate candidate solutions (initial population). This paper proposes a novel initialization approach which employs opposition-based learning to generate initial population. The conducted experiments over a comprehensive set of benchmark functions demonstrate that replacing the random initialization with the opposition-based population initialization can accelerate convergence speed.

A novel population initialization method for accelerating evolutionary algorithms

For many soft computing methods, we need to generate random numbers to use either as initial estimates or during the learning and search process. Recently, results for evolutionary algorithms, reinforcement learning and neural networks have been reported which indicate that the simultaneous consideration of randomness and opposition is more advantageous than pure randomness. This new scheme, called opposition-based learning, has the apparent effect of accelerating soft computing algorithms. This paper mathematically and also experimentally proves this advantage and, as an application, applies that to accelerate differential evolution (DE). By taking advantage of random numbers and their opposites, the optimization, search or learning process in many soft computing techniques can be accelerated when there is no a priori knowledge about the solution. The mathematical proofs and the results of conducted experiments confirm each other.

Opposition versus randomness in soft computing techniques

Computer simulation often is used to study complex physical and engineering processes. Although a computer simulator often can be viewed as an inexpensive way to gain insight into a system, it still can be computationally costly. Much of the recent work on the design and analysis of computer experiments has focused on scenarios where the goal is to fit a response surface or process optimization. In this article we develop a sequential methodology for estimating a contour from a complex computer code. The approach uses a stochastic process model as a surrogate for the computer simulator. The surrogate model and associated uncertainty are key components in a new criterion used to identify the computer trials aimed specifically at improving the contour estimate. The proposed approach is applied to exploration of a contour for a network queuing system. Issues related to practical implementation of the proposed approach also are addressed.

https://acadiau.ca/~pranjan/research/Ranjan_Bingham_Michailidis.pdf

J. Andre

Papers

An improvement of the standard genetic algorithm fighting premature convergence in continuous optimization