Mutation in differential evolution (DE) is of considerable importance for the performance of the algorithm. It directly impacts exploration and exploitation. Thus, it represents the driving force for ...discovering unvisited regions of the search space, whilst also enabling the utilisation of promising points in that space. Since mutation performs search around the base vector, its selection plays a prominent role in directing it. In that regard, a low selection pressure contributes to exploration, whereas a high selection pressure contributes to exploitation. However, a balance between the two is paramount for high and consistent performance. This paper proposes a novel mutation scheme that employs k-tournament selection for choosing the base vector. Each population member is associated with a tournament size that is adapted during the search process with the aim of controlling exploration and exploitation. The mechanism mixes adaptation on an individual and population level. Results of the experimental analysis conducted on a wide range of numerical benchmark problem instances affirm its competitive performance and the benefits of the adaptation of tournament sizes, suggesting it to be a viable measure for increasing DE algorithm performance. Finally, the automatic design of radial basis function networks for classification was tackled. The proposed mutation scheme proved to be effective when dealing with that task as the canonical algorithm incorporating it yielded better fit models than competing approaches.
•A novel mutation scheme for differential evolution is proposed.•The mutation scheme is based on adaptive k-tournaments.•Tournament sizes are adapted on a population and member level.•Results suggest competitive performance and benefits of the adaptation mechanism.•Results on the problem of automatic RBFN design for classification affirm its utility.
•Presenting a GMB algorithm to conceal secret bits in n pixels with least distortion.•GMB offers greater flexibility providing large payloads or high image quality.•Introducing four binary conversion ...schemes to carry an extra bit for concealment.•Deriving mathematical expressions to predict expected payloads and image quality.•GMB scheme outperforms ten current state-of-the-art competitors.
This paper presents a general multiple-base (GMB) data embedding algorithm to conceal a serial secret bit stream equivalent to an M-ary secret digit in a pixel-cluster consisting of n pixels, where M is automatically determined by the initial input (n, F) given by the end user. Through the change of two parameters, n and M, the proposed algorithm offers a multiple-purpose message embedding style to produce a high quality embedded image or provide a large embedding payload. Inspired by a single base (SB) data embedding approach, this study first introduces a multiple-base (MB) scheme which adopts an n-tuple optimal base vector (OBV) to conceal a secret M-ary digit with minimal pixel distortion, where M is the product of all vector components in the OBV. This study extends the MB scheme to develop the GMB algorithm, which supports a serial secret bit stream as a secret message. Four binary to M-ary conversion schemes are introduced, allowing the GMB algorithm to carry an extra secret bit per pixel-cluster, offering a larger payload without increasing the pixel distortion caused by data embedding. The proposed algorithm is analyzed, and mathematical expressions are derived so that prior to a real message embedding, it is possible to predict the expected payloads and the corresponding image quality. Finally, we extend the GMB algorithm to support content-adaptive data embedding. To the best of the authors' knowledge, the proposed algorithm is the first multiple-purpose data embedding technique, providing greater flexibility and offering large payloads or high image quality. Experimental results demonstrate that the proposed scheme outperforms current state-of-the-art competitors.
In order to avoid the problem of local optimality and low convergence accuracy, an improved differential evolution algorithm was proposed by combining the base vector scaling with the mirror ...crossover operation. Based on the basic difference algorithm, the base vector scaling coefficient is introduced to jump out of the local optimal value. In the process of crossover, mirror crossover is introduced to improve the probability of the better trial vector entering the selection step and promote the algorithm evolution. In order to verify the effectiveness of the improved differential evolution algorithm, the simulation results of 10 benchmark functions are compared with those of other algorithms in this paper. The results show that the proposed algorithm can avoid the algorithm from falling into local optimum and achieve better convergence performance.
In this paper we show how approximate matrix factorisations can be used to organise document summaries returned by a search engine into meaningful thematic categories. We compare four different ...factorisations (SVD, NMF, LNMF and K-Means/Concept Decomposition) with respect to topic separation capability, outlier detection and label quality. We also compare our approach with two other clustering algorithms: Suffix Tree Clustering (STC) and Tolerance Rough Set Clustering (TRC). For our experiments we use the standard merge-then-cluster approach based on the Open Directory Project web catalogue as a source of human-clustered document summaries.
Differential evolution algorithm with base vector group is proposed. In this new algorithm, all individuals are ordered according to their fitness from high to low. Then a certain number of ...individuals in front will be chosen to form a base vector group. For each target vector, its mutation base vector is chosen from the base vector group when mutation is operated. With the introduction of base vector group, the control effect of the best individual for DE algorithms with best mutation base can be reduced and their reliability will be increased. For DE with random mutation base, their efficiency will be increased. Five standard test functions are used to prove the new algorithm. The results obtained show that a good balance of between reliability and efficiency can be achieved and the new algorithm is feasible and effective.
The method of least squares support vector machine has been improved based on base vector space theory, which solved the problem of weak handling ability of nonlinear, sparsity and variable multiple ...correlation in the fault diagnosis process for LSSVM. This article proposed a double sections fault diagnosis algorithm combined PLS with LSSVMBVS, it first builds regression analysis model, then puts the detected fault data in the trained LSSVMBVS classifier, diagnosing troubles. It verified the algorithm has better prediction accuracy and generalization performance by the TE platform.
One of the keys leading to the success of differential evolution is its mechanism of differential mutation for generating mutant vectors. In the community of differential evolution, the mutation ...operator is usually marked as x/y where x indicates how the base vector is chosen and y (ges1) is the number of vector differences added to the base vector. It is noted that rand/1 has been the most widely used mutation operator. However, a comprehensive comparative parametric study on differential evolution shows that strategies applying random base vector are neither efficient nor robust.
We propose Simple Sampling Reduction (SSR) that makes Schnorr’s Random Sampling Reduction (RSR) practical. We also introduce generalizations of SSR that yield bases with several short basis vectors ...and that, in combination, generate shorter basis vectors than SSR alone. Furthermore, we give a formula for Pr||v||2 ≤x provided v is randomly sampled from SSR’s search space. We describe two algorithms that estimate the probability that a further SSR iteration will find an even shorter vector, one algorithm based on our formula for Pr||v||2 ≤x, the other based on the approach of Schnorr’s RSR analysis. Finally, we report on some cryptographic applications.
Differential evolution (DE) is an evolutionary algorithm designed for global numerical optimization. This chapter presents a new, rotationally invariant DE algorithm that eliminates drift bias from ...its trial vector generating function by projecting randomly chosen vector differences along lines of recombination. In this way, the natural distribution of vector differences drives both mutation and recombination. The new method also eliminates drift bias from survivor selection, leaving recombination as the only migration pathway. A suite of scalable test functions benchmarks the performance of drift-free DE against that of the algorithm from which it was derived.
PDF
