The sine-cosine algorithm (SCA) is a new population-based meta-heuristic algorithm. In addition to exploiting sine and cosine functions to perform local and global searches (hence the name sine-cosine), the SCA introduces several random and adaptive parameters to facilitate the search process. Although it shows promising results, the search process of the SCA is vulnerable to local minima maxima due to the adoption of a fixed switch probability and the bounded magnitude of the sine and cosine functions (from -1 to 1). In this paper, we propose a new hybrid Q-learning sine-cosine- based strategy, called the Q-learning sine-cosine algorithm (QLSCA). Within the QLSCA, we eliminate the switching probability. Instead, we rely on the Q-learning algorithm (based on the penalty and reward mechanism) to dynamically identify the best operation during runtime. Additionally, we integrate two new operations (Le´vy flight motion and crossover) into the QLSCA to facilitate jumping out of local minima maxima and enhance the solution diversity. To assess its performance, we adopt the QLSCA for the combinatorial test suite minimization problem. Experimental results reveal that the QLSCA is statistically superior with regard to test suite size reduction compared to recent state-of-the-art strategies, including the original SCA, the particle swarm test generator (PSTG), adaptive particle swarm optimization (APSO) and the cuckoo search strategy (CS) at the 95 confidence level. However, concerning the comparison with discrete particle swarm optimization (DPSO), there is no significant difference in performance at the 95 confidence level. On a positive note, the QLSCA statistically outperforms the DPSO in certain configurations at the 90 confidence level.
Despite the significant number of proposed algorithms in this field, the adoption of new meta-heuristic algorithms is most welcome. The no free lunch (NFL) theorem @cite_14 suggests that no single meta-heuristic algorithm can outperform others even when there is a slight change in the problem of ( @math ) configurations. Therefore, the NFL theorem allows researchers to propose new algorithms or modify current ones to enhance the current solution. In fact, the results could also be applied in other fields.
@cite_14
2151554678 1897981530 2122379760 8060374
A framework is developed to explore the connection between effective optimization algorithms and the problems they are solving. A number of "no free lunch" (NFL) theorems are presented which establish that for any algorithm, any elevated performance over one class of problems is offset by performance over another class. These theorems result in a geometric interpretation of what it means for an algorithm to be well suited to an optimization problem. Applications of the NFL theorems to information-theoretic aspects of optimization and benchmark measures of performance are also presented. Other issues addressed include time-varying optimization problems and a priori "head-to-head" minimax distinctions between optimization algorithms, distinctions that result despite the NFL theorems' enforcing of a type of uniformity over all algorithms. The No Free Lunch theorems are often used to argue that domain specific knowledge is required to design successful algorithms. We use algorithmic information theory to argue the case for a universal bias allowing an algorithm to succeed in all interesting problem domains. Additionally, we give a new algorithm for off-line classification, inspired by Solomonoff induction, with good performance on all structured problems under reasonable assumptions. This includes a proof of the efficacy of the well-known heuristic of randomly selecting training data in the hope of reducing misclassification rates. This paper introduces a new method for learning algorithm evaluation and selection, with empirical results based on classification. The empirical study has been conducted among 8 algorithms classifiers with 100 different classification problems. We evaluate the algorithms' performance in terms of a variety of accuracy and complexity measures. Consistent with the No Free Lunch theorem, we do not expect to identify the single algorithm that performs best on all datasets. Rather, we aim to determine the characteristics of datasets that lend themselves to superior modelling by certain learning algorithms. Our empirical results are used to generate rules, using the rule-based learning algorithm C5.0, to describe which types of algorithms are suited to solving which types of classification problems. Most of the rules are generated with a high confidence rating. We applied two state-of-the-art machine learning techniques to the problem of selecting a good heuristic in a first-order theorem prover. Our aim was to demonstrate that sufficient information is available from simple feature measurements of a conjecture and axioms to determine a good choice of heuristic, and that the choice process can be automatically learned. Selecting from a set of 5 heuristics, the learned results are better than any single heuristic. The same results are also comparable to the prover's own heuristic selection method, which has access to 82 heuristics including the 5 used by our method, and which required additional human expertise to guide its design. One version of our system is able to decline proof attempts. This achieves a significant reduction in total time required, while at the same time causing only a moderate reduction in the number of theorems proved. To our knowledge no earlier system has had this capability.