text: 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.
  @cite_42: Abstract This paper proposes a novel population-based optimization algorithm called Sine Cosine Algorithm (SCA) for solving optimization problems. The SCA creates multiple initial random candidate solutions and requires them to fluctuate outwards or towards the best solution using a mathematical model based on sine and cosine functions. Several random and adaptive variables also are integrated to this algorithm to emphasize exploration and exploitation of the search space in different milestones of optimization. The performance of SCA is benchmarked in three test phases. Firstly, a set of well-known test cases including unimodal, multi-modal, and composite functions are employed to test exploration, exploitation, local optima avoidance, and convergence of SCA. Secondly, several performance metrics (search history, trajectory, average fitness of solutions, and the best solution during optimization) are used to qualitatively observe and confirm the performance of SCA on shifted two-dimensional test functions. Finally, the cross-section of an aircraft's wing is optimized by SCA as a real challenging case study to verify and demonstrate the performance of this algorithm in practice. The results of test functions and performance metrics prove that the algorithm proposed is able to explore different regions of a search space, avoid local optima, converge towards the global optimum, and exploit promising regions of a search space during optimization effectively. The SCA algorithm obtains a smooth shape for the airfoil with a very low drag, which demonstrates that this algorithm can highly be effective in solving real problems with constrained and unknown search spaces. Note that the source codes of the SCA algorithm are publicly available at http: www.alimirjalili.com SCA.html .
summary: By building on and complementing the work mentioned above, our work explores the hybridization of the Q-learning algorithm with a recently developed meta-heuristic algorithm called the SCA @cite_42 . Unlike most meta-heuristic algorithms that mimic certain physical or natural phenomena, the equation transformation used in the SCA is solely based on the sine and cosine operations. Therefore, the learning curve of the SCA is low. Although its exploitation is commendable, the exploration of the SCA is strictly bounded due to the (adaptive) shrinking magnitude of the sine and cosine functions’ multipliers during the search process. To address the issues mentioned above, we propose a new algorithm, the QLSCA. Moreover, we augment the QLSCA with two further operations (Lévy flight motion and crossover) to counterbalance its exploration and exploitation. Then, we use the Q-learning algorithm (which is based on the penalty and reward mechanism) to dynamically identify on the best operation (sine, cosine, Lévy flight motion, or crossover) during runtime.