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This study introduces an improved three-term conjugate gradient (CG) algorithm which fulfills the descent conditions and exhibits good global convergence properties. The development of this new algorithm is based on the findings of recently introduced generalized RMIL CG technique. The algorithm has been modified so that the search direction would always meet the sufficient descent condition no matter the line-search techniques employed. Under some given assumptions, the algorithm’s global convergence result for the general nonconvex functions is established. The numerical efficacy of the suggested three-term CG algorithm is assessed through comparisons with four other CG algorithms. The assessment is performed using an array of unconstrained optimization benchmark functions. The acquired findings indicate that all the considered algorithms exhibit similar performance, particularly the variants of the RMIL method. One algorithm is more robust and slightly faster than the rest. However, it is essential to highlight that the newly developed CG formula outperforms all the other algorithms, including a recently presented three-term PRP algorithm. The study further expanded the proposed method to address an image restoration problem. The computational experiments yielded promising results, proving that the proposed CG algorithm surpasses others. It produces higher-quality output images, requires less CPU time (sec), and achieves higher PSNR values.

A sequence of analytical solutions explore the spectrum of response patterns expected from numerical codes for flood and tide propagation in channels. Complete analytical details of the solutions are provided, together with specific suggestions for an associated set of analytical benchmark tests. Illustrations of predicted response patterns provide the basis for a discussion of many significant physical aspects and their representation in discrete numerical codes.

Differential evolution (DE), an evolutionary optimization technique is receiving greater attention due to its simplicity and ability to handle nonlinear and non-differentiable functions. Recently, we proposed differential evolution with tabu list (DETL) by incorporating the concept of tabu search (TS) (i.e., avoiding re-visits during the search) using tabu list in the generation step of DE (Srinivas and Rangaiah, 2007b). In this chapter^†, implementing tabu list in the evaluation step of DEis studied. These two versions: DETL-G and DETL-E are then evaluated for several benchmark problems and challenging phase stability problems. Benchmark problems consist of 2 to 20 variables and a few to hundreds of local minima whereas phase stability problems involve multiple components and comparable minima. A new benchmark problem with similar characteristics as in phase stability problems is also proposed and used. The results show that the performance of the two versions of DETL is comparable; both of them are better than DE in terms of function evaluations and better than TS in terms of reliability.