Hybrid Whale Optimization Algorithm Based on Three Spiral Searching Strategies and Sine Cosine Operator with Convergence Factor

Whale Optimization Algorithm (WOA) is a swarm intelligence algorithm inspired by whale hunting behavior. Aiming at the defect that the spiral update mechanism in WOA may exceed the search range, three different spiral searching strategies are first proposed. The agents search with a more reasonable and broader route distribution so as to improve population diversity and traversal. Secondly, an improved sine cosine operator based on the convergence factor was proposed to improve the search efficiency of WOA, where sine search is used for global exploration and cosine search is used for local exploitation. The proposed convergence factor enables search agents to adaptively balance the exploration and exploitation phases with iterations. In the simulation experiment, the effectiveness of three spiral search strategies and sine cosine operator is verified. Then, the whale optimization algorithm (WOA), salp swarm algorithm (SSA), firefly algorithm (FA), moth-flame optimization (MFO) algorithm, fireworks algorithm (FWA), sine cosine algorithm (SCA) and improved WOA are selected for comparison experiments. Finally, the improved WOA is applied to two engineering problems (three-bar truss design problem and the welded beam optimization problem). The experimental results show that compared with other optimization algorithms, the improved WOA has the advantages of high search accuracy, fast convergence speed, and avoiding falling into local optimal values.

On the quasi-Fredholm and Saphar spectrum of strongly continuous Cosine operator function

Let (C(t))t∈𝕉 be a strongly continuous cosine family and A be its infinitesimal generator. In this work, we prove that, if C(t) – coshλt is Saphar (resp. quasi-Fredholm) operator and λt /∉iπ𝕑, then A – λ2 is also Saphar (resp. quasi-Fredholm) operator. We show by counter-example that the converse is false in general.

On a cosine operator function framework of approximation processes in Banach space

We introduce the cosine-type approximation processes in abstract Banach space setting. The historical roots of these processes go back to W. W. Rogosinski in 1926. The given new definitions use a cosine operator functions concept. We proved that in presented setting the cosine-type operators possess the order of approximation, which coincide with results known in trigonometric approximation. Moreover, a general method for factorization of certain linear combinations of cosine operator functions is presented. The given method allows to find the order of approximation using the higher order modulus of continuity. Also applications for the different type of approximations are given.

Disjoint topological transitivity for cosine operator functions on groups

In this paper, we study finite sequences of operators, generated by the powers of weighted translations on discrete groups, and give sufficient conditions for such sequences to be disjoint topologically transitive and mixing in terms of the group elements and weights. The sequences of operators are cosine operator functions. Moreover, we also obtain necessary conditions for cosine operator functions to be disjoint transitive and mixing.

Recurrence of Cosine Operator Functions on Groups

In this note, we study the recurrence and topologically multiple recurrence of a sequence of operators on Banach spaces. In particular, we give a sufficient and necessary condition for a cosine operator function, induced by a sequence of operators on the Lebesgue space of a locally compact group, to be topologically multiply recurrent.