As many real-life optimization problems are difficult to solve by exact optimization methods, a number of metaheuristics are developed over the years to search for viable solutions, e.g., river formation dynamics (RFD) algorithm. RFD algorithm is based on the analogy that water drops traverse from source to destination by following a random probabilistic search strategy. This search strategy is employed to solve various optimization problems in practice. However, the search strategy of RFD algorithm lacks theoretical analysis and the convergence property of RFD algorithm needs mathematical reasoning for comprehensive understanding of the working mechanism. In this paper, the random search strategy of RFD algorithm is analyzed mathematically and the convergence property of the algorithm is examined by using Markov chain theory. Several conditions for convergence are showcased and it is proved that RFD algorithm can indeed satisfy these conditions to achieve global optimality efficiently. Further, several experiments are performed on a set of single objective test functions to demonstrate the convergence of RFD algorithm in practice.

The Cooperative Co-evolution framework is an effective approach for decomposing large scale global optimization problems into multiple sub-components. Every subcomponent uses different optimization algorithms which evolve cooperatively and are independent of each other. These subcomponents contribute in a different way to the overall improvement of the optimal solution. Hence, the computation cost can be decreased by separating out the stagnant subcomponents of the population. Therefore, it is appropriate to allocate resources in an intelligent manner to increase the computational efficiency. In this paper, we illustrate a decomposition strategy to solve large scale global optimization problems which is scalable to millions of variables. The proposed strategy improves computational efficiency and enables embracing parallelization. The framework presented in this paper constitutes Cooperative Co-evolution based Genetic Algorithm with Scalar Distance Grouping technique (CCGA-SDG) derived from Cooperative Co-evolution based Genetic Algorithm (CCGA). In our proposed scheme, a novel scalar distance grouping technique is employed that collates the dependent variables together. The stagnant sub-components of the population are detected using this grouping method and resource reallocation is performed accordingly to increase the computational efficiency. Using our proposed methodology, a benchmark function $f_{6}$ of CEC'08 benchmark composed of 10 million variables is evaluated in 1759.79 seconds using 04 processors connected with Message Passing Interface (MPI) exhibiting better accuracy as compared to other methods. Moreover, for ${f}3$ and $f_{6}$ functions we achieve a better accuracy and for rest of the benchmark functions we achieve acceptable solutions.

Over the past decade, several approximate adders have been proposed in the literature based on the design concept ofEqual Segment Adder(ESA). In this approach, an$N$-bit adder is segmented into several smaller and independent equally sized accurate sub-adders. An$N$-bit ESA has two primary design parameters: (i) Segment size ($k$), which represents the maximum length of carry propagation; and (ii) Overlapping bits ($l$), which represents the minimum number of bits used in carry prediction, where$1 \leq k < N$and$0 \leq l < k$. Based on the combinations of$k$and$l$, an$N$-bit ESA has$N(N-1)/2$possible configurations. In this paper, we analyse ESAs and propose analytical models to estimate accuracy, delay, power and area of ESAs. The key features of the proposed analytical models are that: (i) They are generalized, i.e., work for all possible configurations of an$N$-bit ESA; and (ii) They are superior (i.e., estimate more accurately) or at par to the existing analytical models. From the proposed analytical models, we observe that in an$N$-bit ESA, there exist multiple (more than one) configurations which exhibit similar accuracy. However, these configurations exhibit different delay, power and area. Therefore, for a given accuracy, the configurations which provide minimal delay, power and/or area need to be known apriori for efficient, intelligent and goal oriented implementations of ESAs. In this regard, we present an optimization framework that exploits the proposed analytical models to find the optimal configurations of an$N$-bit ESA. Further, we know that accuracy of an ESA does not depend on the adder architecture used to implement it, however, its delay, power and area depend significantly. Consequently, the optimal configurations vary with adder architectures used to implement the ESA. In order to cover a wide range of adders, we consider three types of adder architecture in our analysis: (i) Architectures having smaller area ($O(N)$); (ii) Architectures having smaller delay ($O(log_2N)$); and (iii) Architectures having in-between delay ($O(N/4)$) and area ($O(2N)$).