Grey wolf optimization (GWO) algorithm is a relatively recent and novel optimization approach. GWO showed performance improvement over all competing algorithms. However, the relevant literature identified that the primary GWO due to it’s position update equation shows superiority in exploitation, but is inefficient in exploration. It shows slow convergence and low precision, too. Motivated by the outlined issues in the primary GWO, this work presents two new and improved GWO algorithms. The first proposed variant modifies all the three models, encircling model of prey, position update equation and the hunting equation of canonical GWO. Further, a new parameter is introduced to scale the encircling and position update equations. As a result, the exploration issue of the algorithm is tackled. Unlike the first variant, the second proposed variant does not modify the position update models, but it incorporates Minkowski’s information into GWO. To the best of our knowledge, no such modifications to GWO have been done before. The proposed modified versions of GWO are tested on a well-known test functions suit and then compared with different population-based algorithms, including fast evolutionary programming and particle swarm optimization. It was identified from the simulation results that proposed algorithms outperform different algorithms in comparison on majority of problems. The sensitivity study of the proposed algorithms to their various parameters is also provided.

The effect of entropy optimization on an axisymmetric Darcy–Forchheimer Powell–Eyring nanofluid flow caused by a horizontally permeable stretching cylinder, as well as non-linear thermal radiation, was investigated in this research work. The leading equations of the current problem were changed into ODEs by exhausting appropriate transformations. To deduce the reduced system, the numerical method bvp4c was used. The outcome of non-dimensional relevant factors on velocity, entropy, concentration, temperature, Bejan number, drag force, and Nusselt number is discussed and demonstrated using graphs and tables. It is perceived that, with a higher value of volume fraction parameter, the skin friction falls down. Likewise, it is found that the Nusselt number drops with enhancing the value of the volume fraction. Moreover, the result reveals that the entropy generation increases as the volume fraction, curvature parameter, and Brinkman number increase.

The China-Pakistan Economic Corridor (CPEC), a major development project in China’s fast-evolving Belt and Road Initiative (BRI), is arguably the most comprehensive of the six BRI economic and infrastructure corridors on land. For Pakistan, it is perceived “as the harbinger of a new era of connectivity and integration” that will not only transform the region’s economic development but also the well-being of Pakistanis. It investigates the impact of CPEC as perceived by the local communities in its ZoI. It also evaluates CPEC’s potential challenges: public support and local communities’ concerns such as their awareness, acceptance, and ownership of CPEC. To accomplish our research objectives, we analyze original microdata from 1,585 respondents living proximate to propose CPEC route(s) of Khyber Pakhtunkhwa province, in Pakistan. After aggregating the data on the basis of age, education, income, and social status, we conduct descriptive, bivariate, and multivariate analyses in an attempt to answer three research questions. We find significantly high level of awareness of CPEC across the board in the older age group of respondents (i.e., 40 years or older), hereinafter referred to as mature, highly educated, that is, respondents with university education. Older respondents expect more environmental and economic benefits than younger respondents, even as the latter expect lower social change and effect on migration than do the former. However, those in the upper social class expect higher economic and political benefits from CPEC, compared with those in the lower social class—an early indication of possible elite capture.

Teaching learning based optimization (TLBO) algorithm is a distinguished nature-inspired population-based meta-heuristic, which is basically designed for unconstrained optimization. TLBO mimics teaching learning process through which learners acquire knowledge from their teachers, and improve their results/grades, accordingly. Stochastic ranking (SR) is a constrained handling technique (CHT), which produces greediness among solutions to improve their fitness values and feasibility. Violation constraint handling (VCH) technique produces more feasibility among the existing superiority of feasibility CHTs due to its additional factor of ranking based on the number of constraints violated (NCV). This work brings in a new variant of SR, namely hybrid stochastic ranking (HSR), which combines SR and VCH. For constrained optimization, the integration of some CHT with TLBO is essential. In this paper, HSR is integrated with TLBO and a new constrained version of TLBO called HSR-TLBO is designed. The efficiency of HSRTLBO is checked on constrained test functions of the suit CEC 2017. The experimental results show that HSR-TLBO got prominent position when compared and ranked with the top four papers and our two newly designed constrained variants of TLBO, MSR-TLBO and MVCH-TLBO, based on the provided budget and ranking criteria of the mentioned suit.

Self-adaptive variants of evolutionary algorithms (EAs) tune their parameters on the go by learning from the search history. Adaptive differential evolution with optional external archive (JADE) and self-adaptive differential evolution (SaDE) are two well-known self-adaptive versions of differential evolution (DE). They are both unconstrained search and optimization algorithms. However, if some constraint handling techniques (CHTs) are incorporated in their frameworks, then they can be used to solve constrained optimization problems (COPs). In an early work, an ensemble of constraint handling techniques (ECHT) is probabilistically hybridized with the basic version of DE. The ECHT consists of four different CHTs: superiority of feasible solutions, self-adaptive penalty, $\epsilon$ -constraint handling technique and stochastic ranking. This paper employs ECHT in the selection schemes, where offspring competes with their parents for survival to the next generation, of JADE and SaDE. As a result, JADE-ECHT and SaDE-ECHT are developed, which are the constrained variants of JADE and SaDE. Both algorithms are tested on 24 COPs and the experimental results are collected and compared according to algorithms’ evaluation criteria of CEC’06. Their comparison, in terms of feasibility rate (FR) and success rate (SR), shows that SaDE-ECHT surpasses JADE-ECHT in terms of FR, while JADE-ECHT outperforms SaDE-ECHT in terms of SR.

In this paper, a wavelet based collocation method is formulated for an approximate solution of (1 + 1)- and (1 + 2)-dimensional time fractional diffusion wave equations. The main objective of this study is to combine the finite difference method with Haar wavelets. One and two dimensional Haar wavelets are used for the discretization of a spatial operator while time fractional derivative is approximated using second order finite difference and quadrature rule. The scheme has an excellent feature that converts a time fractional partial differential equation to a system of algebraic equations which can be solved easily. The suggested technique is applied to solve some test problems. The obtained results have been compared with existing results in the literature. Also, the accuracy of the scheme has been checked by computing $L_2$ and $L_{\infty }$ error norms. Computations validate that the proposed method produces good results, which are comparable with exact solutions and those presented before.