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.

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.

The costs of different fuels are increasing gradually, for operation of power production units. Thus new optimization techniques are needed to tackle the problems of Economic Load Dispatch (ELD). Metaheuristics are very helpful for policy makers in achieving the best results by minimizing the cost function. In this paper, we have updated the Grasshopper Optimization Algorithm (GOA) with a better initialization strategy to balance the search capability of GOA. The new algorithm is named as Improved Grasshopper Algorithm (IGOA). GOA is inspired by the swarms of grasshopper and mimics their biological behavior. Furthermore, IGOA is used to solve the ELD problems by tacking four case studies from literature. The objective in these problems is to find best decision variables for dispatching the available power with lowest cost, efficiency and reliability. To validate the efficiency of our proposed algorithm, we have tested it by solving 4 case studies of ELD with 1263MW, 600MW, 800MW and 2500MW demands respectively. IGOA is better in terms of convergence rate and quality of solutions obtained for the problems considered in literature for other metaheuristics.

Adaptive penalty function methods (APFMs) are promising constraints handling techniques. In an APFM, a penalty parameter which balances constrains’ violations and objective function values is adaptively adjusted. This work modifies an APFM that uses a near feasibility threshold (NFT), a portion around the feasible region where infeasible solutions are considered as good ones, for constrained multiobjective optimization. The modified APFM with five different settings of NFT is embedded in a prominent multiobjective evolutionary algorithm based on decomposition, MOEA/D. This brings in five constrained variants of the base algorithm, denoted by CMOEA/D-TAP1 to CMOEA/D-TAP5. These variants are tested on well-known constrained multiobjective benchmark test suits, the CTP series and the CF series. The proposed variants are compared with four best performing algorithms through HV metric (hyper volume metric) statistics for CTP series, and with seven state-of-the-art algorithms through Wilcoxon rank sum test employed to mean values of both HV and IGD (inverted generational distance matric) metrics for CF series. Simulation results reflect that overall performance of the newly introduced variants is better than the competitors for the taken benchmark test suits.