Soft Computing https://doi.org/10.1007/s00500-018-3075-3 FOCUS Solving permutation flow-shop scheduling problem by rhinoceros search algorithm Suash Deb 1,2 · Zhonghuan Tian 3 · Simon Fong 3 · Rui Tang 3 · Raymond Wong 4 · Nilanjan Dey 5 © Springer-Verlag GmbH Germany, part of Springer Nature 2018 Abstract In this paper, a novel meta-heuristic search algorithm inspired by rhinoceros’ natural behaviour is proposed, namely rhinoceros search algorithm (RSA). Similar to our earlier version called elephant search algorithm, RSA simplifies certain habitual characteristics of rhinoceros and stream-lines the search operations, thereby reducing the number of operational parameters required to configure the model. Via computer simulation, it is shown that RSA is able to outperform certain classical meta- heuristic algorithms. Different dimensions of optimization problems are tested, and good results are observed by RSA. The RSA is also implemented on permutation flow-shop scheduling problem (PFSP) with some representation method. Four different problem scales are used. Compared with partible swarm optimization (PSO) on PFSP, the RSA outperforms PSO on different problem scales with a 3% improvement. Keywords Rhinoceros search algorithm · Elephant search algorithm · Meta-heuristic · Optimization problems Communicated by S. Deb, T. Hanne, K. C. Wong. B Simon Fong ccfong@umac.mo Suash Deb suashdeb@gmail.com Zhonghuan Tian mb45440@umac.mo Rui Tang yb57463@umac.mo Raymond Wong wong@cse.unsw.edu.au Nilanjan Dey nilanjan.dey@tict.edu.in 1 IT and Educational Consultant, Ranchi, India 2 Decision Sciences and Modelling Program, Victoria University, Melbourne, Australia 3 Department of Computer and Information Science, University of Macau, Taipa, Macau SAR, China 4 School of Computer Science and Engineering, University of New South Wales, Sydney, NSW 2052, Australia 5 Department of Information Technology, Techno India College of Technology, Kolkata, West Bengal, India 1 Introduction Proposed by Deb et al. (2015), elephant search algorithm (ESA) is a newly natural-inspired meta-heuristic algorithm. In elephant groups, male elephant scouts afar to find new habitat, while female elephants surrounding the group leader step by step move toward new habitat. By giving differ- ent gender agents different search responsibility, ESA can adjust its search emphasis accordingly. ESA has changeable gender ratio and thus gives the opportunity of handling the algorithm’s inclination on global exploration or local inten- sification. This feature provides broad applicability when facing different types of optimization problems. However, ESA is designed with too much mechanism that includes but not limited to bounce mechanism, random walk mechanism, and death-and-reborn mechanism. Consequently, ESA con- sists of too many parameters to achieve its complex search mechanism, and these make ESA too time consuming. Generally, meta-heuristic algorithms are stochastic algo- rithms. They do not have strict rules and deterministic process to follow. In most cases, some random walk patterns are used to search for the promising solution space. Compared to deterministic algorithms, they are more flexible and universal in terms of movements in their searches. Meta-heuristic algo- rithms can be divided into three branches. The first branch is evolutionary algorithm. The algorithm which belongs to 123