Agricultural Water Management 255 (2021) 107003 Available online 8 June 2021 0378-3774/© 2021 Elsevier B.V. All rights reserved. Optimization algorithms as training approaches for prediction of reference evapotranspiration using adaptive neuro fuzzy inference system Dilip Kumar Roy a, * , Alvin Lal b , Khokan Kumer Sarker c , Kowshik Kumar Saha d , Bithin Datta e a Irrigation and Water Management Division, Bangladesh Agricultural Research Institute, Gazipur 1701, Bangladesh b Discipline of Civil Engineering, School of Information Technology, Engineering, Mathematics & Physics, University of the South Pacific, Fiji c Soil and Water Management Section, Horticultural Research Center, Bangladesh Agricultural Research Institute, Gazipur 1701, Bangladesh d Department of Agromechatronics, Technical University of Berlin, 10623 Berlin, Germany e Discipline of Civil Engineering, College of Science and Engineering, James Cook University, QLD 4811, Australia A R T I C L E INFO Handling Editor: J.E. Fern´andez Keywords: Reference evapotranspiration Hybridized ANFIS models Shannon’s entropy Grey relational analysis Variation coefficient ABSTRACT Reference evapotranspiration (ET 0 ), widely used in efficient and meaningful scheduling of irrigation events, is an essential component of agricultural water management strategy for proper utilization of limited water resources. Accurate and early prediction of ET 0 can provide the basis for designing effective irrigation scheduling and help in resourceful management of water in agriculture. This study aims to evaluate and compare the performances of different hybridized Adaptive Neuro Fuzzy Inference System (ANFIS) models with optimization algorithms for predicting daily ET 0 . The FAO-56 Penman-Monteith method was used to estimate daily ET 0 values using his- torical weather data obtained from a weather station in Bangladesh. The obtained climatic variables and the estimated ET 0 values form the input-output training patterns for the hybridized ANFIS models. The performances of these hybridized ANFIS models were compared with the classical ANFIS model tuned with combined Gradient Descent method and the Least Squares Estimate (GD-LSE) algorithm. Performance ranking of these ANFIS models was performed using Shannon’s Entropy (SE), Variation Coefficient (VC), and Grey Relational Analysis (GRA) based decision theories supported by eight statistical indices. Results indicate that both SE and VC based decision theories provided the similar ranking though the numeric values of weights differed. On the other hand, GRA provided a slightly different sequence of ranking. Both SE and VC identified Firefly Algorithm-ANFIS (FA-ANFIS) as the best performing model followed by Particle Swarm Optimization-ANFIS. In contrast, FA-ANFIS was found to be the second-best performing model according to the ranking provided by GRA with a negligible difference in weight between FA-ANFIS and the classical ANFIS model (GD-LSE-ANFIS). Therefore, FA-ANFIS can be considered as the best model, which can be utilized to predict daily ET 0 values for areas with similar climatic conditions. The findings of this research is of great importance for the planning of effective irrigation scheduling. 1. Introduction Changing weather patterns have been responsible for affecting agriculture to a great extent in recent years. As such, accurate and reliable prediction of weather variability have achieved a particular importance in agriculture related water resources planning and man- agement problems. Reference evapotranspiration (ET 0 ) is the key parameter affecting efficient water management strategies in agricul- ture and is an important component in hydrological and ecological processes controlling agricultural water management. Accurate and early prediction of ET 0 provide the basis for designing efficient irrigation scheduling strategies in which actual crop evapotranspiration, ET a can be obtained from the computed ET 0 when the crop coefficient values of the region of interest are known. Therefore, the applicability of ET 0 has gained wider popularity as it can be admirably adapted to various crops through the incorporation of crop coefficient values (Xiang et al., 2020). Accurate measurements of ET 0 can be obtained through lysimeters, which is generally used to develop and validate other indirect methods of ET 0 estimation (Allen et al., 2011; L´ opez-Urrea et al., 2006). These indirect methods are typically mathematical models that employ few meteorological information (e.g., air temperatures, relative humidity, solar radiation, and wind speed) obtained from meteorological stations of interest for estimating ET 0 . As direct measurements through lysime- ters and other approaches are cost intensive, indirect measurements * Corresponding author. E-mail address: dilip.roy@my.jcu.edu.au (D.K. Roy). Contents lists available at ScienceDirect Agricultural Water Management journal homepage: www.elsevier.com/locate/agwat https://doi.org/10.1016/j.agwat.2021.107003 Received 17 October 2020; Received in revised form 13 May 2021; Accepted 29 May 2021