Snow water equivalent (SWE) is a key parameter in hydrological cycle, and information on regional SWE is required for various hydrological and meteorological applications, as well as for hydropower production and flood forecasting. This study compares the snow depth and SWE estimated by multivariate linear regression (MLR), discriminant function analysis, ordinary kriging, ordinary kriging-multivariate linear regression, ordinary krigingdiscriminant function analysis, artificial neural network (ANN) and neural network-genetic algorithm (NNGA) models. The analysis was performed in the 5.2 km 2 area of Samsami basin, located in the southwest of Iran. Statistical criteria were used to measure the models' performances. The results indicated that NNGA, ANN and MLR methods were able to predict SWE at the desirable level of accuracy. However, the NNGA model with the highest coefficient of determination (R 2 = 0.70, P value \ 0.05) and minimum root mean square error (RMSE = 0.202 cm) provided the best results among the other models. The lower SWE values were registered in the east of study area and higher SWE values appeared in the west of study area where altitude was higher.

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Deriving optimal operation policies for multi-reservoir systems is a complex engineering problem. It is necessary to employ a reliable technique to efficiently solving such complex problems. In this study, five recently-introduced robust evolutionary algorithms (EAs) of Harris hawks optimization algorithm (HHO), seagull optimization algorithm (SOA), sooty tern optimization algorithm (STOA), tunicate swarm algorithm (TSA) and moth swarm algorithm (MSA) were employed, for the first time, to optimal operation of Halilrood multi-reservoir system. This system includes three dams with parallel and series arrangements simultaneously. The results of mentioned algorithms were compared with two well-known methods of genetic algorithm (GA) and particle swarm optimization (PSO) algorithm. The objective function of the optimization model was defined as the minimization of total deficit over 223 months of reservoirs operation. Four performance criteria of reliability, resilience, vulnerability and sustainability were used to compare the algorithms’ efficiency in optimization of this multi-reservoir operation. It was observed that the MSA algorithm with the best value of objective function (6.96), the shortest CPU run-time (6738 s) and the fastest convergence rate (< 2000 iterations) was the superior algorithm, and the HHO algorithm placed in the next rank. The GA, and the PSO were placed in the middle ranks and the SOA, and the STOA placed in the lowest ranks. Furthermore, the comparison of utilized algorithms in terms of sustainability index indicated the higher performance of the MSA in generating the best operation scenarios for the Halilrood multi-reservoir system. The application of robust EAs, notably the MSA algorithm, to improve the operation policies of multi-reservoir systems is strongly recommended to water resources managers and decision-makers.

Simultaneous optimization of several competing objectives requires increasing the capability of optimization algorithms. This paper proposes the multi-objective moth swarm algorithm, for the first time, to solve various multi-objective problems. In the proposed algorithm, a new definition for pathfinder moths and moonlight was proposed to enhance the synchronization capability as well as to maintain a good spread of non-dominated solutions. In addition, the crowding-distance mechanism was employed to select the most efficient solutions within the population. This mechanism indicates the distribution of non-dominated solutions around a particular non-dominated solution. Accordingly, a set of non-dominated solutions obtained by the proposed multi-objective algorithm is kept in an archive to be used later for improving its exploratory capability. The capability of the proposed MOMSA was investigated by a set of multi-objective benchmark problems having 7 to 30 dimensions. The results were compared with three well-known meta-heuristics of multi-objective evolutionary algorithm based on decomposition (MOEA/D), Pareto envelope-based selection algorithm II (PESA-II), and multi-objective ant lion optimizer (MOALO). Four metrics of generational distance (GD), spacing (S), spread (Δ), and maximum spread (MS) were employed for comparison purposes. The qualitative and quantitative results indicated the superior performance and the higher capability of the proposed MOMSA algorithm over the other algorithms. The MOMSA algorithm with the average values of CPU time = 2771 s, GD = 0.138, S = 0.063, Δ = 1.053, and MS = 0.878 proved to be a robust and reliable model for multi-objective optimization.

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