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The main reason for applying evolutionary algorithms in multi-objective optimization problems is to obtain near-optimal nondominated solutions/Pareto fronts, from which decision-makers can choose a suitable solution. The efficiency of multi-objective optimization algorithms depends on the quality and quantity of Pareto fronts produced by them. To compare different Pareto fronts resulting from different algorithms, criteria are considered and applied in multi-objective problems.Each criterion denotes a characteristic of the Pareto front. Thus, ranking approaches are commonly used to evaluate different algorithms based on different criteria. This paper presents three multi-objective optimization methods based on the multi-objective particle swarm optimization (MOPSO) algorithm. To evaluate these methods, bi-objective mathematical benchmark problems are considered. Results show that all proposed methods are successful in finding near-optimal Pareto fronts. A ranking method is used to compare the capability of the proposed methods and the best method for further study is suggested. Moreover, the nominated method is applied as an optimization tool in real multi-objective optimization problems in multireservoir system operations. A new technique in multi-objective optimization, called warm-up, based on the PSO algorithm is then applied to improve the quality of the Pareto front by single-objective search. Results show that the proposed technique is successful in finding an optimal Pareto front.Key words 9 9 9 9 multi-objective particle swarm optimization (MOPSO), multipurpose, multireservoir systems, optimization problems

The Muskingum model is a hydrologic flood routing method in which the accuracy of the parameter estimation affects the routed hydrograph, especially in both the value and time of the flood peak. Meta-heuristic algorithms are good candidates to determine optimal/near-optimal parameters in the Muskingum model. In this paper, two metaheuristic algorithms -the simulated annealing (SA) algorithm and the shuffled frog leaping algorithm (SFLA) -are applied and compared in two benchmark and real case studies, considering the sum of the squared deviation (SSQ) between observed and routed outflows and the sum of the absolute value of deviation (SAD) between observed and routed outflow as the objective functions, and deviation of value and occurrence time of the routed flood peak (DPO and DPOT) as the important parameters on the routed flood hydrograph. Results show that the SFLA improves (decreases) the SSQ and SAD by 0 . 03% and 0 . 39% in the benchmark problem, and by 3 . 59% and 2 . 03% in the real case study, respectively, compared to reported results using various optimisation algorithms. In addition, the SFLA improves (decreases) the DPO of the routed hydrograph in the benchmark problem by 56 . 67% compared to the best (minimum) result using the Tung method.

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