Heuristic algorithms (HAs) are widely used in multi-objective reservoir optimal operation (MOROO) due to the rapidity of the calculation and simplicity of their design. The literature usually focuses on one or two categories of HAs and simply reviews the state of the art. To provide an overall understanding and a specific comparison of HAs in MOROO, differential evolution (DE), particle swarm optimisation (PSO), and artificial physics optimisation (APO), which serve as typical examples of the three categories of HAs, are compared in terms of the development and applications using a designed experiment. Besides, the general model with constraints and fitness function, and the solution process using a hybrid feasible domain restoration method and penalty function method are also presented. Taking a designed experiment with multiple scenarios, the mean average of the optimal objective function values, the standard deviation of optimal objective function values, the mean average of the computational time, and population diversity are used for comparisons. Results of the comparisons show that (a) the problem of optimal multipurpose reservoir long-term operation is a mathematic programming problem with narrow feasible region and monotonic objective function; (b) it is easy to obtain the same optimal objective function value, but different optimal solutions using HAs; and (c) comparisons do not result in a clear winner, but DE can be more appropriate for MOROO.
