Flowing Water Algorithm: A New Approach for Combinatorial Optimization Problems

Abstract

Being greatly inspired by the natural flowing regulation of water, we propose a new meta-heuristic algorithm — <i>Flowing Water Algorithm</i> (FWA) for the solution of combinatorial optimization problems (COPs). Since the solution space of COPs is multidimensional, complex and has many local extreme values, according to our proposed method, it appears to be similar to an endless hilly area with mountains, valleys and plateaus. The downward-flowing water in such area finds its way to the lowest point in the hill. Water always flows downward and eventually converges at the lowest place without any outside intervention except for gravity. Such a flowing course can be deemed as a process for the water to seek for the lowest point. The proposed algorithm is derived from such a water flow process. This algorithm combines a local search strategy with a population-based search strategy to improve both local and global search abilities. Four operators, including the local search, water overflow, drilling water tunnel and evaporation-rain are included in FWA, making this algorithm successfully perform tabu search, positive feedback, “survival of the fittest”, and local optimum escape. Two examples of its application in the traveling salesman problem (TSP) show that FWA outperforms the benchmark methods for both solution quality and convergence speed.