Water Flow-like Algorithm for Object Grouping Problems

This paper presents a novice heuristic algorithm, Water Flow-like Algorithm (WFA), for solving discrete optimization problems, particularly the bin packing problems. WFA simulates solution agents as water flows traversing the terrain mapped from the objective function. Governed by the gravitation force, water flows from higher attitudes to lower ones. Driven by the fluid momentum, water flows adjust their compositions and directions against the landforms by splitting into and merging from other flows. Water flows are allowed to move upward to higher attitudes once they possess enough momentum to overcome the potential barrier. Mostly, at least one flow can travel to the lowest region of the terrain under the consideration. In the atmosphere, some water of a flow will evaporate and return to the ground by precipitation. Inspired by the water flowing of the nature, WFA is designed as an optimization algorithm performing the water flow splitting, merging, and dropping (precipitation) operations to traverse the solution space. The number of solution agents deployed is dynamically changing. WFA is an evolutionary algorithm involving four water flow operations: splitting and moving, merging, evaporation, and precipitation. The computational flow and the four operations are extensively discussed. In addition to general operations of WFA, specific operations for bin packing problems are presented. A designed problem and a benchmark problem from OR-Lib are used to test WFA and to compare results with other methods, such as GA, POS, and EM. Numerical results show that WFA outperforms others in solving these BPPs.