A Composite Function for Understanding Bin-Packing Problem and Tabu Search: Towards Self-adaptive Algorithms

Different research problems (optimization, classification, ordering) have shown that some problem instances are better solved by a certain solution algorithm in comparison to any other. A literature review indicated implicitly that this phenomenon has been identified, formulated, and analyzed in understanding levels descriptive and predictive without obtaining a deep understanding. In this paper a formulation of phenomenon as problem in the explanatory understanding level and a composite function to solve it are proposed. Case studies for Tabu Search and One Dimension Bin Packing were conducted over set P. Features that describe problem instance (structure, space) and algorithm behavior (searching, operative) were proposed. Three algorithm logical areas were analyzed. Knowledge acquired by the composite function allowed designing of self-adaptive algorithms, which adapt the algorithm logic according to the problem instance description in execution time. The new, self-adaptive algorithms have a statistically significant advantage to the original algorithm in an average 91% of problem instances; other results (set P') indicate that when they obtain a best solution quality, it is significant and when they obtain the same or less solution quality, they finish significantly faster than original algorithm. The composite function can be a viable methodology toward the search of theories that permit the design of self-adaptive algorithms, solving real problems optimally.