Computational Creativity by Diversity-Optimized Intelligent Search: An Automatic Approach to Artificial Synthesis of Trigonometric Identities

This article emphasizes an interesting approach to synthesize computational creativity by a process similar to deductive reasoning with a provision for testing the degree of diversity of the generated instances compared to their predecessors. The above two-step process of expansion and testing is developed here using the best-first search (BFS) on an OR-tree, where the nodes denote trial solutions (new creations) and edges represent parent-child connectivity satisfying the rules of the given problem domain. Two alternative extensions of BFS are examined in view of the cost function employed at the nodes to ultimately determine the optimal node in the search tree within a user-defined depth as the solution to the creativity problem. The first algorithm considers maximizing the diversity cost earned by a node with respect to its parent, while the second considers maximizing the difference between the diversity and the penalty cost earned by a node with respect to the root node. The significant contribution of the present research lies in ensuring diversity of the solutions during iterative expansions of the tree as well as the novelty of the optimal solution (best node) across runs of the same program. The relative performances of the two algorithms are compared in the context of their applicability. Performance analysis undertaken reveals that the proposed algorithms outperform their competitors with respect to three important metrics. The proposed algorithms have successfully been employed in developing chapter-end exercises for trigonometric identity proving problems.