Intelligent solution space search and reduction using tree-based learning methods

This thesis presents the development and evaluation of three innovative algorithms aimed at improving the solution performance of optimization problems through the integration of tree-based machine-learning techniques. The first algorithm, "Remove-Add Algorithm Augmented by Population Management," combines machine learning and optimization within a population-based heuristic framework. Extensive computational results on the p-median problem and Quadratic Assignment Problem (QAP) demonstrate its superior performance compared to traditional methods. The second algorithm, "Variable Fixing Algorithm," utilizes rule sets for variable fixing generated by regression trees that utilize active learning and worst leaf node path split decisions. Extensive computational results on the QPLIB instances highlight the approach's effectiveness in enhancing solution diversity, preventing premature convergence, and ensuring computational efficiency. The third algorithm, "Learning-Based Bound Generating Algorithm," uses historical data and regression tree models to generate lower and upper bounds for decision variables that guide the optimization process, effectively narrowing the search space and accelerating convergence. Experimental results show that deeper regression trees improve the quality of generated bounds, particularly for complex optimization landscapes. Through comprehensive experiments and comparative analyses, this research demonstrates the effectiveness of these algorithms in improving solution quality and computational efficiency. The findings underscore the ability of tree-based learning to effectively differentiate between high-quality and low-quality solutions, guiding the algorithm toward highly promising regions of the solution space.