# Higher-Order Thinking Skills Optimizer: A Metaheuristic Algorithm Inspired by Human Behavior and Its Application in Real-World Constrained Engineering Optimization Problems

## TL;DR

This paper introduces HTSO, a new optimization algorithm inspired by human thinking skills, which performs well on complex engineering and UAV path planning problems.

## Contribution

The novel HTSO algorithm is inspired by higher-order thinking skills and demonstrates superior performance on benchmark and real-world optimization problems.

## Key findings

- HTSO outperforms 21 other algorithms on multiple CEC benchmark sets with varying dimensions.
- HTSO achieves best performance on 12 real-world constrained engineering optimization problems.
- HTSO excels in UAV 3D path planning across seven complex mountainous scenarios.

## Abstract

With the increasing complexity of optimization problems, existing methods are often inadequate for addressing these challenges, creating a pressing need for more versatile and robust approaches capable of solving a wide range of optimization problems. Meta-heuristic algorithms have become powerful tools in this regard, owing to their flexibility, ease of implementation, and suitability for high-dimensional and complex problems. This paper introduces the Higher-order Thinking Skills Optimizer (HTSO), a novel meta-heuristic algorithm inspired by Higher-order Thinking Skills (HOTS) from educational theory. HTSO simulates the four key aspects of HOTS: creativity, problem-solving, critical thinking, and decision-making. Creativity reflects the intrinsic human drive for knowledge, prompting exploration of unknown domains. When faced with difficulties, individuals focus on gathering information to solve problems. However, due to the inconsistent quality of information, critical thinking is essential for effectively assessing it. In HTSO, creativity and problem-solving serve as the exploration and exploitation mechanisms, respectively. Crucially, critical thinking functions as a metacognitive controller that evaluates the quality of solutions and dynamically guides the selection and adaptation of creativity strategies, thereby ensuring an effective balance between exploration and exploitation. Moreover, HTSO is designed as a user-friendly algorithm with minimal parameter tuning requirements, and its key parameter demonstrates strong robustness across diverse problem types and dimensions, which enhances its practical applicability. Extensive experiments were conducted across three CEC benchmark sets with multiple dimensions (CEC-2017: 30, 50, 100 dimensions; CEC-2020: 10, 15, 20 dimensions; CEC-2022: 10, 20 dimensions), comparing HTSO with 21 other algorithms, including several CEC champion algorithms. The results demonstrate that HTSO outperforms all comparative algorithms on most test functions, indicating high effectiveness and robustness. Furthermore, HTSO was compared with 14 algorithms on 12 real-world constrained engineering optimization problems. Finally, HTSO and 14 other algorithms were applied to unmanned aerial vehicle 3D path planning in seven different complex mountainous scenarios. HTSO also achieved the best performance across all tested real-world engineering problems and UAV path planning scenarios, consistently outperforming the comparative algorithms. These results demonstrate the effectiveness and potential of HTSO in addressing real-world optimization challenges.