New Tabu Search based global optimization methods outline of algorithms and study of efficiency

Area of Science:

• Computational Mathematics
• Numerical Analysis
• Optimization Theory

Background:

• Global optimization is crucial for solving complex mathematical and engineering problems.
• Existing methods often face challenges with convergence speed and efficiency for high-dimensional functions.
• The Tabu Search strategy offers a robust framework for exploring solution spaces.

Purpose of the Study:

• To introduce and evaluate two novel nonlinear global optimization algorithms: Gradient Only Tabu Search (GOTS) and Tabu Search with Powell's Algorithm (TSPA).
• To compare the performance of GOTS and TSPA against existing global optimization techniques.
• To assess the convergence speed and efficiency of the proposed methods on diverse test functions.

Main Methods:

• Development of the Gradient Only Tabu Search (GOTS) algorithm, utilizing a steepest descent-mildest ascent strategy.
• Development of the Tabu Search with Powell's Algorithm (TSPA), integrating Powell's method within the Tabu Search framework.
• Empirical testing of GOTS and TSPA on a suite of well-known, multi-dimensional test functions to determine global minima.

Main Results:

• The Gradient Only Tabu Search (GOTS) demonstrated significantly faster convergence compared to several established global optimizers across most test cases.
• The Tabu Search with Powell's Algorithm (TSPA) exhibited comparable efficiency to genetic algorithms in global optimization tasks.
• Both algorithms proved effective in finding global minima for functions of varying complexity and dimensionality.

Conclusions:

• GOTS offers a highly efficient and faster alternative for nonlinear global optimization problems.
• TSPA provides a competitive approach, particularly when compared to heuristic methods like genetic algorithms.
• The developed algorithms represent valuable additions to the toolkit for tackling complex optimization challenges.