MAATHA Optimization Algorithm

The MAATHA Optimization Algorithm is designed to solve multi-objective optimization problems

The MAATHA Optimization Algorithm (Multi-Objective Attraction, Avoidance, Thrust, and Hovering Algorithm) is an extension of the AATHA Optimization Algorithm, which is designed to handle multi-objective optimization problems. It incorporates the same principles of Attraction, Avoidance, Thrust, and Hovering but is adapted to simultaneously optimize multiple conflicting objectives.

In a multi-objective optimization problem, there are typically two or more objective functions that need to be optimized simultaneously. These objectives may be in conflict, meaning that improving one objective may worsen another. The goal of a multi-objective optimization algorithm is to find a set of solutions that represent the best trade-offs, known as the Pareto front.

Explanation of the MATLAB Code:

1. Initialization:

• The algorithm starts by initializing a population of solutions, each of which is a set of decision variables (x). These solutions are evaluated based on multiple objective functions (objective1 and objective2).

1. Attraction:

• Each solution is attracted towards the best solution found so far in the population, as measured by the multiple objective functions.

1. Avoidance:

• Solutions that are dominated by other solutions in the population are moved away from these poor areas, promoting diversity in the population.

1. Thrust:

• Thrust is applied dynamically to the solutions to explore potential areas of better trade-offs in the objective space.

1. Hovering:

• This mechanism ensures that solutions do not converge prematurely by allowing exploration of new areas around existing solutions.

1. Dominance Checking:

• Solutions are compared using Pareto dominance. A solution A is considered dominated by another solution B if B is no worse than A in all objectives and strictly better in at least one objective.

1. Pareto Front:

• The algorithm aims to generate solutions that form the Pareto front, which is the set of non-dominated solutions.

Conclusion:

The MAATHA Optimization Algorithm is designed to solve multi-objective optimization problems by finding a set of optimal trade-offs between conflicting objectives. The algorithm uses concepts such as attraction, avoidance, thrust, and hovering to guide the search towards the Pareto front while maintaining population diversity and avoiding premature convergence. This implementation can be extended to handle more complex multi-objective problems with additional objectives or constraints.