A Review on Optimality Investigation Strategies for the Balanced Assignment Problem

TL;DR

This paper reviews various strategies for solving the Balanced Assignment Problem, focusing on analyzing their computational complexity and efficiency through comparative metrics.

Contribution

It provides a comparative analysis of different solution methods for the Balanced Assignment Problem based on computational time complexity.

Findings

Different solution approaches vary significantly in computational time.

Some methods demonstrate superior efficiency for large problem instances.

The analysis offers insights into selecting appropriate strategies based on problem size.

Abstract

Mathematical Selection is a method in which we select a particular choice from a set of such. It have always been an interesting field of study for mathematicians. Accordingly, Combinatorial Optimization is a sub field of this domain of Mathematical Selection, where we generally, deal with problems subjecting to Operation Research, Artificial Intelligence and many more promising domains. In a broader sense, an optimization problem entails maximising or minimising a real function by systematically selecting input values from within an allowed set and computing the function's value. A broad region of applied mathematics is the generalisation of metaheuristic theory and methods to other formulations. More broadly, optimization entails determining the finest virtues of some fitness function, offered a fixed space, which may include a variety of distinct types of decision variables and contexts. In this work, we will be working on the famous Balanced Assignment Problem, and will propose a comparative analysis on the Complexity Metrics of Computational Time for different Notions of solving the Balanced Assignment Problem.