Title: A Review on Optimality Investigation Strategies for the Balanced Assignment Problem Show Chinese title

Title: 关于平衡分配问题最优性研究策略的综述

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. Show Chinese abstract

Abstract: 数学选择是一种从一组选项中选择特定选项的方法。 它一直是数学家们感兴趣的研究领域。 因此，组合优化是数学选择领域的一个子领域，我们通常处理受运筹学、人工智能和许多其他有前景领域约束的问题。 从更广泛的意义上说，优化问题涉及通过系统地从允许的集合中选择输入值并计算函数值来最大化或最小化一个实函数。 应用数学的一个广阔领域是对元启发式理论和方法的推广到其他表述形式。 更广泛地说，优化涉及在给定空间内确定某些适应度函数的最佳属性，该空间可能包括各种不同类型的决策变量和上下文。 在本工作中，我们将研究著名的平衡分配问题，并对解决平衡分配问题的不同概念的计算时间复杂度指标进行比较分析。