### Mathematical Modelling and Applications

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### Novel Method for Solving Balance and Unbalance Assignment Problem Using New Approach for Ant Colony Algorithm

Assignment Problem (AP) is the fundamental application of TP studied in the area of Operations research. The AP is also an essential problem in the field of optimization, where the goal is to optimize production time or cost by allocating one task to one machine, one machine to one job, one destination to one source, or one source to one destination. Various solutions for resolving the assignment problem have been offered in the literature. Excellent response to task problems is obtained using the Hungarian technique. In this study, however, we are discussing a novel alternative strategy that is the almost best performance. Here, we are looking at another technique to resolve algorithm and solution steps AP. In addition, we present an innovative alternative strategy that provides the best performance of APs by utilizing a modified ant colony optimization (ACO) algorithm. A few revisions to the ant colony algorithm (Transition Rule and Pheromone Update Rule) are created, resulting in a solution that is extremely close to the ideal solution. This method is also to be noticed that, requires the least number of steps to reach optimality as compare the obtained results with other well-known meta-heuristic algorithms. Finally, a numerical example is provided to demonstrate this procedure.

Optimal Solution, Assignment Problem, Feasible Solution, Alternate Method, Hungarian Method

APA Style

Ekanayake E. M. U. S. B. (2021). Novel Method for Solving Balance and Unbalance Assignment Problem Using New Approach for Ant Colony Algorithm. Mathematical Modelling and Applications, 6(4), 101-106. https://doi.org/10.11648/j.mma.20210604.13

ACS Style

Ekanayake E. M. U. S. B. Novel Method for Solving Balance and Unbalance Assignment Problem Using New Approach for Ant Colony Algorithm. Math. Model. Appl. 2021, 6(4), 101-106. doi: 10.11648/j.mma.20210604.13

AMA Style

Ekanayake E. M. U. S. B. Novel Method for Solving Balance and Unbalance Assignment Problem Using New Approach for Ant Colony Algorithm. Math Model Appl. 2021;6(4):101-106. doi: 10.11648/j.mma.20210604.13