Weighted Tchebycheff Optimization Technique Under Uncertainty

Abstract

In a multi-objective optimization problem there is more than one objective function and there is no single optimal solution which simultaneously optimizes all of the given objective functions. For these unsuitable conditions the decision makers always search for the most ‘‘preferred’’ solution, in contrast to the optimal solution. A number of mathematical programming methods, namely Weighted-sum method, Goal programming, Lexicographic method, Weighted min–max method, Exponential weighted criterion, Weighted product method, Bounded objective function method and Weighted Tchebycheff optimization methods have been applied in the recent past to find the optimal solution. In this paper weighted Tchebycheff optimization methods has been applied to find the optimal solution of a multi-objective optimization problem. A solution procedure of weighted Tchebycheff technique has been discussed to find the optimal solution of the multi-objective optimization problems. For the most part, the parameters of a multi-objective optimization model are thought to be deterministic and settled. Nonetheless, the qualities watched for the parameters in true multi-objective optimization problems are frequently loose and subject to change. In this way, we utilize multi-objective optimization model inside a vulnerability based system and propose a multi-objective optimization model whose coefficients are uncertain in nature. We accept the uncertain variables (UVs) to have linear uncertainty distributions. Finally, a numerical example is solved weighted Tchebycheff technique.