Parametric approach to quadratically constrained multi-level multi-objective quadratic fractional programming

The paper proposed a method to study and obtain a set of Pareto optimal solutions or a set of representative solutions to a quadratically constrained multi-level multiobjective quadratic fractional programming problem. This problem involves several objectives to be fulfilled at multi levels under a common set of quadratic constraints. Initially, we used parametric approach to convert the fractional programming model to an equivalent non-fractional programming model by allocating a parametric vector to each fractional objective. Then, $$\varepsilon$$ -constraint method is used to convert this multiobjective programming model into an equivalent model with single objective. The solution of every previous level is followed by the next level in succession to find a solution which is suitable to each level decision maker. An algorithm and numerical example are also presented at the end of the paper to validate the proposed methodology for the Model.