Optimization for multi-objective sum of linear and linear fractional programming problem: fuzzy nonlinear programming approach
The paper introduces a method to obtain Pareto solutions of the so-called multi-objective linear plus linear fractional programming problem, which is defined by linear constraints and the objective function \(f=(f_1,f_2,\ldots,f_k):\mathbb{R}^n\to \mathbb{R}^k\), \[f_i(x)=p_i^tx+\theta_i+\frac{c^t_ix+\alpha_i}{d^t_ix+\beta_i},\quad\forall x\in \mathbb{R}^n,\] where \(p_i,c_i,d_i\in \mathbb{R}^n\) and \(\theta_i,\alpha_i,\beta_i\in \mathbb{R}\). The proposed method is based on reformulating the problem into a multi-objective nonlinear programming problem by applying hyperbolic and exponential membership functions to each component of a fuzzy version of the original multi-objective programming problem, which is built by considering an aspiration level and a tolerance limit for each component \(f_i\). The obtained multi-objective nonlinear programming problem is solved by applying a fuzzy goal programming approach to its linear approximation. The introduced procedure is compared with some existing methods in the literature and it is illustrated through two numerical examples and a real-life application problem.
multi-objective nonlinear programming problem
multi-objective linear plus linear fractional programming problem
scientific article; zbMATH DE number 7372035
scientific article