Summary: In general, there is no single optimal solution in multiobjective problems, but rather a set of non-inferior (or Pareto optimal) solutions from which the decision maker must select the most preferred solution as the one to implement. The generation of the entire Pareto optimal solution set is not practical for most real world problems. This paper deals with a combined interactive approach for solving \(E\)-convex multiobjective nonlinear programming problems which was introduced by E. A. Youness [J. Optimization Theory Appl. 102, No. 2, 439–450 (1999; Zbl 0937.90082); Chaos Solitons Fractals 12, No. 9, 1737–1745 (2001; Zbl 1026.90093); Appl. Math. Comput. 151, No. 3, 755–761 (2004; Zbl 1056.90127)], where the decision space is effected by an operator \((E:\mathbb{R}^n \rightarrow \mathbb{R}^n)\). This kind of convexity is called \(E\)-convexity which has some important applications in various branches of mathematical science. The proposed approach in this paper combines the reference direction method introduced by S. C. Narula, L. Kirilov and V. Vassilev [in: G. H. Tzeng (ed.) et al., Multiple criteria decision making. Proceedings of the 10th international conference: Expand and enrich the domains of thinking and application. New York: Springer. 119–127 (1994; Zbl 0817.90097)] and the reference point method introduced by A. P. Wierzbicki [Lect. Notes Econ. Math. Syst. 177, 468–486 (1980; Zbl 0435.90098)], the Tchebycheff method introduced by R. E. Steuer [Multiple criteria optimization: theory, computation, and application. Malabar, FL: Robert E. Krieger Publishing Co. (1989; Zbl 0742.90068)], the satisfying trade-off method introduced by H. Nakayama [in: P. M. Pardalos (ed.) et al., Advances in multicriteria analysis. Dordrecht: Kluwer Academic Publishers. Nonconvex Optim. Appl. 4, 147–174 (1995; Zbl 0868.90101)] and the combined in attainable reference point (ARP) method introduced by X. M. Wang, Z. L. Qin and Y. D. Hu [“An interactive algorithm for multicriteria decision making: the attainable reference point method”, IEEE Trans. Syst. Man Cybern. 31, No. 3, 194–198 (2001), doi:10.1109/3468.925659]. The main development of the proposed approach is starting with a weak efficient solution say \(x^{**}\) corresponding to \(s^{**}\) as the first step and uses \(s^{**}\) to improve the weighting coefficients of the augmented lexicographic Tchebycheff problem where we improve the value \(\bar s - \tilde s\) inserted in ARP by the value \(\bar s - s^{**}\) and hence modify the reference point in the case of an unsatisfactory solution for the decision maker as he wishes. An illustrative numerical example is given to demonstrate the theory developed and the quality and effectiveness of the presented approach.