An Angle-Based Bi-Objective Optimization Algorithm for Redundancy Allocation in Presence of Interval Uncertainty

Uncertainty is a practical issue in system design optimization because some characteristics of components, such as reliability and cost, cannot be determined precisely in many situations. Considering the imprecise characteristics of components, few works have focused on the multi-objective optimization for the redundancy allocation due to the challenges of comparing multi intervals. To tackle the issue, a novel angle-based bi- objective redundancy allocation algorithm is proposed in this study, introducing three original contributions: 1) An angle-based interval crowding distance (ICA) is especially designed for effective performance and reduced computational time; 2) Two techniques are applied to tackle the problem: An elite selection for mutation is presented for generating better offsprings; A penalty-guided constraint handling technique is introduced for converting the problem into an unconstrained one. 3) Since a set of optimal solutions is obtained by the proposed method and no preference on uncertainties is provided, this paper proposes a novel knee interval method to help DMs make a decision. To be specific, the proposed ICA can describe the distribution of the whole population intuitively and effectively, considering not only the angle between two compared individuals but also the angle range of the interval values. The computational results from two typical experiments demonstrate that the proposed algorithm is more efficient than other state-of-the-art algorithms, generating Pareto sets with less repeating individuals, stronger convergence, wider distribution, less imprecision, and reduced computational time. Note to Practitioners—This article is motivated by two practical problems in multi-objective redundancy allocation in presence of interval uncertainty: First, this paper tries to solve the multi-objective redundancy allocation problem with the imprecise characteristics of components, which is rarely considered in the field of reliability optimization design. Second, the calculation of the crowding distance needs extra time cost and is less efficient. To tackle this issue, an interval crowding angle is especially designed, considering not only the angle between two compared individuals, but also the angle range of the interval values. The proposed method can be embedded in most multi-objective interval evolutionary algorithms to compute the diversity of the individuals. The goal of this study is to allocate the economy and high-reliable components for practitioners. The computational results verify its effectiveness and efficiency. Besides, in many cases the practitioners know only few or no preferences, this paper proposes a knee point analysis of interval values that allows practitioners to select the optimal solution with large hypervolume and less imprecision among a set of solutions.