Efficient micro immune optimization approach solving constrained nonlinear interval number programming

Abstract

This work investigates a possibility degree-based micro immune optimization approach to seek the optimal solution of nonlinear interval number programming with constraints. Such approach is designed under the guideline of the theoretical results acquired in the current work, relying upon interval arithmetic rules, interval order relation and immune theory. It involves in two phases of optimization. The first phase, based on a new possibility degree approach, assumes searching efficient solutions of natural interval extension optimization. This executes five modules -constraint bound handling, population division, dynamic proliferation, mutation and selection, with the help of a varying threshold of interval bound. The second phase collects the optimal solution(s) from these efficient solutions after optimizing the bounds of their objective intervals, in terms of the theoretical results. The numerical experiments illustrated that such approach with high efficiency performs well over one recent nested genetic algorithm and is of potential use for complex interval number programming.

Optimization of Regional Water-Energy-Food Systems Based on Interval Number Multi-Objective Programming: A Case Study of Ordos, China

“…Interval number programming expresses the uncertainty of parameters in the form of interval numbers [ 42 ]. In the optimization of interval number programming, the possible variation range of any uncertain parameter is represented by an interval, which is only the upper and lower limits of the parameter need to be known, and the precise probability distribution or fuzzy membership function is not needed [ 43 ]. The interval range covers a variety of advantages in terms of uncertainty and complexity [ 44 ].…”