Multi-objective immune genetic algorithm solving nonlinear interval-valued programming

This work studies one multi-objective immune genetic algorithm with small population to solve a general kind of unconstrained multi-objective interval-valued programming. In this optimization approach, those competitive individuals are discriminated based on interval arithmetic rules and a possibility model; a crowding degree model in interval-valued environments is developed to eliminate redundant individuals; the current population promotes different individuals to evolve towards specific directions by population sorting and immune evolution, while those elitist individuals found accelerate to explore the desired regions through genetic evolution. The theoretical analysis has showed that the computational complexity of the proposed approach depends mainly on the elitist population size. Comparative experiments have illustrated that the approach can take a rational tradeoff between effect and efficiency. It can perform well over the compared approaches as a whole, and has the potential to solving multi-modal and hard multi-objective interval-valued programming problems. A general unconstrained multi-objective interval-valued programming is solved.A crowding degree model is developed to measure the crowding degrees of individuals in interval environments.A multi-objective immune genetic approach is designed to handle multi-objective interval-valued problems.The computational complexity of the approach is studied expensively.A test set is acquired based on the reported benchmark problems with different characteristics. This, along with an engineering example, is used to help us examine the performances of both the approach and several compared algorithms. Display Omitted