Intelligent Optimization Approaches Solving Multi-objective Interval-valued Programming

With the frequent appearance of uncertain programming problems, multi-objective interval-valued programming problems will become more and more important, as they include interval coefficients and multiple sub-objectives to be optimized simultaneously. However, since such kind of problem is extremely difficult in seeking its Pareto optimal solutions, few breakthrough achievements have been reported in the literature. Based the fact that multi-objective interval problems have comprehensive engineering application background and scientific value, this dissertation, inspired by some response metaphors of immune systems, probes into immune genetic algorithms and immune optimization ones for solving non-constrained or constrained multi-objective interval-valued programming and non-constrained many-subobjective intervalvalued programming problems, while some studies are made with respect to computational complexity, numerical experiments, and so on. The main work and achievements acquired are summarized below.A. An immune genetic algorithm is developed to cope with the problem of non-constrained bi-objective interval-valued programming. In the design of algorithm, those competitive individuals are discriminated by means of interval arithmetic rules, possibility models and non-dominated sorting. A crowding degree model, based on the position relation between rectangles in the objective space, is designed to eliminate redundant individuals presented in the process of evolution. Additionally, the current population is divided into superior and inferior sub-populations among which each moves along specific directions, relying upon population division and immune evolution. After collecting superior individuals, the elitist population accelerates to transform its individuals towards the desired region in which Pareto optimal solutions exist, based on genetic evolution models. The algorithm has some merits such as micro population, few parameters and structural simplicity. The computational complexity analysis has demonstrated that the complexity of the algorithm is decided by the size of the elitist population. The comparative experiments have showed that the proposed algorithm has the potential to solving complex bi-objective interval-valued programming problems.B. For the problem of bi-objective interval-valued programming with interval constraints, an immune optimization algorithm is designed. In this problem, those constraints of interval equalities and inequalities are converted into deterministic constraints through interval possibility models, and further one such problem is transformed into non-constrained interval-valued programming problems. In this approach, the current population is divided into feasible and infeasible sub-populations according to individuals' constraint violations. Afterwards, different kinds of individuals evolve along different directions according to their important levels. The computational complexity analysis has demonstrated that the complexity of the approach is determined by the size of the elitist population. The numerical experiments have showed that the population division scheme can effectively enhance the ability of population evolution and guide the current population to move towards the region in which Pareto optimal solutions exist. In other words, one such algorithm is effective for complex bi-objective interval-valued problems with interval constraints.C. An immune genetic algorithm is constructed to handle with non-constrained many-objective interval-valued programming problems, based on a new model of individual dominance and immune response inspirations. In this approach, those redundant individuals are deleted by means of a reported crowding degree model. The current population is divided into superior and inferior sub-populations according to individual importance, among which each sub-population finds high-quality and diverse individuals through special operators of immune and genetic evolution. The comparative experiments have illustrated that the proposed algorithm can effectively acquire some solutions sets with uniform distributions and wide coverage scopes and also has the potential to complex many-objective interval-valued problems.