Immune Optimization Algorithms For Solving Chance Constrained P-Model And Its Applications

Chance constrained programming with comprehensive engineering application background is a stochastic programming problem with chance constraints, including probabilistic optimization which the objective function is subject to a special probabilistic inequality. Based on a fact that uncertain programming problems with stochastic factors frequently appear in engineering applications, an important topic, i.e., studying optimization approaches to solve probabilistic optimization problems, will become popular in the field of optimization because of few achievements. This dissertation, inspired by immunological characteristics and immune response mechanisms focuses on probing into several types of immune optimization approaches for solving non-constrained or constrained single or multi-objective probabilistic optimization models. Some theoretical analyses, comparative experiments and applications are made. The main works and some achievements acquired are summarized as follows:A. An adaptive sampling based micro-population immune optimization approach is developed to address non-constrained single-objective probabilistic optimization problems. In this approach, an implicit parallel optimization mechanism is designed based on the popular immune theory in immunology- danger theory. Those competitive individuals in the current population are discriminated by an adaptive sampling method, while the danger zones of individuals and individual sub-populations are determined through dynamically adjusting individuals' hazard radiuses. Multiple kinds of mutation strategies are adopted to guide that different individuals perform global and local search with multiple directions. Theoretically, the computational complexity of the algorithm depends on its iterative number, problem dimension and population size. It has the merits of small population, few adjustable parameters, structural simplicity, and so on. Finally, by virtue of some theoretical test examples and a bus scheduling problem, the comparative experiments have showed that the proposed approach has some advantages of solution quality, noisy suppression and execution efficiency, and also the potential to complex probabilistic optimization problems.B. Another adaptive sampling based micro-population immune optimization algorithm is designed to handle constrained single-objective probabilistic optimization problems. In this algorithm, some inherent immune metaphors and mechanisms from the danger theory are used to execute population division by means of danger radius update. A constrained handling scheme is constructed to estimate the probabilities of individuals, while those reliable individuals get their sample sizes through an adaptive sampling scheme. Those high-quality individuals are produced through mutation and intercommunication. The computational complexity analysis has showed that the complexity of the algorithm is determined by multiple factors. The comparative experiments have illustrated that the algorithm, with the merits of few adjustable parameters, structural simplicity, practicality and so forth, can work well over the compared approaches and has the potential to constrained engineering optimization problems.C. For constrained multi-objective probabilistic optimization problems, an adaptive samplingbased multi-objective immune optimization algorithm is proposed tentatively. In this algorithm design, the probabilities of individuals and the sample sizes of non-dominated individuals are estimated and decided by the above constraint handling and adaptive sampling approaches, respectively. After the current population is divided into non-dominated and dominated sub-populations, those non-dominated individuals are enforced the Gaussian mutation in order to find high-quality individuals, while those dominated individuals move towards multiple directions so that diverse individuals are produced. The complexity analysis has showed that the computational complexity of the algorithm is determined by individuals' sanple sizes and algorithm iterative number. The comparative numerical experiments can draw a conclusion that the algorithm is of satisfactory population diversity and the capability of strong evolution and also has the potential value to multi-objective engineering optimization problems.