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Differential Evolution (DE) is a population-based algorithm that belongs to the Evolutionary algorithm family. During recent years, DE has become a popular algorithm in optimization due to its strength solving different types of optimization problems and due to its easy usage and implementation.

However, how to choose proper mutation strategy and control parameters for DE presents a major difficulty in many real applications. Since both mutation strategy and DE control parameters are highly problem dependent, they have to be adapted to suite different search spaces and different problems. Failure in proper assignment for them will cause slow convergence in search or stagnation with a local optimum.

Many researches have been conducted to tackle the above issues. The major efforts have been made in the following three directions. First, some works have been proposed that adapt the selection between various mutation strategies. But the choice of strategies in these methods has not considered the difference of quality of individuals in the population, which means that all individuals will acquire the same probability to select a mutation strategy from the candidates. This does not seem a very desired practice since solutions of large difference would require different mutation operators to reach improvement. Second, many works have been focusing on the adaptation of the control parameters of DE (mutation factor (F) and crossover rate (CR)). They mainly rely on previous successful F and CR values to update the probability functions that are used to generate new F and CR values. By doing this, they ignore the stochastic nature of the operators in DE such that weak F and CR values can also get success in producing better trial solutions. The use of such imprecise experiences of success would prevent the DE parameters from being adapted towards the most effective values in coming generations. Third, various local search methods have been incorporated into DE to enhance exploitation in promising regions so as to speed up the convergence to optima. It is important to properly adjust the characteristics of the local search in DE to achieve well balanced exploratory/exploitative behavior to solve complex optimization problems.

This thesis aims to further improve the performance of DE by new adaptation and local search methods. The main results can be summarized in the following three aspects:

1) Proposal of a new rank-based mutation adaptation method, which takes into account the quality of solutions in the population when adapting the selection probabilities of mutation strategies. This makes possible to treat solutions with distinct ranks (in quality) differently by using different selection probabilities for mutation operators.

2) Development of improved parameter adaptation methods for DE, which emphasizes more reliable and fair evaluation of candidates (F and CR assignments) during the search process. It is suggested that greedy search being used as a fast and cheap technique to look for better parameter assignment for F and CR respectively in the neighborhood of a current candidate. Further, a joint parameter adaptation method is proposed that enables continuous update of the selection probabilities for F and CR pairs based on feedback acquired during the search.

3) Proposal of new methods for better incorporation of local search into a DE algorithm. The Eager Random Search method is investigated as local search inside DE, which exhibits different exploratory-exploitative characteristics by using different probability density functions. More importantly, we propose a novel memetic framework in which Alopex local search (ALS) is performed in collaboration with a DE algorithm. The framework favors seamless connection between exploration and exploitation in the sense that the behavior of exploitation by ALS can be controlled by the status of global exploration by DE.

The proposed methods and algorithms have been tested in a number of benchmark problems, obtaining competitive results compared with the state-of-the-art algorithms. Additionally, the Greedy Adaptive DE (GADE) algorithm (developed based on greedy search for DE parameters) has been tested in a real industrial problem, i.e., finding best component parameters to optimize the performance of harmonic filters for power transmission. GADE is shown to produce better harmonic filter systems with lower harmonic distortion than the standard DE.