out of local areas by increasing diversity - but the acceleration effect is not obvious.
Conversely, the aggregate growth strategy can accelerate the convergence speed of the population significantly, but it may may lead to a population falling into local areas as mentioned above. The combination of both strategies, however, can balance their shortcomings and achieve better performance. Furthermore, in any case we can say that our proposals are low cost, high return strategies.
We apply the Friedman test and the Holm multiple comparison test among the four variants to check for significant difference. From the results of statistical test, the aggregate growth strategy demonstrated better acceleration than the mutation strategy in lower dimensions. However, the mutation strategy shows stronger effects in some cases with an increase in the number of dimensions. This is because the probability of a high-dimensional individual experiencing mutation becomes higher;
the higher the dimension, the more obvious the effect therefore is. For F15 and F16, our proposal has not played any role, and even worsened the performance. It may be because there are too many local optima, and these have made our proposal fall into local optima and hindered evolution. This indicates to us that for such problems, increasing randomness may be beneficial in that it allows the population to jump out of the local optima. More detailed explanations require our further analysis, which will allow us to develop more suitable strategies for VEGE.
plants, such as e.g. a dynamic population mechanism and adaptive parameter tun-ing, to improving the performance of VEGE and use it to solve many real world applications.
Chapter 10
Discussions and Conclusions
10.1 Main Contribution
Since EC has been applied to various industrial problems and achieved great success, many practitioners try to further improve its performance to solve new and complex problems. How to theoretically enhance the performance of EC algorithm has thus become one of the most promising research topics. The main contribution of this dissertation is to track this topic within three research directions, and to propose multiple strategies to accelerate EC algorithms in each of those direction.
The first direction is to use estimated convergence point(s) as elite individual(s) to accelerate EC algorithms from a new perspective. The basic estimation method uses evolutionary information from two consecutive generations rather than mul-tiple iterations of the population to find the possible area of the global optimum.
Not limited to a particular EC algorithm, the basic estimation method can be com-bined with any EC algorithm without changing the original optimization framework.
Although an additional fitness calculation is needed to evaluate the estimated con-vergence point, when it has high accuracy and is close to the optimum, it can help save a lot of resources and converge the optimum quickly in later generations. When it is not close to the global optimum, the elite may unfortunately not be remark-able - but it is still better than the worst individual which it replaces. We can say that the basic estimation method is a low risk, high return strategy and makes an innovative contribution to the EC community. In this dissertation, we extend the basic estimation method to multimodal and multi-objective tasks, discuss the possibility of using it in IEC, and propose new strategies to improve the precision of the estimated convergence point. There are still many valuable research topics in this direction which deserve further attention.
The second direction is to analyze the characteristics of existing EC algorithms and then propose targeted improvement strategies to overcome their original short-comings and improve performance. In this dissertation, we focus on developing variants of FWA and DE by integrating proposed strategies. Taking FWA as an example, we propose new explosion strategies which use local fitness information to better guide evolution, and integrate competitive strategies into DE to quickly eliminate poorer individuals. Generally, most practitioners are more committed to improving the performance of existing EC algorithms as opposed to developing a new one. Although it is difficult to make a breakthrough work via minor improvements,
once they receive sufficient attention, they can also speed up the spread of these EC algorithms into industry. Improving the performance of existing EC algorithms is thus of great significance and an important means to enrich the EC community.
The third direction is to develop a more powerful EC algorithm inspired by the growth of plants and the spread of their seeds. So far, most EC algorithms are inspired by biological evolution, natural phenomena, and human behavior; in each case, they repeatedly simulate the extracted mechanism from to find the global opti-mum. Few practitioners focus on obtaining inspiration from the widely distributed and very successful plants to propose a new optimization framework. Actually, plant life accounts for by far the most life on Earth, and plants are scattered every-where; they have evolved a variety of mechanisms to deal with complex environments through long-term evolution. In this dissertation, we roughly summarize the growth patterns of vegetation and propose a new population-based algorithm: VEGE. We hope that this work may attract the attention of other researchers, and various effective strategies can be drawn from natural plants to further improve VEGE performance, or even propose other new EC algorithms.
We use multiple benchmark functions that contain a variety of different char-acteristics extracted from real-world problems to evaluate the performance of our proposed strategies. The results of statistical tests indicate that all our propos-als have shown stronger performance in most cases and the performance is usually more prominent as the dimension increases. Besides, we realize that the estimation method has great potential to solve expensive problems because it can use very lit-tle information to estimate the optimal solution and omit a lot of fitness iterative process. Improving existing EC algorithms can help us understand the underlying optimization mechanism well, their advantages and disadvantages, understand their applicable scenarios, and help to design new EC algorithms. Finally, a vertical com-parison among various EC algorithms confirm that VEGE has stronger performance thanks to balance exploitation and exploration well by alternately emphasizing two different abilities. In short, the experimental results show that these strategies have more or less enhanced performance but still have room for improvement.