A number of benchmark problems exist for evaluating multi-objective evolutionary algorithms (MOEAs) in the objective space. However, the decision space performance analysis is a recent and relatively less explored topic in evolutionary multi-objective optimization research. Among other implications, such analysis can lead to designing more realistic test problems, gaining better understanding about optimal and robust design areas, and design and evaluation of knowledge-based optimization algorithms. This paper complements the existing research in this area and proposes a new method to generate multi-objective optimization test problems with clustered Pareto sets in hyper-rectangular defined areas of decision space. The test problem is parametrized to control number of decision variables, number and position of optimal areas in the decision space and modality of fitness landscape. Three leading MOEAs, including NSGA-II, NSGA-III, and MOEA/D, are evaluated on a number of problem instances with varying characteristics. A new metric is proposed that measures the performance of algorithms in terms of their coverage of the optimal areas in the decision space. The empirical analysis presented in this research shows that the decision space performance may not necessarily be reflective of the objective space performance and that all algorithms are sensitive to population size parameter for the new test problems.
This paper puts forward for the first time a combined transmission matrix (TM) method to measure the monochromatic TM of scattering media without a reference beam. This method can be named a sequential semi-definite programming method which combines the sequential algorithm and the semi-definite programming method. Firstly, each part of the TM is calculated respectively in proper sequence. Then every part of TM is combined to form a complete TM in accordance with a certain rule. The phase modulation of the incident light is achieved by using a high speed digital mirror device with the superpixel method. We have experimentally demonstrated that the incident light field is focused at the target through scattering media using the measured TM to optimize the wavefront of the incident light. Compared with the semidefinite programming method, our method takes less computational time and occupies less memory space. The sequential semi-definite programming method shows potential applications in imaging through biological tissues.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.