Design optimization of broadband extreme ultraviolet polarizer in high-dimensional objective space

With the purpose of designing the extreme ultraviolet polarizer with many objectives, a combined application of multiobjective genetic algorithms is theoretically proposed. Owing to the multiobjective genetic algorithm, the relationships between different designing objectives of extreme ultraviolet polarizer have been obtained by analyzing the distribution of nondominated solutions in the 4D objective space, and the optimized multilayer design can be obtained by guiding the searching in the desired region based on the multiobjective genetic algorithm with reference direction. Comparing with the conventional method of multilayer design, our method has a higher probability of achieving the optimal multilayer design. Our work should be the first research in optimizing the optical multilayer designs in the high-dimensional objective space, and our results demonstrate a potential application of our method in the designs of optical thin films.

Improving the Performance of Multiobjective Genetic Algorithms: An Elitism-Based Approach

Today, many complex multiobjective problems are dealt with using genetic algorithms (GAs). They apply the evolution mechanism of a natural population to a “numerical” population of solutions to optimize a fitness function. GA implementations must find a compromise between the breath of the search (to avoid being trapped into local minima) and its depth (to prevent a rough approximation of the optimal solution). Most algorithms use “elitism”, which allows preserving some of the current best solutions in the successive generations. If the initial population is randomly selected, as in many GA packages, the elite may concentrate in a limited part of the Pareto frontier preventing its complete spanning. A full view of the frontier is possible if one, first, solves the single-objective problems that correspond to the extremes of the Pareto boundary, and then uses such solutions as elite members of the initial population. The paper compares this approach with more conventional initializations by using some classical tests with a variable number of objectives and known analytical solutions. Then we show the results of the proposed algorithm in the optimization of a real-world system, contrasting its performances with those of standard packages.

Optical Satellite Multiobjective Genetic Algorithms for Investigation of MH370 Debris

At present, there is no precise method that can inform where the lost flight MH370 is. This chapter proposes a new approach to search for the missing flight MH370. To this end, multiobjective genetic algorithms are implemented. In this regard, a genetic algorithm is taken into consideration to optimize the MH370 debris that is notably based on the geometrical shapes and spectral signatures. Currently, there may be three limitations to optical remote sensing technique: (1) strength constraints of the spacecraft permit about two hours of scanning consistently within the day, (2) cloud cover prevents unique observations, and (3) moderate information from close to the ocean surface is sensed through the scanner. Needless to say that the objects that are spotted by different satellite data do not scientifically belong to the MH370 debris and could be just man-made without accurate identifications.

Multiobjective Genetic Algorithms for Reinforcing Equal Population in Congressional Districts

Redistricting is the process of partitioning a set of basic units into a given number of larger groups for electoral purposes. These groups must follow federal and state requirements to enhance fairness and minimize the impact of manipulating boundaries for political gain. In redistricting tasks, one of the most important criteria is equal population. As a matter of fact, redistricting plans can be rejected when the population deviation exceeds predefined limits. In the literature, there are several methods to balance population among districts. However, further discussion is needed to assess the effectiveness of these strategies. In this paper, we considered two different strategies, mean deviation and overall range. Additionally, a compactness measure is included to design well-shaped districts. In order to provide a wide set of redistricting plans that achieve good trade-offs between mean deviation, overall range, and compactness, we propose four multiobjective metaheuristic algorithms based on NSGA-II and SPEA-II. The proposed strategies were applied in California, Texas, and New York. Numerical results show that the proposed multiobjective approach can be a very valuable tool in any real redistricting process.