Diversity Of Solution Set Research Articles

MaOEA/D with adaptive external population guided weight vector adjustment

In order to make multiobjective evolutionary algorithm based on decomposition (MOEA/D) have better performance in dealing with many-objective optimization problems (MaOPs) with different Pareto fronts (PFs), this paper proposes a MOEA/D with adaptive external population guided weight vector adjustment (MaOEA/D-AEW). The algorithm modifies the MOEA/D method of constructing mating pools by calculating the utility function value of individuals in the population to produce high-quality offspring. For the maintenance of non-dominated solutions in the external population (EP), solutions exceeding the capacity of the EP are removed by the method of minimum Euclidean distance combined with the aggregation function value to ensure the convergence and diversity of non-dominated solutions in the EP. For the addition of weight vectors, a new sparsity evaluating method (SL+) is proposed to determine the sparsity of weight vectors by multiplying parallel distances between individuals. For the deletion of the weight vector, the minimum Euclidean distance combined with the aggregation function value is used to delete the weight vector corresponding to invalid or crowded individuals in the population. Comparing MaOEA/D-AEW with six state-of-the-art algorithms on regular PF and irregular PF test problems respectively, simulation results show that the proposed algorithm can adapt well to MaOPs with different PFs and significantly outperforms other comparative algorithms in terms of convergence and diversity of solution sets.

Research on Forecast of Macroeconomic Indicators Based on Multiobjective Optimization

In recent years, with China’s economic development entering a new normal, the total scale and complexity of economic development have increased unprecedentedly, and the requirements of government management and regulation of the economy are getting higher and higher. Traditional management concepts, methods, and tools are difficult to meet the needs of the new situation. Therefore, using computer science and technology to fully consider the correlation between various industries and explore new laws of economic operation under the new normal can provide new technical support for promoting the precision of government governance. In previous studies, Most of them take statistics and econometrics as the theoretical basis of macroeconomic decision-making research. This study is based on the analysis of the relationship between the macroeconomic indicators, the establishment of forecasting models to predict the trend of the macroeconomic indicators, and according to the relationship between various economic indicators to build a multiobjective optimization problem, through the multiobjective optimization algorithm to obtain optimal data for the government decision-making basis. In the research process, we focus on solving the problem of prediction overfitting caused by small samples of economic index data and high feature dimension of samples and how to balance the convergence and diversity of solution set in high-dimensional multiobjective optimization problems. In view of the above problems, we propose two economic index forecasting models to solve a variety of fitting problems. On the premise of optimizing space decomposition, an adaptive generation strategy based on inflection point and center point is proposed, and an adaptive solution set selection strategy based on included angle, inflection point, and strong dominance relationship is proposed to balance the convergence and diversity of the multiobjective optimization algorithm.

A Discrete Multi-Objective Rider Optimization Algorithm for Hybrid Flowshop Scheduling Problem Considering Makespan, Noise and Dust Pollution

Many optimization algorithms have been proposed to solve hybrid flowshop scheduling problem (HFSP). However, with the development of industry and society, labor right and labor safety have become important problem to consider in production scheduling. So the green HFSP considering makespan, noise and dust pollution becomes an urgent problem to be solved. In this paper, the rider optimization algorithm (ROA) is modified into the multi-objective rider optimization algorithm (MOROA) using Pareto archive and neighborhood sorting techniques. The Pareto archive and neighborhood sorting technology make the Pareto optimal solution set of MOROA have higher coverage and more solutions. Then MOROA is discretized into discrete MOROA (DMOROA) to solve the HFSP considering makespan, noise and dust pollution. DMOROA is tested on 10, 30 and 50 jobs HFSP considering makespan, noise and dust pollution. The test results are compared with two multi-objective algorithms to verify the performance of DMOROA. And the test results verify that the DMOROA is superior to the comparison algorithms in search accuracy, number of non-dominated solutions, diversity of solution set and stability. Therefore, DMOROA is effective in solving multi-objective HFSP considering makespan, noise and dust pollution.

Comparing Ideation Techniques for Beginning Designers

Concept generation techniques can help to support designers in generating multiple ideas during design tasks. However, differences in the ways these techniques guide idea generation are not well understood. This study investigated the qualities of concepts generated by beginning engineering designers using one of three different idea generation techniques. Working individually on an open-ended engineering design problem, 102 first year engineering students learned and applied one of three different ideation techniques—design heuristics, morphological analysis, or individual brainstorming (using brainstorming rules to generate ideas working alone)—to a given design problem. Using the consensual assessment technique, all concepts were rated for creativity, elaboration, and practicality, and all participants' concept sets were rated for quantity and diversity. The simplest technique, individual brainstorming, led to the most concepts within the short (25 minute) ideation session. All three techniques produced creative concepts averaging near the scale midpoint. The elaboration of the concepts was significantly higher with design heuristics and morphological analysis techniques, and the practicality was significantly higher using design heuristics. Controlling for number of concepts generated, there were no significant differences in diversity of solution sets across groups. These results demonstrate that the use of design heuristics does not limit the creativity of ideation outcomes, and helps students to develop more elaborate and practical ideas. Design heuristics show advantages in the initial idea generation phase for beginning engineering students. These findings point to specific strengths in different ideation techniques, and the value of exposing beginning designers to multiple techniques for idea generation.

An Entropy-Based Multiobjective Evolutionary Algorithm with an Enhanced Elite Mechanism

Multiobjective optimization problem (MOP) is an important and challenging topic in the fields of industrial design and scientific research. Multi-objective evolutionary algorithm (MOEA) has proved to be one of the most efficient algorithms solving the multi-objective optimization. In this paper, we propose an entropy-based multi-objective evolutionary algorithm with an enhanced elite mechanism (E-MOEA), which improves the convergence and diversity of solution set in MOPs effectively. In this algorithm, an enhanced elite mechanism is applied to guide the direction of the evolution of the population. Specifically, it accelerates the population to approach the true Pareto front at the early stage of the evolution process. A strategy based on entropy is used to maintain the diversity of population when the population is near to the Pareto front. The proposed algorithm is executed on widely used test problems, and the simulated results show that the algorithm has better or comparative performances in convergence and diversity of solutions compared with two state-of-the-art evolutionary algorithms: NSGA-II, SPEA2 and the MOSADE.