Multiple objectives to be optimized simultaneously are prevalent in real-life problems. This paper develops a new Pareto Method for bi-objective optimization which yields analytical solutions. The Pareto optimal front...Multiple objectives to be optimized simultaneously are prevalent in real-life problems. This paper develops a new Pareto Method for bi-objective optimization which yields analytical solutions. The Pareto optimal front is obtained in closed-form, enabling the derivation of various solutions in a convenient and efficient way. The advantage of analytical solution is the possibility of deriving accurate, exact and well-understood solutions, which is especially useful for policy analysis. An extension of the method to include multiple objectives is provided with the objectives being classified into two types. Such an extension expands the applicability of the developed techniques.展开更多
In this study, we visualize Pareto-optimum solutions derived from multiple-objective optimization using spherical self-organizing maps (SOMs) that lay out SOM data in three dimensions. There have been a wide range of ...In this study, we visualize Pareto-optimum solutions derived from multiple-objective optimization using spherical self-organizing maps (SOMs) that lay out SOM data in three dimensions. There have been a wide range of studies involving plane SOMs where Pareto-optimal solutions are mapped to a plane. However, plane SOMs have an issue that similar data differing in a few specific variables are often placed at far ends of the map, compromising intuitiveness of the visualization. We show in this study that spherical SOMs allow us to find similarities in data otherwise undetectable with plane SOMs. We also implement and evaluate the performance using parallel sphere processing with several GPU environments.展开更多
In this article, a novel scalarization technique, called the improved objective-constraint approach, is introduced to find efficient solutions of a given multiobjective programming problem. The presented scalarized pr...In this article, a novel scalarization technique, called the improved objective-constraint approach, is introduced to find efficient solutions of a given multiobjective programming problem. The presented scalarized problem extends the objective-constraint problem. It is demonstrated that how adding variables to the scalarized problem, can lead to find conditions for (weakly, properly) Pareto optimal solutions. Applying the obtained necessary and sufficient conditions, two algorithms for generating the Pareto front approximation of bi-objective and three-objective programming problems are designed. These algorithms are easy to implement and can achieve an even approximation of (weakly, properly) Pareto optimal solutions. These algorithms can be generalized for optimization problems with more than three criterion functions, too. The effectiveness and capability of the algorithms are demonstrated in test problems.展开更多
文摘Multiple objectives to be optimized simultaneously are prevalent in real-life problems. This paper develops a new Pareto Method for bi-objective optimization which yields analytical solutions. The Pareto optimal front is obtained in closed-form, enabling the derivation of various solutions in a convenient and efficient way. The advantage of analytical solution is the possibility of deriving accurate, exact and well-understood solutions, which is especially useful for policy analysis. An extension of the method to include multiple objectives is provided with the objectives being classified into two types. Such an extension expands the applicability of the developed techniques.
文摘In this study, we visualize Pareto-optimum solutions derived from multiple-objective optimization using spherical self-organizing maps (SOMs) that lay out SOM data in three dimensions. There have been a wide range of studies involving plane SOMs where Pareto-optimal solutions are mapped to a plane. However, plane SOMs have an issue that similar data differing in a few specific variables are often placed at far ends of the map, compromising intuitiveness of the visualization. We show in this study that spherical SOMs allow us to find similarities in data otherwise undetectable with plane SOMs. We also implement and evaluate the performance using parallel sphere processing with several GPU environments.
文摘In this article, a novel scalarization technique, called the improved objective-constraint approach, is introduced to find efficient solutions of a given multiobjective programming problem. The presented scalarized problem extends the objective-constraint problem. It is demonstrated that how adding variables to the scalarized problem, can lead to find conditions for (weakly, properly) Pareto optimal solutions. Applying the obtained necessary and sufficient conditions, two algorithms for generating the Pareto front approximation of bi-objective and three-objective programming problems are designed. These algorithms are easy to implement and can achieve an even approximation of (weakly, properly) Pareto optimal solutions. These algorithms can be generalized for optimization problems with more than three criterion functions, too. The effectiveness and capability of the algorithms are demonstrated in test problems.
