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Interactive Decision Maps
The Interactive Decision Maps technique of multi-objective optimization is based on approximating the Edgeworth-Pareto Hull (EPH) of the feasible objective set, that is, the feasible objective set broadened by the objective points dominated by it. Alternatively, this set is known as Free Disposal Hull. It is important that the EPH has the same Pareto front as the feasible objective set, but the bi-objective slices of the EPH look much simpler. The frontiers of bi-objective slices of the EPH contain the slices of the Pareto front. It is important that, in contrast to the Pareto front itself, the EPH is usually stable in respect to disturbances of data. The IDM technique applies fast on-line display of bi-objective slices of the EPH approximated in advance. Since the bi-objective slices of the EPH for two selected objectives are extending (or shrinking) monotonically, while the value of one of the other objectives (the "third" objective) changes monotonically, the frontiers of the sl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Multi-objective Optimization
Multi-objective optimization (also known as multi-objective programming, vector optimization, multicriteria optimization, multiattribute optimization or Pareto optimization) is an area of multiple criteria decision making that is concerned with mathematical optimization problems involving more than one objective function to be optimized simultaneously. Multi-objective optimization has been applied in many fields of science, including engineering, economics and logistics where optimal decisions need to be taken in the presence of trade-offs between two or more conflicting objectives. Minimizing cost while maximizing comfort while buying a car, and maximizing performance whilst minimizing fuel consumption and emission of pollutants of a vehicle are examples of multi-objective optimization problems involving two and three objectives, respectively. In practical problems, there can be more than three objectives. For a nontrivial multi-objective optimization problem, no single solutio ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Francis Ysidro Edgeworth
Francis Ysidro Edgeworth (8 February 1845 – 13 February 1926) was an Anglo-Irish philosopher and political economist who made significant contributions to the methods of statistics during the 1880s. From 1891 onward, he was appointed the founding editor of ''The Economic Journal''. Life Ysidro Francis Edgeworth- the order of his forenames later reversed- was born in Edgeworthstown, County Longford, Ireland, son of Francis Beaufort Edgeworth and his wife, Rosa Florentina, daughter of Catalan general Antonio Eroles. Francis Beaufort Edgeworth, when "a restless philosophy student at Cambridge on his way to Germany", had met Rosa, a teenage Spanish refugee, on the steps of the British Museum, and they subsequently eloped. Francis Beaufort Edgeworth was son of the politician, writer, and inventor Richard Lovell Edgeworth (father also of the writer Maria Edgeworth), by his fourth wife, the botanical artist and memoirist Frances Anne, daughter of the Anglican clergyman and geog ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Interactive Decision Maps Screen Shot
Across the many fields concerned with interactivity, including information science, computer science, human-computer interaction, communication, and industrial design, there is little agreement over the meaning of the term "interactivity", but most definitions are related to interaction between users and computers and other machines through a user interface. Interactivity can however also refer to interaction between people. It nevertheless usually refers to interaction between people and computers – and sometimes to interaction between computers – through software, hardware, and networks. Multiple views on interactivity exist. In the "contingency view" of interactivity, there are three levels: #Not interactive, when a message is not related to previous messages. #Reactive, when a message is related only to one immediately previous message. #Interactive, when a message is related to a number of previous messages and to the relationship between them. One body of research ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Convex Polytope
A convex polytope is a special case of a polytope, having the additional property that it is also a convex set contained in the n-dimensional Euclidean space \mathbb^n. Most texts. use the term "polytope" for a bounded convex polytope, and the word "polyhedron" for the more general, possibly unbounded object. Others''Mathematical Programming'', by Melvyn W. Jeter (1986) p. 68/ref> (including this article) allow polytopes to be unbounded. The terms "bounded/unbounded convex polytope" will be used below whenever the boundedness is critical to the discussed issue. Yet other texts identify a convex polytope with its boundary. Convex polytopes play an important role both in various branches of mathematics and in applied areas, most notably in linear programming. In the influential textbooks of Grünbaum and Ziegler on the subject, as well as in many other texts in discrete geometry, convex polytopes are often simply called "polytopes". Grünbaum points out that this is solely to avoi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Vilfredo Pareto
Vilfredo Federico Damaso Pareto ( , , , ; born Wilfried Fritz Pareto; 15 July 1848 – 19 August 1923) was an Italian polymath (civil engineer, sociologist, economist, political scientist, and philosopher). He made several important contributions to economics, particularly in the study of income distribution and in the analysis of individuals' choices. He was also responsible for popularising the use of the term "elite" in social analysis. He introduced the concept of Pareto efficiency and helped develop the field of microeconomics. He was also the first to discover that income follows a Pareto distribution, which is a power law probability distribution. The Pareto principle was named after him, and it was built on his observations that 80% of the wealth in Italy belonged to about 20% of the population. He also contributed to the fields of sociology and mathematics. According to the mathematician Benoit Mandelbrot and Richard L. Hudson: Biography Pareto was born of an e ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Multiple-criteria Decision Analysis
Multiple-criteria decision-making (MCDM) or multiple-criteria decision analysis (MCDA) is a sub-discipline of operations research that explicitly evaluates multiple conflicting criteria in decision making (both in daily life and in settings such as business, government and medicine). Conflicting criteria are typical in evaluating options: cost or price is usually one of the main criteria, and some measure of quality is typically another criterion, easily in conflict with the cost. In purchasing a car, cost, comfort, safety, and fuel economy may be some of the main criteria we consider – it is unusual that the cheapest car is the most comfortable and the safest one. In portfolio management, managers are interested in getting high returns while simultaneously reducing risks; however, the stocks that have the potential of bringing high returns typically carry high risk of losing money. In a service industry, customer satisfaction and the cost of providing service are fundamen ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
