Certain investigations on optimization problems and their applications

Abstract

Optimization is a procedure of finding and comparing feasible newlinesolutions until no better solution can be found. A significant portion of research newlineand application in the field of optimization considers a single objective, although newlinemost real-world problems involve more than one objective. Such problems newlineare solved by a number of mathematical methods. Those approaches are newlineclassified as traditional and evolutionary approaches. Classical optimization newlinemethods can at best find one solution in one simulation run, there by making newlinethose methods inconvenient to solve multi-objective optimization problems. newlineEvolutionary algorithms, on the other hand, can find multiple optimal solutions newlinein one single simulation run due to their population approach. Therefore, newlineevolutionary approaches are designed to provide better and optimal solutions newlineto complex problems. Traditional optimization techniques and methods have newlinebeen successfully applied for years to solve problems with a well-defined newlinestructure/configuration, sometimes known as hard systems. Unfortunately, newlinereal-world situations are often not deterministic. There exist various types of newlineuncertainties in social, industrial, and economic systems, such as imprecision newlineand ambiguity of system data and linguistic vagueness, etc. These due to various newlinereasons, including errors of measurement, deficiency in history and statistical newlinedata, insufficient theory, incomplete knowledge expression, and the subjectivity newlineand preference of judgment, etc. Fuzzy set theory is allowed to solve newline