Related Research Articles
Pareto efficiency or Pareto optimality is a situation where no action or allocation is available that makes one individual better off without making another worse off. The concept is named after Vilfredo Pareto (1848–1923), Italian civil engineer and economist, who used the concept in his studies of economic efficiency and income distribution. The following three concepts are closely related:
Mathematical optimization or mathematical programming is the selection of a best element, with regard to some criterion, from some set of available alternatives. It is generally divided into two subfields: discrete optimization and continuous optimization. Optimization problems of sorts arise in all quantitative disciplines from computer science and engineering to operations research and economics, and the development of solution methods has been of interest in mathematics for centuries.
In computational intelligence (CI), an evolutionary algorithm (EA) is a subset of evolutionary computation, a generic population-based metaheuristic optimization algorithm. An EA uses mechanisms inspired by biological evolution, such as reproduction, mutation, recombination, and selection. Candidate solutions to the optimization problem play the role of individuals in a population, and the fitness function determines the quality of the solutions. Evolution of the population then takes place after the repeated application of the above operators.
In computational science, particle swarm optimization (PSO) is a computational method that optimizes a problem by iteratively trying to improve a candidate solution with regard to a given measure of quality. It solves a problem by having a population of candidate solutions, here dubbed particles, and moving these particles around in the search-space according to simple mathematical formula over the particle's position and velocity. Each particle's movement is influenced by its local best known position, but is also guided toward the best known positions in the search-space, which are updated as better positions are found by other particles. This is expected to move the swarm toward the best solutions.
A fitness function is a particular type of objective function that is used to summarise, as a single figure of merit, how close a given design solution is to achieving the set aims. Fitness functions are used in evolutionary algorithms (EA), such as genetic programming and genetic algorithms to guide simulations towards optimal design solutions.
Multi-disciplinary design optimization (MDO) is a field of engineering that uses optimization methods to solve design problems incorporating a number of disciplines. It is also known as multidisciplinary system design optimization (MSDO), and Multidisciplinary Design Analysis and Optimization (MDAO).
In computer science and mathematical optimization, a metaheuristic is a higher-level procedure or heuristic designed to find, generate, or select a heuristic that may provide a sufficiently good solution to an optimization problem, especially with incomplete or imperfect information or limited computation capacity. Metaheuristics sample a subset of solutions which is otherwise too large to be completely enumerated or otherwise explored. Metaheuristics may make relatively few assumptions about the optimization problem being solved and so may be usable for a variety of problems.
In mathematical folklore, the "no free lunch" (NFL) theorem of David Wolpert and William Macready appears in the 1997 "No Free Lunch Theorems for Optimization". Wolpert had previously derived no free lunch theorems for machine learning. The name alludes to the saying "there ain't no such thing as a free lunch", that is, there are no easy shortcuts to success.
In computational complexity and optimization the no free lunch theorem is a result that states that for certain types of mathematical problems, the computational cost of finding a solution, averaged over all problems in the class, is the same for any solution method. The name alludes to the saying "there ain't no such thing as a free lunch", that is, no method offers a "short cut". This is under the assumption that the search space is a probability density function. It does not apply to the case where the search space has underlying structure that can be exploited more efficiently than random search or even has closed-form solutions that can be determined without search at all. For such probabilistic assumptions, the outputs of all procedures solving a particular type of problem are statistically identical. A colourful way of describing such a circumstance, introduced by David Wolpert and William G. Macready in connection with the problems of search and optimization, is to say that there is no free lunch. Wolpert had previously derived no free lunch theorems for machine learning. Before Wolpert's article was published, Cullen Schaffer independently proved a restricted version of one of Wolpert's theorems and used it to critique the current state of machine learning research on the problem of induction.
In computer science and operations research, Genetic fuzzy systems are fuzzy systems constructed by using genetic algorithms or genetic programming, which mimic the process of natural evolution, to identify its structure and parameter.
In multi-objective optimization, the Pareto front is the set of all Pareto efficient solutions. The concept is widely used in engineering. It allows the designer to restrict attention to the set of efficient choices, and to make tradeoffs within this set, rather than considering the full range of every parameter.
Multi-objective 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.
Group method of data handling (GMDH) is a family of inductive algorithms for computer-based mathematical modeling of multi-parametric datasets that features fully automatic structural and parametric optimization of models.
OptiY is a design environment software that provides modern optimization strategies and state of the art probabilistic algorithms for uncertainty, reliability, robustness, sensitivity analysis, data-mining and meta-modeling.
Red Cedar Technology is a software development and engineering services company. Red Cedar Technology was founded by Michigan State University professors Ron Averill and Erik Goodman in 1999. The headquarters is located in East Lansing, Michigan, near MSU's campus. Red Cedar Technology develops and distributes the HEEDS Professional suite of design optimization software. HEEDS is based on spin-out technology from Michigan State University. On June 30, 2013 Red Cedar Technology was acquired by CD-adapco. CD-adapco was acquired in 2016 by Siemens Digital Industries Software.
Optimus is a Process Integration and Design Optimization (PIDO) platform developed by Noesis Solutions. Noesis Solutions takes part in key research projects, such as PHAROS and MATRIX.
The MOEA Framework is an open-source evolutionary computation library for Java that specializes in multi-objective optimization. It supports a variety of multiobjective evolutionary algorithms (MOEAs), including genetic algorithms, genetic programming, grammatical evolution, differential evolution, and particle swarm optimization. As a result, it has been used to conduct numerous comparative studies to assess the efficiency, reliability, and controllability of state-of-the-art MOEAs.
David Hilton Wolpert is an American mathematician, physicist and computer scientist. He is a professor at Santa Fe Institute. He is the author of three books, three patents, over one hundred refereed papers, and has received numerous awards. His name is particularly associated with a group of theorems in computer science known as "no free lunch".
optiSLang is a software platform for CAE-based sensitivity analysis, multi-disciplinary optimization (MDO) and robustness evaluation. It is developed by Dynardo GmbH and provides a framework for numerical Robust Design Optimization (RDO) and stochastic analysis by identifying variables which contribute most to a predefined optimization goal. This includes also the evaluation of robustness, i.e. the sensitivity towards scatter of design variables or random fluctuations of parameters. In 2019, Dynardo GmbH was acquired by Ansys.
References
- ↑ "www.cyberdyne.it". Cyber Dyne s.r.l.
- ↑ Iacca, Giovanni; Mininno, Ernesto (2016), "Introducing Kimeme, a Novel Platform for Multi-disciplinary Multi-objective Optimization", Communications in Computer and Information Science, Springer International Publishing, pp. 40–52, doi:10.1007/978-3-319-32695-5_4, hdl: 11572/196443 , ISBN 9783319326948
- ↑ Wolpert, D.H., Macready, W.G. (1997), "No Free Lunch Theorems for Optimization," IEEE Transactions on Evolutionary Computation1, 67. http://ti.arc.nasa.gov/m/profile/dhw/papers/78.pdf
- ↑ Neri, F. & Cotta, C. 2011. "A primer on memetic algorithms". In "F. Neri, C. Cotta & P. Moscato (Eds.) Handbook of Memetic Algorithms", "Springer. Studies in Computational Intelligence".
- ↑ Saltelli, A., Chan, K. and Scott, E.M.: Sensitivity Analysis. John Wiley & Sons Chichester, New York 2000
- ↑ Oakley J.E., O´Hagan A.: Probabilistic Sensitivity Analysis of Computer Models: a Bayesian Approach. Journal of the Royal Statistical Society, Series B, 66:751-769, 2004