ClearForest was an Israeli software company that developed and marketed text analytics and text mining solutions. == History == Founded in 1998, ClearForest had its headquarters just outside Boston and a development center in Or Yehuda. The company was acquired by Reuters in April, 2007. It now markets its services under the names Calais, OpenCalais, and OneCalais. ClearForest was previously venture-backed; its last funding round was led by Greylock Ventures and closed in 2005. Other investors included DB Capital Partners, Pitango, Walden Israel, Booz Allen, JP Morgan Partners and HarbourVest Partners. On February 7, 2008 Reuters announced the launch of Open Calais, a named-entity recognition and semantic analysis service that uses ClearForest technology. On April 30, 2007, Reuters announced that it would acquire ClearForest. Sources estimate the acquisition to be for $25 Million. == Solutions and products == ClearForest offers several hosted solutions, including: OpenCalais, a free web service and open API (for commercial and non-commercial use) that performs named-entity recognition and enables automatic metadata generation using the ClearForest financial module. Semantic Web Services (SWS), an on-demand service that makes ClearForest's natural language processing tools available as a standard web service. A subset of ClearForest's capabilities is available via SWS at no cost. Gnosis, a free Firefox extension that uses SWS to analyze the content of a web page. Gnosis identifies named entities such as people, companies, organizations, geographies and products on the page being viewed. Gnosis also automatically processes pages from Wikipedia, providing additional links for people, geographies and other entities which were not explicitly linked within the subject article. Harvest, a real-time machine-readable news service that uses SWS to process a company's news and document feeds and return machine-readable information about people, companies, locations and over 200 other entities facts and events. ClearForest also offers Text Analytics solutions targeted at specific business problems, including: Equity valuation for hedge funds and alternative investments firms Metadata & database creation for publishers and information providers/services Tapping "voice of customer" for market and survey research firms Quality Early Warning for vehicle, capital equipment & durable goods manufacturers
Aphelion (software)
The Aphelion Imaging Software Suite is a software suite that includes three base products - Aphelion Lab, Aphelion Dev, and Aphelion SDK for addressing image processing and image analysis applications. The suite also includes a set of extension programs to implement specific vertical applications that benefit from imaging techniques. The Aphelion software products can be used to prototype and deploy applications, or can be integrated, in whole or in part, into a user's system as processing and visualization libraries whose components are available as both DLLs or .Net components. == History and evolution == The development of Aphelion started in 1995 as a joint project of a French company, ADCIS S.A., and an American company, Amerinex Applied Imaging, Inc. (AAI) Aphelion's image processing and analysis functions were made from operators available from the KBVision software developed and sold by Amerinex's predecessor, Amerinex Artificial Intelligence Inc. In the 1990s, the XLim software library was developed at the Center of Mathematical Morphology of Mines ParisTech, and both companies carried out its development tasks. The first version of Aphelion was completed and released in April 1996. Successive versions were released before the first official stable release in December 1996 at the Photonics East conference in Boston and the Solutions Vision show in Paris in January 1997, where at the latter it competed with Stemmer Imaging's CVB imaging toolbox. In 1998, version 2.3 of Aphelion for Windows 98 was released, and its user base was growing in both France and the United States. Version 3.0, totally rewritten to take advantage of Microsoft's then-recent ActiveX technology, was officially released in 2000. It also became available as a « Developer » version, for rapid prototyping of applications using its intuitive GUI and the macro recording capability, and a « Core » version, including the full library as a set of ActiveX components to be used by software developers, integrators and original equipment manufacturers (OEM). As AAI turned its focus to security, in 2001, ADCIS took the lead on developing Aphelion. AAI focused on millimeter wave scanners for concealed weapon detection at airports, and eventually merged with Millimetrics to become Millivision. In 2004, ADCIS specified version 4.0 of Aphelion. The set of image processing/analysis functions was rewritten one more time to be compatible with the .NET technology and the emergence of 64 bit architecture PCs. In addition, the GUI was redesigned to address two usage types: a semi-automatic use where the user is guided through the different steps of functions, and a fully automatic use where the expert user can quickly invoke imaging functions. Its first release was presented at the IPOT exhibition in Birmingham, UK the same year. During the Vision Show in Paris in October 2008, the new Aphelion Lab product was launched for users that are not specialists in image processing. It is easier to use, and only includes fewer image processing functions. It was then included in the Aphelion Image Processing Suite, consisting of Aphelion Dev (replacing Aphelion Developer), Aphelion Lab, Aphelion SDK (replacing Aphelion Core), and a set of extensions. Nowadays, ADCIS is still working on the suite, and updated versions with new extensions and functionalities continually become available from the websites of both companies. In 2015, support was added for very large images and scan microscope images (virtual slides compound into a very large JPEG 2000 image) for high throughput imaging, and new specific extensions were also added. In late 2015, ADCIS announced Aphelion's port for tablets and smartphones, for vertical applications. The name "Aphelion" comes from the astronomical term of the same name, meaning the point on a planet rotating around the Sun where it lies farthest from it, applying the term in a metaphorical sense. Unix was the operating system used on scientific workstations in the 1990s, such as on the workstations manufactured by market leader Sun Microsystems, which Windows suite Aphelion was quite removed from. == Description == Aphelion is a software suite to be used for image processing and image analysis. It supports 2D and 3D, monochrome, color, and multi-band images. It is developed by ADCIS, a French software house located in Saint-Contest, Calvados, Normandy. Aphelion is widely used in the scientific/industry community to solve basic and complex imaging applications. First, the imaging application is quickly developed from the Graphical User Interface, involving a set of functions that can be automatically recorded into a macro command. The macro languages available in Aphelion (i.e. BasicScript, Python, and C#) help to process batch of images, and prompt the user if needed for specific parameters that are applied to the imaging functions. All Aphelion image processing functions are written in C++, and the Aphelion user interface is written in C#. C++ functions can be called from the C# language thanks the use of dedicated wrappers. The main principle of image processing is to automatically process pixels of a digital image, then extract one or more objects of interest (i.e. cells in the field of biology, inclusions in the field of material science) and compute one or more measurements on those objects to quantify the image and generate a verdict (good image, image with defects, cancerous cells). In other words, starting from an image, pixels are processed by a set of successive functions or operators until only measurements are computed and used as the input of a 3rd party system or a classification software that will classify objects of interest that have been extracted during the imaging process. An acquisition system such as a digital camera, a video camera, an optical or electron microscope, a medical scanner, or a smartphone can be used to capture images. The set of values or pixels can be processed as a 1D image (1D signal), a 2D image (array of pixel values corresponding to a monochrome or color image), or a 3D image displayed using volume rendering (array of voxels in the 3D space) or displaying surfaces by using 3D rendering. A 2D color image is made of 3 value pixels (typically Red, Green, and Blue information or another color space), and a 3D image is made of monochrome, color (indexed color are often used), multispectral, or hyperspectral data. When dealing with videos, an additional band is added corresponding to temporal information. The Aphelion Software Suite includes three base products, and a set of optional extensions for specific applications: Aphelion Lab: Entry-level package for non-experts in image processing. It helps to quickly segment an image in a semi-automatic or manual ways, and compute a set of measurements computed on objects of interest that have been extracted during the segmentation process. A set of wizards guides the user from image acquisition to report generation. Aphelion Dev: Full imaging environment including over 450 functions to develop and deploy an application that involves image processing and analysis. It also includes a set of macro-command languages to automate any application to be invoked from the user interface. It also helps to run the imaging algorithm on more than one image that are stored on disk, available on the network, or captured by an acquisition device. Aphelion libraries for image processing and visualization are provided in Aphelion Dev as DLLs and .Net components. Aphelion SDK: A set of libraries to develop a stand-alone application with a custom interface based on the Aphelion libraries. This software development kit including display, processing and analysis functions that can be used by software developers and OEMs. It is provided as DLLs and .Net components. The stand-alone application is typically developed in C# on one computer, and then deployed on multiple PCs and systems. A set of optional extensions can be added to the « Aphelion Dev » product, depending on the application. An evaluation version of Aphelion can be run on a PC for 30 days. A permanent version of Aphelion is available based on a perpetual license. Upgrades are available through a maintenance agreement based on a yearly fee. Technical support is provided by the engineers who are developing the product. The goal of image processing is usually to extract object(s) of interest in an image, and then to classify them based on some characteristics such as shape, density, position, etc. Using Aphelion, this goal is achieved by performing the following tasks: Load an image from disk or acquire an image using an acquisition device. Enhance the image removing noise or modifying its contrast. Segment the image extracting objects of interest to be measured and analyzed. Typically, for simple applications, a threshold is performed to generate a binary image. Then, morphological operators are applied to clean the image and only keep obj
Dynamic Bayesian network
A dynamic Bayesian network (DBN) is a Bayesian network (BN) which relates variables to each other over adjacent time steps. == History == A dynamic Bayesian network (DBN) is often called a "two-timeslice" BN (2TBN) because it says that at any point in time T, the value of a variable can be calculated from the internal regressors and the immediate prior value (time T-1). DBNs were developed by Paul Dagum in the early 1990s at Stanford University's Section on Medical Informatics. Dagum developed DBNs to unify and extend traditional linear state-space models such as Kalman filters, linear and normal forecasting models such as ARMA and simple dependency models such as hidden Markov models into a general probabilistic representation and inference mechanism for arbitrary nonlinear and non-normal time-dependent domains. Today, DBNs are common in robotics, and have shown potential for a wide range of data mining applications. For example, they have been used in speech recognition, digital forensics, protein sequencing, and bioinformatics. DBN is a generalization of hidden Markov models and Kalman filters. DBNs are conceptually related to probabilistic Boolean networks and can, similarly, be used to model dynamical systems at steady-state.
Soft independent modelling of class analogies
Soft independent modelling by class analogy (SIMCA) is a statistical method for supervised classification of data. The method requires a training data set consisting of samples (or objects) with a set of attributes and their class membership. The term soft refers to the fact the classifier can identify samples as belonging to multiple classes and not necessarily producing a classification of samples into non-overlapping classes. == Method == In order to build the classification models, the samples belonging to each class need to be analysed using principal component analysis (PCA); only the significant components are retained. For a given class, the resulting model then describes either a line (for one Principal Component or PC), plane (for two PCs) or hyper-plane (for more than two PCs). For each modelled class, the mean orthogonal distance of training data samples from the line, plane, or hyper-plane (calculated as the residual standard deviation) is used to determine a critical distance for classification. This critical distance is based on the F-distribution and is usually calculated using 95% or 99% confidence intervals. New observations are projected into each PC model and the residual distances calculated. An observation is assigned to the model class when its residual distance from the model is below the statistical limit for the class. The observation may be found to belong to multiple classes and a measure of goodness of the model can be found from the number of cases where the observations are classified into multiple classes. The classification efficiency is usually indicated by Receiver operating characteristics. In the original SIMCA method, the ends of the hyper-plane of each class are closed off by setting statistical control limits along the retained principal components axes (i.e., score value between plus and minus 0.5 times score standard deviation). More recent adaptations of the SIMCA method close off the hyper-plane by construction of ellipsoids (e.g. Hotelling's T2 or Mahalanobis distance). With such modified SIMCA methods, classification of an object requires both that its orthogonal distance from the model and its projection within the model (i.e. score value within the region defined by the ellipsoid) are not significant. == Application == SIMCA as a method of classification has gained widespread use especially in applied statistical fields such as chemometrics and spectroscopic data analysis.
Count sketch
Count sketch is a type of dimensionality reduction that is particularly efficient in statistics, machine learning and algorithms. It was invented by Moses Charikar, Kevin Chen and Martin Farach-Colton in an effort to speed up the AMS Sketch by Alon, Matias and Szegedy for approximating the frequency moments of streams (these calculations require counting of the number of occurrences for the distinct elements of the stream). The sketch is nearly identical to the Feature hashing algorithm by John Moody, but differs in its use of hash functions with low dependence, which makes it more practical. In order to still have a high probability of success, the median trick is used to aggregate multiple count sketches, rather than the mean. These properties allow use for explicit kernel methods, bilinear pooling in neural networks and is a cornerstone in many numerical linear algebra algorithms. == Intuitive explanation == The inventors of this data structure offer the following iterative explanation of its operation: at the simplest level, the output of a single hash function s mapping stream elements q into {+1, -1} is feeding a single up/down counter C. After a single pass over the data, the frequency n ( q ) {\displaystyle n(q)} of a stream element q can be approximated, although extremely poorly, by the expected value E [ C ⋅ s ( q ) ] {\displaystyle {\mathbf {E}}[C\cdot s(q)]} ; a straightforward way to improve the variance of the previous estimate is to use an array of different hash functions s i {\displaystyle s_{i}} , each connected to its own counter C i {\displaystyle C_{i}} . For each i, the E [ C i ⋅ s i ( q ) ] = n ( q ) {\displaystyle {\mathbf {E}}[C_{i}\cdot s_{i}(q)]=n(q)} still holds, so averaging across the i range will tighten the approximation; the previous construct still has a major deficiency: if a lower-frequency-but-still-important output element a exhibits a hash collision with a high-frequency element even for one of the s i {\displaystyle s_{i}} hashes, n ( a ) {\displaystyle n(a)} estimate can be significantly affected. Avoiding this requires reducing the frequency of collision counter updates between any two distinct elements. This is achieved by replacing each C i {\displaystyle C_{i}} in the previous construct with an array of m counters (making the counter set into a two-dimensional matrix C i , j {\displaystyle C_{i,j}} ), with index j of a particular counter to be incremented/decremented selected via another set of hash functions h i {\displaystyle h_{i}} that map element q into the range {1..m}. Since E [ C i , h i ( q ) ⋅ s i ( q ) ] = n ( q ) {\displaystyle {\mathbf {E}}[C_{i,h_{i}(q)}\cdot s_{i}(q)]=n(q)} , averaging across all values of i will work. == Mathematical definition == 1. For constants w {\displaystyle w} and t {\displaystyle t} (to be defined later) independently choose d = 2 t + 1 {\displaystyle d=2t+1} random hash functions h 1 , … , h d {\displaystyle h_{1},\dots ,h_{d}} and s 1 , … , s d {\displaystyle s_{1},\dots ,s_{d}} such that h i : [ n ] → [ w ] {\displaystyle h_{i}:[n]\to [w]} and s i : [ n ] → { ± 1 } {\displaystyle s_{i}:[n]\to \{\pm 1\}} . It is necessary that the hash families from which h i {\displaystyle h_{i}} and s i {\displaystyle s_{i}} are chosen be pairwise independent. 2. For each item q i {\displaystyle q_{i}} in the stream, add s j ( q i ) {\displaystyle s_{j}(q_{i})} to the h j ( q i ) {\displaystyle h_{j}(q_{i})} th bucket of the j {\displaystyle j} th hash. At the end of this process, one has w d {\displaystyle wd} sums ( C i j ) {\displaystyle (C_{ij})} where C i , j = ∑ h i ( k ) = j s i ( k ) . {\displaystyle C_{i,j}=\sum _{h_{i}(k)=j}s_{i}(k).} To estimate the count of q {\displaystyle q} s one computes the following value: r q = median i = 1 d s i ( q ) ⋅ C i , h i ( q ) . {\displaystyle r_{q}={\text{median}}_{i=1}^{d}\,s_{i}(q)\cdot C_{i,h_{i}(q)}.} The values s i ( q ) ⋅ C i , h i ( q ) {\displaystyle s_{i}(q)\cdot C_{i,h_{i}(q)}} are unbiased estimates of how many times q {\displaystyle q} has appeared in the stream. The estimate r q {\displaystyle r_{q}} has variance O ( m i n { m 1 2 / w 2 , m 2 2 / w } ) {\displaystyle O(\mathrm {min} \{m_{1}^{2}/w^{2},m_{2}^{2}/w\})} , where m 1 {\displaystyle m_{1}} is the length of the stream and m 2 2 {\displaystyle m_{2}^{2}} is ∑ q ( ∑ i [ q i = q ] ) 2 {\displaystyle \sum _{q}(\sum _{i}[q_{i}=q])^{2}} . Furthermore, r q {\displaystyle r_{q}} is guaranteed to never be more than 2 m 2 / w {\displaystyle 2m_{2}/{\sqrt {w}}} off from the true value, with probability 1 − e − O ( t ) {\displaystyle 1-e^{-O(t)}} . === Vector formulation === Alternatively Count-Sketch can be seen as a linear mapping with a non-linear reconstruction function. Let M ( i ∈ [ d ] ) ∈ { − 1 , 0 , 1 } w × n {\displaystyle M^{(i\in [d])}\in \{-1,0,1\}^{w\times n}} , be a collection of d = 2 t + 1 {\displaystyle d=2t+1} matrices, defined by M h i ( j ) , j ( i ) = s i ( j ) {\displaystyle M_{h_{i}(j),j}^{(i)}=s_{i}(j)} for j ∈ [ w ] {\displaystyle j\in [w]} and 0 everywhere else. Then a vector v ∈ R n {\displaystyle v\in \mathbb {R} ^{n}} is sketched by C ( i ) = M ( i ) v ∈ R w {\displaystyle C^{(i)}=M^{(i)}v\in \mathbb {R} ^{w}} . To reconstruct v {\displaystyle v} we take v j ∗ = median i C j ( i ) s i ( j ) {\displaystyle v_{j}^{}={\text{median}}_{i}C_{j}^{(i)}s_{i}(j)} . This gives the same guarantees as stated above, if we take m 1 = ‖ v ‖ 1 {\displaystyle m_{1}=\|v\|_{1}} and m 2 = ‖ v ‖ 2 {\displaystyle m_{2}=\|v\|_{2}} . == Relation to Tensor sketch == The count sketch projection of the outer product of two vectors is equivalent to the convolution of two component count sketches. The count sketch computes a vector convolution C ( 1 ) x ∗ C ( 2 ) x T {\displaystyle C^{(1)}x\ast C^{(2)}x^{T}} , where C ( 1 ) {\displaystyle C^{(1)}} and C ( 2 ) {\displaystyle C^{(2)}} are independent count sketch matrices. Pham and Pagh show that this equals C ( x ⊗ x T ) {\displaystyle C(x\otimes x^{T})} – a count sketch C {\displaystyle C} of the outer product of vectors, where ⊗ {\displaystyle \otimes } denotes Kronecker product. The fast Fourier transform can be used to do fast convolution of count sketches. By using the face-splitting product such structures can be computed much faster than normal matrices.
WebPlus
Serif WebPlus was a website design program for Microsoft Windows, developed by the software company, Serif. It allows users to design, create and upload their website onto the internet without any knowledge of HTML or other web technologies. Much like Microsoft Word, WebPlus uses WYSIWYG drag and drop editing to add and position text, images and links as they would appear on the finished web page. Once a user has designed their site, WebPlus can preview the site in a web browser before uploading the site using the in-built FTP. The software comes with a variety of pre-designed sample websites containing Filler text like Lorem ipsum, which can be used as a template for quickly designing a site. It also provides drawing tools for creating and editing buttons and web graphics. == Free WebPlus Starter Edition == Previously Serif had made available feature limited Starter Editions of their software, based on older versions, which could be obtained and used free of charge. For WebPlus the final free edition was based on version X5 and this was released in September 2012. This continued to be available from Serif's server until it was withdrawn around March 2016. WebPlus was then only available as a paid-for version X8. == Program Withdrawal == In March 2016, Serif announced that WebPlus X8 would be the final version, and that there were no current plans to design an application to replace it. Sales of WebPlus X8 by Serif were ended around December 2016. In early 2018, Serif announced that Serif Web Resources, hosted on Serif servers and required to implement some advanced web-site functionality in WebPlus created sites, would no longer work after 31 August 2018. In 2018, Serif also shutdown the servers that generated the "Plus" software registration numbers on-line from the product version and the individual generated installation number. Serif revealed the alternative was to use a universal master registration number, which is 881887. This is known to work with post 2003 Serif "Plus" software (e.g. verified to work with PagePlus v5.02). However, later Serif "Plus" software still registers itself automatically if within a certain recent period of a previous Serif software registration on the same PC. == Supported platforms == WebPlus was developed for Microsoft Windows "Win32" graphical desktop interface and is fully compatible with Windows XP, Windows Vista (32/64bit), Windows 7 (32/64bit) and Windows 8. == Features == Web hosting to upload websites to the internet with the address www.sitename.webplus.net and email [email protected]. E-Commerce tool to create online stores with providers such as PayPal. Form wizard generates online forms to collect information from website visitors. Add blogs, forums, hit counters, online polls and content management systems to websites using Smart Objects. Google Maps tool embeds maps and optional navigation markers within a website. Site navigation bars adopt a website's structure providing a tool for navigating around the website. Photo gallery groups a collection of images together and displays them as an animated slideshow. Search engine optimization (SEO) tools optimise a websites search ranking with the likes of Google, Yahoo! and Bing. Collect website metrics such as page popularity and number of website hits using Google Analytics. WebPlus X5 introduced a button studio for creating button graphics. Restrict access to specific pages on a website with a secure member's area. WebPlus automatically converts images and graphics into a web targeted format, optimising them for fast download. Embed YouTube videos within a web page. Add animated effects to a website with Animated GIFs, Animated Marquees or by importing Flash videos. Stream news and information feeds to a website using RSS and podcasts. Automated Site Checker analyses and corrects potential problems with a website. AdSense tool incorporates Google AdSense advertisements into a website In-built FTP transfers files onto a web server, uploading a website to the internet. In-built Basic Photo Editor the PhotoLab can make automatic adjustments and "Quick Fix's" to photos. From X5, WebPlus offers image editing and filters, through its PhotoLab and also provides a dedicated background-removal tool in the form of Cutout Studio. Display images, Flash videos and web pages using animated Lightboxes. Filter Effects can be applied to the graphical objects, giving convincing, realistic effects such as glass, metallic, plastic and other 2D/3D filters. WebPlus also provides QuickShapes for creating button and web graphics. These predefined shapes can be quickly modified with sliders to adjust certain parameters, for example creating rounded rectangles, etc. Shapes include: rectangles, ellipses, stars, spirals, cogs, petals, etc.
Fitness function
A fitness function is a particular type of objective or cost function that is used to summarize, as a single figure of merit, how close a given candidate solution is to achieving the set aims. It is an important component of evolutionary algorithms (EA), such as genetic programming, evolution strategies or genetic algorithms. An EA is a metaheuristic that reproduces the basic principles of biological evolution as a computer algorithm in order to solve challenging optimization or planning tasks, at least approximately. For this purpose, many candidate solutions are generated, which are evaluated using a fitness function in order to guide the evolutionary development towards the desired goal. Similar quality functions are also used in other metaheuristics, such as ant colony optimization or particle swarm optimization. In the field of EAs, each candidate solution, also called an individual, is commonly represented as a string of numbers (referred to as a chromosome). After each round of testing or simulation the idea is to delete the n worst individuals, and to breed n new ones from the best solutions. Each individual must therefore to be assigned a quality number indicating how close it has come to the overall specification, and this is generated by applying the fitness function to the test or simulation results obtained from that candidate solution. Two main classes of fitness functions exist: one where the fitness function does not change, as in optimizing a fixed function or testing with a fixed set of test cases; and one where the fitness function is mutable, as in niche differentiation or co-evolving the set of test cases. Another way of looking at fitness functions is in terms of a fitness landscape, which shows the fitness for each possible chromosome. In the following, it is assumed that the fitness is determined based on an evaluation that remains unchanged during an optimization run. A fitness function does not necessarily have to be able to calculate an absolute value, as it is sometimes sufficient to compare candidates in order to select the better one. A relative indication of fitness (candidate a is better than b) is sufficient in some cases, such as tournament selection or Pareto optimization. == Requirements of evaluation and fitness function == The quality of the evaluation and calculation of a fitness function is fundamental to the success of an EA optimisation. It implements Darwin's principle of "survival of the fittest". Without fitness-based selection mechanisms for mate selection and offspring acceptance, EA search would be blind and hardly distinguishable from the Monte Carlo method. When setting up a fitness function, one must always be aware that it is about more than just describing the desired target state. Rather, the evolutionary search on the way to the optimum should also be supported as much as possible (see also section on auxiliary objectives), if and insofar as this is not already done by the fitness function alone. If the fitness function is designed badly, the algorithm will either converge on an inappropriate solution, or will have difficulty converging at all. Definition of the fitness function is not straightforward in many cases and often is performed iteratively if the fittest solutions produced by an EA is not what is desired. Interactive genetic algorithms address this difficulty by outsourcing evaluation to external agents which are normally humans. == Computational efficiency == The fitness function should not only closely align with the designer's goal, but also be computationally efficient. Execution speed is crucial, as a typical evolutionary algorithm must be iterated many times in order to produce a usable result for a non-trivial problem. Fitness approximation may be appropriate, especially in the following cases: Fitness computation time of a single solution is extremely high Precise model for fitness computation is missing The fitness function is uncertain or noisy. Alternatively or also in addition to the fitness approximation, the fitness calculations can also be distributed to a parallel computer in order to reduce the execution times. Depending on the population model of the EA used, both the EA itself and the fitness calculations of all offspring of one generation can be executed in parallel. == Multi-objective optimization == Practical applications usually aim at optimizing multiple and at least partially conflicting objectives. Two fundamentally different approaches are often used for this purpose, Pareto optimization and optimization based on fitness calculated using the weighted sum. === Weighted sum and penalty functions === When optimizing with the weighted sum, the single values of the O {\displaystyle O} objectives are first normalized so that they can be compared. This can be done with the help of costs or by specifying target values and determining the current value as the degree of fulfillment. Costs or degrees of fulfillment can then be compared with each other and, if required, can also be mapped to a uniform fitness scale. Without loss of generality, fitness is assumed to represent a value to be maximized. Each objective o i {\displaystyle o_{i}} is assigned a weight w i {\displaystyle w_{i}} in the form of a percentage value so that the overall raw fitness f r a w {\displaystyle f_{raw}} can be calculated as a weighted sum: f r a w = ∑ i = 1 O o i ⋅ w i w i t h ∑ i = 1 O w i = 1 {\displaystyle f_{raw}=\sum _{i=1}^{O}{o_{i}\cdot w_{i}}\quad {\mathsf {with}}\quad \sum _{i=1}^{O}{w_{i}}=1} A violation of R {\displaystyle R} restrictions r j {\displaystyle r_{j}} can be included in the fitness determined in this way in the form of penalty functions. For this purpose, a function p f j ( r j ) {\displaystyle pf_{j}(r_{j})} can be defined for each restriction which returns a value between 0 {\displaystyle 0} and 1 {\displaystyle 1} depending on the degree of violation, with the result being 1 {\displaystyle 1} if there is no violation. The previously determined raw fitness is multiplied by the penalty function(s) and the result is then the final fitness f f i n a l {\displaystyle f_{final}} : f f i n a l = f r a w ⋅ ∏ j = 1 R p f j ( r j ) = ∑ i = 1 O ( o i ⋅ w i ) ⋅ ∏ j = 1 R p f j ( r j ) {\displaystyle f_{final}=f_{raw}\cdot \prod _{j=1}^{R}{pf_{j}(r_{j})}=\sum _{i=1}^{O}{(o_{i}\cdot w_{i})}\cdot \prod _{j=1}^{R}{pf_{j}(r_{j})}} This approach is simple and has the advantage of being able to combine any number of objectives and restrictions. The disadvantage is that different objectives can compensate each other and that the weights have to be defined before the optimization. This means that the compromise lines must be defined before optimization, which is why optimization with the weighted sum is also referred to as the a priori method. In addition, certain solutions may not be obtained, see the section on the comparison of both types of optimization. === Pareto optimization === A solution is called Pareto-optimal if the improvement of one objective is only possible with a deterioration of at least one other objective. The set of all Pareto-optimal solutions, also called Pareto set, represents the set of all optimal compromises between the objectives. The figure below on the right shows an example of the Pareto set of two objectives f 1 {\displaystyle f_{1}} and f 2 {\displaystyle f_{2}} to be maximized. The elements of the set form the Pareto front (green line). From this set, a human decision maker must subsequently select the desired compromise solution. Constraints are included in Pareto optimization in that solutions without constraint violations are per se better than those with violations. If two solutions to be compared each have constraint violations, the respective extent of the violations decides. It was recognized early on that EAs with their simultaneously considered solution set are well suited to finding solutions in one run that cover the Pareto front sufficiently well. They are therefore well suited as a-posteriori methods for multi-objective optimization, in which the final decision is made by a human decision maker after optimization and determination of the Pareto front. Besides the SPEA2, the NSGA-II and NSGA-III have established themselves as standard methods. The advantage of Pareto optimization is that, in contrast to the weighted sum, it provides all alternatives that are equivalent in terms of the objectives as an overall solution. The disadvantage is that a visualization of the alternatives becomes problematic or even impossible from four objectives on. Furthermore, the effort increases exponentially with the number of objectives. If there are more than three or four objectives, some have to be combined using the weighted sum or other aggregation methods. === Comparison of both types of assessment === With the help of the weighted sum, the total Pareto front can be obtained by a suitable choice of weights, provided that it is convex