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Playalong for Clarinet 1. Contemporary Sax Styles. By The Super Grooves. Featuring Frank Villafranca sax and Andrew D.

These stylistic influences are frequently associated with smooth jazz. James Bond Playalong for Saxophone: 10 Songs in melody arrangements with specially recorded backing tracks 1.

Playalong for Saxophone 1. Litrtle Overture, 2. Berceuse, 3. March of the Toy Soldiers, 4. Air and Variations, 5.

Chicago 22,00 22,00 22,00 19,00 27 Blues, 6. Moto perpetuo, 7. Song of Farewell, 8. Promenade, 9.

September Song, Bb or B. Menuet in C major HWV, 2. Polonaise No. Theme from the Piano Sonata in A major K , Moment musical Nr. Polka from Album for the Young Op.

Funky, 2. Jazz, 3. WEaltz, 4. Klez Rozhinkes mit Mandlen, 4. Menuette Hob. XVI:1, 4, 5, 7, 2. Menuett Hob. IX:3, Nr. Trio Hob. XVI, 4. Menuett und 2 Trios aus "6 leichte Menuette, 5.

Trios, 6. Menuett aus "12 Menuette" Hob. IX, Nr. Courtly Gossip, 2. Wanderers, 3. Are We in Tune? Spring Dance, 3.

In the Cathedral, 4. Norwegian Morning, 5. March of the Mice, 6. Evening Song, 7. Forward March, 8. Russian Mood, 9.

Nordic Saga, Pardon Me? At the Fair, Minor Melody, The Music Box, Pogo Sticks, Ukrainian Dance, Airs and Graces, Hoedown, Take Your Partners, Gypsy Dong, In a Gondola, Back to the Start, Classical Theme, Summer Sonatina, Austrian Polka, In the Urals, Two Together, At Home, On the Carousel, The Spice of Life, Wonderland Waltz, Masque, Monday Minuet, The Pied Piper, Serious Study, Two-Part Invention, Hungarian Dance, Swiss Air, Ah, this Parting will slay me!

Waltz; 2. Rain; 3. Hippo Waltz; 4. Cha-Cha-Cha; 5. Blues; 6. Chicken Dance; 7. The Mermaid; 8. March of the Fleas; 9. Neapolitan Song; Mazurka; Calypso; The Little Lamb; Caravan; Cobra-Tango; Flatfooted; The Ferryman's Song; Gangster-Tango; Butterflies; Dance; Immortelle moderate ; 2.

Presto moderate ; 3. Gigue difficult ; 4. Scherzo difficult ; 5. Aus Zu zweien durch den Tonkreis: 1. Marsch, 2.

Munter, 3. Fanfare I, 4. Leicht beschwingt, 5. Schnell, 6. Fugato, 7. Leichthin, 9. Munter, Gigue, Sehr geschwind, Fanfare II easy to moderate ; 6.

Aus vier Arietten Kanon easy ; 7. Aus Triludi: 1. Signal, 3. Rondo, 4. Kanon, 7. Mobile, Marsch easy ; 8.

Aus Trio: Allegro grazioso difficult ; 9. Ain't Misbehavin', 2. All The Things You Are, 3. Hello, Young Lovers, 4.

Oh, What A Beautiful Mornin', 6. The Sound Of Music, 7. Come Rain Or Come Shine, 8. I'll Be Seeing You, 9. Skylark, Smoke Gets In Your Eyes, The Song Is You, This Nearly Was Mine, Hungarian Dance No.

Marche Funebre from Sonata Op. Minuet from String Quintet Op. Ode To Joy from Symphony No. Piano Concerto No. Rondeau from Symphonic Suite No.

Second Movement from Symphony No. The Happy Farmer Op. Susato: Danserye, ; 3. Attaingnant: Dix huit basses dances, ; 5.

Por Jesus Benites R. Pepita, 2. Divagacion, 3. Armonias de America, 4. Cordoba, 5. Estudio en Sol menor, 6. Maxixe, 7. Vidalita, 8.

Don Perez Freire, 9. A mi madre Sonatina , Minueto en Sol, Moonlight Claro de Luna , Preludio No. Hoochy Blues, 3. Yes We Can, 6. Got Soul, One Trick Blues, Come a Cropper, The Bluesman Cometh, Blues For Ennnio, Attack Of The Walking Chords, Just Us.

Licks, Tricks, Tones, and Tips for the Aspiring Lead Guitarist [Explores a variety of improvisational concepts and techniques, backed up with fingering patterns, exercises, and lick examples galore.

In addition, each chapter includes several extended solos in the styles of rock, blues, funk, jazz, and country based entirely on the techniques brought forth in each lesson.

Furthermore, each chapter features Quick Theory Tutorials that you can refer to if you need to brush up on your music theory.

You'll also find a section called Tone Tips that precedes each solo. Here you get suggestions for guitar, amp, and effects settings. Classic Songs from the Early Years.

Melody Line and Chord Symbols. Standard Notation and TAB 1. Anthem, 2. Closer to the Heart, 3. The Spirit of Radio, 4.

The Temples of Syrinx, 5. Tom Sawyer, 6. The Alphabet Song, 2. The Animal Fair, 3. A-Tiskit, A-Tasket, 4. Black Sheep, 5. The Big Rock Candy Mountain, 6.

B-I-N-G-O, 7. Black-Eyed Susie, 8. The Bold Fisherman, 9. Chime Again, Beautiful Bells, Cindy, Colinbda, The Cuckoo, The Fairy Ship, The Farmer, The Farmer in the Dell, The Fox, Free Little Bird, German Cradle Song, The Glendy Burk, Goober Peas, Goodnightt, Ladies, Green Corn, Green Grass Grew All Around, How Old Are You?

Humpty Dumpty, This Itsy-Bitsy Spider, Jenny Jenkins, Jenny Jones, John Jacob Jingleheimer Schmidt, Johnny Get Your Haircut, Juanita, The King of France, Lazy Mary, Lightly Row, Listen to the Mockingbird, The Little Lamb, The Little Old Sod Shanty, London Bridge, Looby Loo, Mary Wore Her Red Dress, The Muffin Man, The Mulberry Bush, Nelly Bly, Oats, Peas, Beans, and Barley Grow, Susanna, Old Abe Lincoln Came out of the Wilderness, Old Blue, The Old Chisholm Trail, Old Dan Tucker, Old McDonald Had a Farm, Old Rattler, Old Smoky, Over the River and Through the Woods, Paper of Pins, Pick a Bale of Cotton, The Pine Tree, Polly, Put the Kettle On, Polly Wolly Doodle, Railroad Bill, Reuben and Rachel, The Riddle Song, Ring Around a Rosy, Robinson Crusoe, Rock-ABye Baby E.

Rock That Cradle, Lucy, Rond and Round the Village, Sally Goodin, Sandy Land, Shoo Fly, Sing a Song of Sixpence, Sing Song Kitty, Sleep, Baby, Sleep!

Slumber Song, The Sow Took the Measles, Suzanna Gal, Ten Little Kangaroes, Three Little Kittens, Three Sight-Challenged Mice, Tirra-Lirra-Lirra, Welcome to Spring, What Can the Matter Be?

When I Was a Lady, Winter Waltz, Prelude, 2. Lullaby, 3. Ballad, 4. Bossa, 6. Impression, 8. March, 9. In Old Style, BLUR: Song 2, Turkey in the Straw, 2.

Skip to My Lou, 3. Eensy Weensy Spider, 6. Wheels on the Bus, 7. London Bridge, 8. Old MacDonald, 9. Mary Had a Little Lamb, Twinkle, Twinkle Little Star, Camptown Races, Farmer in the Del, On Top of Old 19,75 16,50 36 Smoky, Three Blind Mice, Oh Susanna, Bah, Bah Black Sheep, Row, Row, Row Your Boat, Editorial SIGEVO Officers utumn has been good to us and we received enough material to publish a double issue packed with really good stuff!

Urbanowicz for complex classification problems like the ones found in bioinformatics and epidemiology. We have a paper by Ricky Vesel who uses genetic algorithms in Race Optimal, a project aimed at creating an effective and fully automated process for racing line optimization to apply to all the circuits around the world.

We also have a paper by Alwyn V. Husselmann about an approach to visualize populations of Karva expressions, also used for the cover of the newsletter.

At the end, there are the summaries of two new PhD theses available. We hope Winter will be even better and we look forward to receiving more contributions to complete the last issue of this volume.

So if you have something interesting for the newsletter, just drop an email! This year there will be no deadline extension, pretty scary huh? This issue was possible only with the help of Ryan J.

Urbanowicz, Ricky Vesel, Alwyn V. Urbanowicz Ricky Vesel Alwyn V. It offers an accessible, user friendly LCS platform for supervised rule-based machine learning, classification, data mining, prediction, and knowledge discovery.

ExSTraCS seeks to make no assumptions about the data, and is therefore model free and particularly well suited to complex problems that are multi-factorial, interacting nonlinear , heterogeneous, noisy, class imbalanced, multi-class, or largerscale.

A simple example problem is used illustrate this. This makes them somewhat of ensemble learners all on their own.

These rule-based algorithms combine the global search of evolutionary computing i. They also apply iterative, rather than batch-wise learning, meaning that rules are evaluated and evolved one instance at a time.

They can also offer transparency, in that individual rules can be unambiguously interpreted, and straightforward strategies have been developed to derive global knowledge from the rule population as a whole through the use of LCS rule-population metrics, significance testing, and visualizations [7].

Algorithm Overview ExSTraCS was primarily developed for application to bioinformatic and epidemiological problems involving the detection, modeling, and characterization of predictive attributes associated with common complex diseases [4].

While developed with bioinformatics applications in mind, ExSTraCS would be well suited to any supervised learning problem, especially when complexity is an issue.

ExSTraCS brings together a number of recently developed LCS advancements designed to provide users with better performance, data flexibility, and new ways to get information out of LCS learning.

All features are directly integrated into ExSTraCS and utilized by default, allowing the user to run the algorithm without having to worry about setting a large number of run parameters.

Key features include; 1 Adaptive data management: which automatically differentiates discrete from continuous attributes in a dataset loaded by the user.

Post-training, these scores can be applied to characterize patterns of association such as heterogeneity within the dataset [6]. As summarized in [4], A ExSTraCS will accept a finite training dataset and an optional testing dataset in order to evaluate the predictive performance of the algorithm.

Adaptive data management initially determines and stores key characteristics of this dataset for use during learning iterations.

Expert knowledge EK attribute weights are loaded or discovered from the dataset. B The core ExSTraCS algorithm repeats the following 10 steps up to a maximum number of learning iterations: 1 A single training instance is taken from the dataset without replacement.

Rule parameters are updated for rules within [C] and [I]. A similar subsumption mechanism is also applied to new rules generated by the genetic algorithm GA.

The GA applies two well known discovery operators: crossover and mutation. All rules in [C] and [I] are returned to [P]. For performance tracking and classification prediction, a prediction array is generated for the [M] formed from each training or testing instance.

A class prediction is made by a fitness weighted vote of all rules within [M]. These outputs may be evaluated and visualized to facilitate knowledge discovery as described in [7].

It is a crossplatform program written entirely in Python 2. It is freely available for download from sourceforge.

ExSTraCS 2. Included with both versions of ExSTraCS is an exhaustive users guide that details command line operation, run parameters, and code modules.

Minimum System Requirements Python 2. This problem can be completely and accurately captured by only 8 rules each specifying only three attributes.

For instance a rule with condition 0,1, ,1, , and class 1 would be optimal for making an accurate prediction on the instance given in Figure 2.

Another example of an optimal rule would be 1,1, , , ,0 with class 0. The first two bits highlighted Example Problem To demonstrate how ExSTraCS is set up, run, and its output analyzed, we will consider the multiplexer problem as an example.

N-bit multiplexer problems are scalable supervised learning toy problems with Boolean attribute states, and a Boolean class. These problems involve attribute interactions as well as overlapping patterns of heterogeneity.

Typically these problems do not include any noise, nor do they include any nonpredictive attributes.

N-bit multiplexer problems have been regularly applied to test and compare many different LCS algorithms, as well as other machine learning algorithms, particularly in the context of algorithm scalability.

For simplicity, we examine the 6-bit multiplexer problem illustrated in Figure 2. In any multiplexer problem, the initial address bits point to some register bit, and the value at this register bit will give the class of the instance.

Essentially in the 6-bit multiplexer, 3 attributes states determine the class of a given instance. The dataset we use in this example to train ExSTraCS includes all 64 unique 6-bit strings as instances along with the correct corresponding class labels.

SIGEVOlution Volume 7, Issue in orange are considered to be address bits and the remaining 4 bits are considered to be register bits. The class for this instance is highlighted in grey.

Notice that in the multiplexer problem, the class is always equivalent to the Boolean value at the register bit specified by the address bits.

First, make sure that Python 2. Second, make sure that you have a properly formatted training dataset file. Third, make sure that you have a properly formatted configuration file that specifies, at minimum, the set of 4 run parameters that have not been assigned a default value within ExSTraCS.

Additionally, the class column can be located anywhere, as ExSTraCS identifies this column by the class label.

While most run parameters in ExSTraCS include a default value, a handful of parameters must be specified within the configuration file.

Names can be given without paths if respective files are in or will be placed in the working directory. To get ExSTraCS running on the small simulated genetics training and testing datasets included with the software, leave this configuration file as is.

As we will largely rely on default values, we will only make a few key updates to this file itemized below. See the ExSTraCS users guide included with the software for a detailed review of all run parameters, their function, and expected impact on algorithm performance.

N, which specifies the maximum rule population size, is assigned We will discuss them in a bit more detail in a moment.

First, in order to run this 6-bit multiplexer analysis simply type the ExSTraCS run command as before, this time specifying the edited configuration file.

While users can certainly rely on default parameters to get started, we quickly review the impact of setting these key parameters below.

The user can specify any number of learning checkpoints, however the iteration numbers should be increasing up to some maximum number of iterations, and individual values should be separated by a period.

For larger datasets, or more complex problems, the user may wish to increase the number of learning iterations. Alternatively, if the user wants the algorithm to run for less time the number of learning iterations should be decreased.

Note that for this 6-bit multiplexer problem we are running ExSTraCS for a total of 10, iterations, but pausing after only iterations for a complete evaluation of the rule population.

N: This parameter specifies the maximum population size that ExSTraCS is allowed to reach before the deletion mechanism turns on and maintains this maximum number.

If N is too large, ExSTraCS will take longer to run, and the resulting rule population will likely be much bigger than necessary, and potentially harder to interpret.

In datasets with a small number of attributes i. In most real-world problems this knowledge would not be available. In this 6-bit multiplexer problem we have set this parameter to 10, as is applied in most LCS algorithms.

These outputs can be analyzed to evaluate performance and provide a window inside the rule population and the patterns of association captured within.

Using the 6-bit multiplexer example we will explore the ExSTraCS output and see how a solution distributed over a rule population can be interpretable.

We examine each output file separately below. This is the classification or prediction accuracy of the solution. Most importantly this file provides training accuracy, testing accuracy, global run time, coverage i.

Next, this file includes three summary statistics introduced in [7] that can be used for knowledge discovery to identify attributes that were of particular importance in making class predictions.

These statistics include the specificity sum, the accuracy sum, and the attribute tracking global sum.

For each statistic a sum is calculated for every attribute in the training data. Attributes that consistently have the highest sums for these three metrics are likely to be most important for making accurate predictions.

For our 6-bit multiplexer example we observe that the two address bit attributes consistently yield the highest scores for all three metrics.

This is clearly in-line with the multiplexer solution, that requires optimal rules within which the address bits are always specified, along with one other register bit.

In problems where only a subset of attributes are predictive, these metrics can be applied as feature selection to identify attributes that the algorithm identified as important vs.

Statistical significance values i. The rule population can be explored through manual rule inspection. The most effective way to identify the most important rules in the population as part of manual interpretation, is to rank rules by decreasing numerosity.

This can be accomplished quickly in software like Microsoft Excel. Rules with the largest numerosity are typically most important. Doing this for our 6-bit multiplexer problem we quickly observe that all 8 optimal rules have been identified within the 14 rules with the largest numerosities out of all 95 rules in the population.

This can be particularly useful in noisy problems, or in problems where only some attributes are predictive. As described in [6], hierarchical clustering can be performed on instances, and attributes within this file to identify groups of instances with similar patterns of attributes with high attribute tracking scores in order to identify potentially heterogeneous instance subgroups and better characterize relationships between attributes predictive of class.

Similar to the rule population visualization, these scores can be visualized as a heatmap, wherein instances vs.

In this article we have used a somewhat simple problem to illustrate how the training, evaluation, and interpretation of an LCS algorithm has been made more approachable in the context of the ExSTraCS software.

ExSTraCS is under active development and improvement, to further enhance performance, interpretability, and flexibility to different types of data and analysis.

Over the next year we also plan to 1 add the ability for ExSTraCS to learn on data with continuous endpoints, referred to as quantitative trait analysis, 2 further improve overall learning speed and performance, and 4 provide a graphical user interface GUI for ExSTraCS to facilitate use and incorporate live learning visualizations.

We encourage user feedback, application to new problem domains, collaborative or independent development of ExSTraCS, and competitive comparison of this new LCS framework to other cutting edge machine learning strategies.

Learning Tracking References This file ranks top pairs of attributes that are co-specified in rules across [P]. Permutation testing can be also be applied as described in [7] to assign p-values to these sums.

For our 6-bit multiplexer example, the top co-occuring attribute pair is A0 and A1, which captures the most important interacting attribute pair i.

This file includes all of the estimated learning performance updates, output throughout ExSTraCS learning. This file can be used to graph learning progress over time.

This software seeks to take the flexible and powerful LCS algorithm framework and make it user-friendly, and transparent such that classification and data mining on complex domains can be performed with confidence and understanding.

A mixed discrete-continuous attribute list representation for large scale classification domains. ACM, Accuracy-based learning classifier system: models, analysis and applications to classification tasks.

Rapid rule compaction strategies for global knowledge discovery in a supervised learning classifier system. An extended Michigan-style learning classifier system for flexible supervised learning, classification, and data mining.

Addressing scalability with a rule specificity limit in a Michigan-style supervised learnign classifier system for classification, prediction, and knowledge discovery.

In Review, Instance-linked attribute tracking and feedback for Michigan-style supervised learning classifier systems. An analysis pipeline with statistical and visualization-guided knowledge discovery for Michigan-style learning classifier systems.

Using expert knowledge to guide covering and mutation in a Michigan-style learning classifier system to detect epistasis and heterogeneity. Springer, About the author Ryan Urbanowicz is a post-doctoral research associate at Dartmouth College where he received his PhD in genetics in He also holds a B.

Eng in Biological Engineering from Cornell University. His main research interests include bioinformatics, data mining, machine learning, evolutionary algorithms, epidemiology, and learning classifier systems.

On the topic of learning classifier systems he has received two best paper awards, written a widely cited review of the field, and served as organizer for the international workshop for the past four years.

Homepage: www. Classifier fitness based on accuracy. The ideal racing line is defined as the trajectory around a track that allows a given vehicle to traverse the circuit in the minimum time.

In practice, it is an abstraction that varies with track, environmental conditions, vehicle type and condition, competitive traffic, and other factors.

A certain extent of the talent possessed by the elite driver is the ability to perceive this optimal path and its variations, as well as to navigate it as quickly as possible.

Until now, automated methods have struggled to match the performance of humangenerated or human-guided racing lines [1]. This article describes the optimization engine and representation scheme used at Race Optimal to compute realistic and high performing racing lines for a wide variety of vehicle types.

R Despite their abstract existence in the world of sport, there is significant use for concretely defined racing lines. Racing video games are quite popular, and require high quality racing lines in order to provide challenging AI competitors [1].

GPS data overlays onto track maps are currently used as driver aids and a logical extension of this approach is to display the generated optimal racing lines for comparison as well.

An optimization process that encompasses vehicle characteristics can further be used for race preparation for example to choose a downforce configuration or transmission setup, as well as to quickly familiarize a driver with a new circuit.

Maximizing the radius of curvature everywhere on the path will then maximize allowable vehicle speed everywhere.

However, a shorter path, though having a smaller radius of curvature, may still take less time to traverse due to the shorter distance.

Thus, one assumption applied in racing line optimization is that the optimal path will be a combination of the maximum curvature path MCP and the shortest distance path SP.

Producing the optimal linear combination of these paths is the accomplished by Braghin et al. This approach can be extended by dividing the track into subsections where the optimal tradeoffs between MCP and SP are optimized independently [3].

A simple point-by-point representation of the racing line may be also applied [3]. Fitness may simply be the measurement of path length or total curvature, but in order to capture the variation of the ideal racing line for different vehicles, some considerations about vehicle dynamics and power level are necessary.

In [3], a robot driver is used in a high quality simulation to evaluate candidate racing lines. The present work also uses a computer simulation, but one that takes into account a much more limited model of vehicle dynamics in order to run as quickly as possible while still capturing the essence of several vehicle types.

A framework for racing line optimization should 1. Allow a high degree of geometric flexibility in racing line representation 2.

Produce a racing line that appears realistic and smooth, without kinks or unnecessary undulations Fig. Produce visually appealing and convincingly accurate racing lines for several vehicle types 4.

Make full utilization of the available track surface, meeting all apexes and borders where necessary 5. Require minimal setup procedure allowing for the analysis of a large number of tracks and vehicles, with a fully automated solution process By applying unique methods of geometric representation, optimization, and physics simulation, we believe these goals have been achieved.

The methodology is described in the following sections. Racing Line Representation One of the biggest challenges was creating a racing line representation scheme that satisfies the above criteria, particularly 1 , 2 , and 4.

Experimentation with different approaches revealed that all of the approaches mentioned above fail to meet criteria 1 alone.

To elaborate, a high degree of flexibility means that the racing line should be able to take on any conceivable shape that is physically realistic for a vehicle traversing a racetrack.

Use of a predefined geometric shape, such as an Euler spiral, while interesting, is obviously too restrictive to satisfy this aim. The blue lines represent the possible locations of the attached control points red.

Adapted from [5]. It quickly becomes clear that a control point approach combined with some sort of smoothing function is necessary.

Thus, in the current work, the control points are allowed to move more freely, within a circle of radius equal to four times the average track width, originating at initial user defined locations.

An example is shown in Figure 3. Each control point is located at the center of its circle. As part of fulfilling Criteria 3 to produce visually appealing racing lines, the line must smoothly connect to itself.

This is important not only for the aesthetic quality, but because if that requirement is not enforced, the line could begin a circuit on a different path than with which it concludes, which is illogical in the context of lapping a racetrack.

Eventually, a more satisfactory solution was arrived upon, which utilizes a periodic smoothing spline [6]. The coefficients of the periodic smoothing spline are then found for the x and y data separately, after which they are plotted together against t to form the smoothly connected racing line.

An example of the resulting not optimized racing line is shown in Figure 4. Geometric Constraints Because we use a control point scheme that allows for a highly variable racing line shape, some method must be employed to restrict the resulting line to the confines of the track.

Any line that fails this test is rejected automatically as invalid, thus ensuring that every candidate at least begins in an allowable position.

The remaining task is to detect which points fall outside the bounds of the circuit, and apply an appropriate penalty. This was initially accomplished by counting the intersections between the borders and the racing line.

Since it is known that the candidate begins inside the track, after one intersection it will be out of bounds, and will remain so until another intersection, and so on.

Even after porting this functionality to C code, this process was unacceptably slow. A racing line typically has about points per mile, and track borders roughly the same point density.

Evaluation often required tens of millions of intersection tests per solution. Typically 10, or more horizontal lines are drawn at equal intervals black and the intersections with the borders are calculated blue.

The resulting valid x-intervals are shown in red. Three lines are shown here for demonstration. A new method was devised to eliminate this bottleneck in the evaluation process, allowing for out-of-bounds points to be found very quickly, after a small initial cost at setup.

In this method, several thousand horizontal lines are superimposed over the track borders, and the points of intersection with the borders are determined Figure 5.

A lookup table is produced that contains, for each line, the x-coordinates that contain the in-bounds sections of track.

For a given point on the racing line, the table row with the closest y-coordinate can be quickly ascertained.

Table 1 contains a sample of the lookup table corresponding to Figure 5. Fitness Evaluation Since this project requires the production of optimal racing lines for several vehicle types, vehicle simulation must obviously come into play to capture these differences.

And because a flexible geometric scheme is utilized, there is no compelling reason to restrict oneself to SP or MCP solutions.

This frees the process from as many assumptions about the optimal geometry as possible. The simulation process is outlined as follows: 1.

Test for intersection with the start-finish line 2. Calculate the maximum allowable velocity at every point, limiting to vehicle top speed 4.

Beginning at the slowest point, iterate forward, limiting acceleration to that allowed by excess grip, vehicle power level, and aerodynamic drag 5.

Iterate backward, limiting deceleration to that allowed by excess grip and aerodynamic drag 6. Enforce smooth input transitions 7.

Calculate lap time 8. Count the out-of-bounds points and apply the appropriate penalty Several items require further explication, beginning with 3.

Thus, when r is above rmax , the maximum velocity is taken to be the vehicle top speed. Steps 4 and 5 translate the maximum allowable speed based on radius into realistic vehicle speed based on simplified vehicle dynamics.

To limit the acceleration in the forward direction, the point at which speed is minimum is selected. The algorithm then looks to the velocity at the next point and computes the desired acceleration.

The actual acceleration and throttle input is then restricted to that allowed by tire grip, engine power, and aerodynamic drag.

After processing the entire path this way, the process is repeated in reverse, treating braking zones as acceleration zones in the backward direction.

For braking, however, aerodynamic drag provides a contribution rather than a cost. Initially this was the extent of the vehicle simulation.

However, some Race Optimal users pointed out the unrealistically fast input transitions, as well as rapid input corrections mid-corner that would likely lead to instability.

Since the vehicle simulations are published on Race Optimal in video form, these shortcomings needed to be addressed. A smoothing process was developed that limits the rate of input transition depending on the cornering load, where maximum cornering load requires the slowest rate of throttle or brake transition.

The details of the smoothing algorithm are beyond the scope of this article, but an example of the results are shown in Figure 7 and Figure 8. Including this limit in the optimization also improved the shape of the final racing line, since the simulation no longer had the luxury of traversing a line in a way that requires instantaneous input corrections.

The optimization uses binary encoding and a population size of 75 members, operating on a set of control point locations.

Selection from the parent population for breeding is made using the roulette wheel approach, where the likelihood of selection is proportional to candidate fitness.

Each generation, a child solution set is created equal in size to the parent generation. In order to combat premature convergence, after generations the population is re-randomized using the current best solution as the seed.

This approach provides generally good results, but not good enough to satisfy Criteria 3, which requires visually appealing and convincingly accurate racing lines.

The optimization would frequently miss apexes by a small to medium distance, and would do this consistently at certain turns on some tracks, despite the fact that clipping the apex resulted in a quicker lap.

Although the difference in lap time was rarely more than one or two tenths of a second, such errors are noticeable in the resulting racing lines, and undermine the credibility of the results.

It was eventually determined that this problem was caused by the solutions becoming overly sensitive to out-of-bounds points at the entrances and exits of some turns.

The racing line converged on the border at the entrance or exit before the apex, and by that time moving closer to the apex pushed the other sectors out of bounds.

Since out-of-bounds points are penalized stiffly in order to prevent them from appearing in the final solution, the result was that the optimization was unable to meet the racing line with the apex of some turns.

To heal a racing line, control points closest to concentrations of out-of-bounds points are incrementally shifted toward the in-bounds direction in an attempt to bring the out-of-bound points back onto the track.

This process involves recalculating the racing line many times for a given solution, and therefore increases the computational burden substantially.

It was found that limiting the likelihood of healing was beneficial both to processing time and final solution quality, as healing every solution tended to interfere too much with the genetic algorithm itself.

Although the optimization still occasionally produces a missed apex, the frequency of this occurring is greatly reduced with the incorporation of the healing sub-process.

Figure 9 shows the MCP and SP solutions compared with the simulation-based optimization in a section of track called the Keyhole.

Figure 10 shows the same results, but for the section of track made up of Turns , a series of connected esses. The simulation-based racing line enters Turn 6 within the MCP-SP area, but thereafter follows a path that deviates substantially from what would be allowed by any linear combination of the two.

Lap times for the three optimizations are shown in Table 2. This is over two seconds slower than the optimal lap time achieved in the simulation; investigations are underway to determine if this discrepancy is a result of optimistic vehicle parameters or possibly other inaccuracies in the simulation.

Nevertheless, the simulation-based result beat the MCP solution by over 4 seconds, and the SP line by over 5 seconds. The time elapsed through Turns can be measured for a better comparison, since there is little variation between the MCP and SP lines, and the MCP line alone is a plausible route through that sequence.

The sector times are shown in Table 2, where the simulationbased solution is 0. Bearing in mind the fourth criteria, to capture the differences in racing line for different vehicles, the same section from Mid-Ohio is shown in Figure 11, via a screen capture from raceoptimal.

The entire track must also be considered in order to assess the accomplishment of the criteria listed in the introduction, and this is shown in Figure 12 for the Mazda Miata.

The result is a fluid racing line that touches the borders in the expected places, and takes a line very similar to what one can observe in professional onboard footage.

Thus, the initial five criteria for an automated process of realistic racing line optimization have been satisfied. Conclusions A racing line optimization procedure has been developed that produces plausible real-world results that are visually pleasing and can capture the behavior of different vehicle types.

The procedure does not rely on assumptions about the geometry of the ideal racing line. It is hoped that future authors will free themselves from the restrictions of predetermined geometry or racing line characterization when undertaking the challenge of racing line optimization.

The black region represents the track accessible by a linear combination of the MCP and SP solutions.

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Johannes DГјrr Video

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