Standard Crossover Research Articles

Improved Evolvability in Genetic Programming with Polyandry

This paper proposes Polyandry, a new nature-inspired modification to canonical Genetic Programming (GP). Polyandry aims to improve evolvability in GP. Evolvability is a critically important GP trait, the maintenance of which determines the arrival of the GP at the global optimum solution. Specifically evolvability is defined as the ability of the genetic operators employed in GP to produce offspring that are fitter than their parents. When GP fails to exhibit evolvability, further adaptation of the GP individuals towards the global optimum solution becomes impossible.
 Polyandry improves evolvability by improving the typically disruptive standard GP crossover operator. The algorithm employs a dual strategy towards this goal. The chief part of this strategy is an incorporation of genetic material from multiple mating partners into broods of offspring. Given such a brood, the offspring in the brood then compete according to a culling function, which we make equivalent to the main GP fitness function. Polyandry’s incorporation of genetic material from multiple GP individuals into broods of offspring represents a more aggressive search for building block information. This characteristic of the algorithm leads to an advanced explorative capability in both GP structural space and fitness space. The second component of the Polyandry strategy is an attempt at multiple crossover points, in order to find crossover points that minimize building block disruption from parents to offspring. This strategy is employed by a similar algorithm, Brood Recombination. 
 We conduct experiments to compare Polyandry with the canonical GP. Our experiments demonstrate that Polyandry consistently exhibits better evolvability than the canonical GP. As a consequence, Polyandry achieves higher success rates and finds solutions faster than the latter. The result of these observations is that given certain brood size settings, Polyandry requires less computational effort to arrive at global optimum solution than the canonical GP.
 We also conduct experiments to compare Polyandry with the analogous nature-inspired modification to canonical GP, Brood Recombination. The adoption of Brood Recombination in order to improve evolvability is ubiquitous in GP literature. Our results demonstrate that Polyandry consistently exhibits better evolvability than Brood Recombination, due to a more explorative nature of the algorithm in both structural and fitness space. As a result, although the two algorithms exhibit similar success rates, the former consistently discovers global optimum GP solutions significantly faster than the latter. The key advantage of Polyandry over Brood Recombination is therefore faster solution discovery. As a consequence Polyandry consistently requires less computational effort to arrive at the global optimum solution compared to Brood Recombination. 
 Further, we establish that the computational effort exerted by Polyandry is competitively low, relative to other Evolutionary Algorithm (EA) methodologies in literature. We conclude that Polyandry is a better alternative to both the canonical GP as well as Brood Recombination with regards to the achievement and maintenance of evolvability.

An optimal multi‐period crossover design for an application in paediatric nephrology

Crossover clinical trials can provide substantial benefits by eliminating inter-patient variation from treatment comparisons and by allowing multiple observations of each patient. They are particularly useful when sample sizes are necessarily small. These advantages proved particularly valuable in an assessment of clot prevention in children undergoing haemodialysis. Only small numbers of children are treated at any given time in any single dialysis unit, but each patient is obliged to attend two or three times each week, suggesting the use of a crossover trial with many periods. Standard crossover trials described in the literature (i) typically have fewer than 10 periods and (ii) are based on a model of questionable applicability to this study. This paper describes the derivation of an optimal crossover trial with 30 periods, which was used to compare two anticoagulants using nine patients. There is also a discussion of the analysis of the data obtained in the trial, which had a distribution markedly different from that anticipated when the study was designed.

생물학적 동등성 시험을 위한 2×k 교차설계법의 통계적 고려

The Korea Food and Drug Administration(KFDA) recommends the use of a crossover design to assess the bioequivalence of generic drugs. However, a standard crossover design for bioequivalence trials is often considered problematic due to ethical and economic issues as highly variable drugs are usually required by large numbers of subjects when designing the trial. To overcome this problem a crossover design has been a recommended option as per US regulations; in addition, a crossover design has also recently drawn special attention as an efficient alternative. The current KFDA regulation requires an ANOVA table for every bioequivalence study; however, ANOVA tables of and crossover designs have never been published in the literature. This study shows the derivation of tables of analysis of variance for a cross-over design and a cross-over design. We also suggest a sample size formulas for , and crossover designs to provide information on the selection of efficient designs for highly variable drugs.

Hedging iTraxx CDS Index Trading on an Intraday Basis: An Empirical Study

In this paper we examine the effectiveness of intraday hedging models for CDS index trading by means of more liquidly traded exchange-based future contracts. We consider the equity and BUND future as financial instruments to hedge standard 5Y iTraxx Euro Main and Crossover indices. Our analysis is based on a 4-month intraday time series for traded prices and quoted spreads, respectively. We find that a DAX future based intraday hedging strategy is the most efficient one. While the cross-asset hedging strategy reduces the intraday market risks of iTraxx Euro positions, the overall hedging efficiency is limited.

Sample Size Calculation for Bioequivalence Studies Assessing Drug Effect and Food Effect at the Same Time With a 3-Treatment Williams Design.

The US Food and Drug Administration issued a guidance in 2002, "Food-Effect Bioavailability and Fed Bioequivalence Studies," in which it states "in addition to a BE [bioequivalence] study under fasting conditions, we recommend a BE study under fed conditions for all orally administered immediate-release drug products" for abbreviated new drug applications. This statement involves 3 studies: a BE study under fasting status, a food-effect (FE) study, and a BE study under fed status. In practice, when it is known that there is no FE with a reference ( R) formulation, a sponsor may choose to run a BE study that assesses the drug effect and food effect with a test ( T) formulation in a single study that includes 3 treatments: R formulation at fasting status, T formulation at fasting status, and T formulation at fed status. Such a study combines the fasting BE study and the FE study on the T formulation and may justify the waiver of the fed BE study if conclusions can be made that there is no FE with the T formulation after this combined study completes. This article discusses how to calculate the sample size for this kind of study with different primary analysis models. Also discussed are (1) sample size calculations with more general BE studies and (2) how they can be implemented using commercial software in a standard 2-treatment, 2-period, and 2-sequence crossover design, as well as (3) a related practical issue of how to retrieve residual intrasubject mean squared error from historical summary results in the literature.

Effective search for Pittsburgh learning classifier systems via estimation of distribution algorithms

Pittsburgh-style learning classifier systems (LCSs), in which an entire candidate solution is represented as a set of variable number of rules, combine supervised learning with genetic algorithms (GAs) to evolve rule-based classification models. It has been shown that standard crossover operators in GAs do not guarantee an effective evolutionary search in many sophisticated problems that contain strong interactions between features. In this paper, we propose a Pittsburgh-style learning classifier system based on the Bayesian optimization algorithm with the aim of improving the effectiveness and efficiency of the rule structure exploration. In the proposed method, classifiers are generated and recombined at two levels. At the lower level, single rules contained in classifiers are produced by sampling Bayesian networks which characterize the global statistical information extracted from the current promising rules in the search space. At the higher level, classifiers are recombined by rule-wise uniform crossover operators to keep the semantics of rules in each classifier. Experimental studies on both artificial and real world binary classification problems show that the proposed method converges faster while achieving solutions with the same or even higher accuracy compared with the original Pittsburgh-style LCSs.

Yavalath: Sample Chapter from Evolutionary Game Design

The following chapter from Evolutionary Game Design (Browne, 2011) describes Yavalath, the first computer-generated board game to be commercially published. LUDI is a software system that creates new combinatorial games by evolving the rule sets of known games into new combinations, then testing them for playability and quality. It was developed as a proof-of-concept for my 2008 PhD thesis Automatic Generation and Evaluation of Recombination Games (previously reviewed in the ICGA Journal by Ingo Althofer (2010)), to test whether automated methods could be harnessed to search for new combinatorial games, and – more importantly – to recognise good games when they arose. A “good” game in this context is one with the potential to interest human players. Once a suitable game description language was defined, and a number of sample games defined for the initial population in the form of symbolic expressions, the generation of new rule sets was then a reasonably straightforward task, using an evolutionary approach and standard genetic programming mutation and crossover operators. A more significant hurdle to be overcome was the subsequent evaluation of the new games. Rule sets for combinatorial games are typically highly optimised and finely tuned by the designer, to play as well as possible with as few rules as possible. Random changes to a rule set will generally not improve a game – a diligent designer will already have tried the obvious variations – but simply break it, hence it could be expected that an evolutionary search would be likely to produce many unplayable games. The quality of each candidate game was estimated by running a number of self-play trials between two AI players; direct evaluation from rule sets is not sufficient, as games reveal their true nature during actual play. A simple playability filter was used to detect blatantly unplayable games, filtering out around 98% of evolved individuals, and the surviving individuals were then studied in more detail and ranked according to a number of aesthetic criteria, previously correlated with human player rankings of the set of source games. Of the 1,389 games evolved by LUDI, 19 proved to be playable, and two – christened Yavalath and Ndengrod by the system – proved to be of notable quality, and were commercially released in 2009 by Spanish publisher nestorgames. 2 Yavalath, especially, has been well received by players, and constitutes the first known case of a high quality (publishable) game to be designed using a fully automated approach. Evolutionary Game Design summarises this earlier work, but goes further to frame it within the context of computational creativity, and to examine where LUDI succeeded and where it failed, with the benefit of hindsight; some interesting developments have emerged over the years as the evolved games are played more and examined in more detail. The author and ICGA editor chose to publish this particular chapter, as Yavalath represents the culmination and highlight of the LUDI project. [The review by Ingo Althofer (2010) has been the trigger for the Editor’s request to Cameron Browne, since the Editor believed that the game and in particular its birth should be communicated extensively to our community. Since clarity of presentation has already been achieved in the book, we reproduce the book chapter with some slight changes so as to fit its publication in the ICGA Journal. We thank the Editorial Director of Springer in the Acknowledgement at the end of the article, where we also provide the references mentioned in this prolegomenon – Ed.]

Sample Size Determination for Alternate Periods of Use Study Designs with Binary Responses

In this article, we consider several study designs that arise in practice, which are variations of standard crossover designs. Often, they may result from modifications made to a standard crossover design due to practical considerations. Characteristic features of the studies we are concerned with are (a) treatments consist of external use of products with little or no possibility of carry over effects, and (b) the periods of use are dictated by the subjects or by some specific event, such as diaper leakage or menstrual flow. We consider a number of such study designs for estimating the difference in the efficacy of two treatments or test products. We provide brief descriptions of studies to motivate the study design, the underlying data structure, and computations of the variances of the usual unbiased estimators of the difference in efficacy, and the sample size formulas. The situations considered here cover a number of popular crossover designs. The objective of our work is to provide guidance to members of a wide audience on how to answer the sample size question for their own nonstandard situations. We conclude the article with a brief report on a simulation study we conducted to investigate the impact of estimation on the sample size determination and consequently on the actual power realized in an effort to promote the “best practice” of checking whether the recommended sample sizes indeed achieve the desired level of power.

A distance between populations for one-point crossover in genetic algorithms

Genetic algorithms use transformation operators on the genotypic structures of the individuals to carry out a search. These operators define a neighborhood. To analyze various dynamics of the search process, it is often useful to define a distance in this space. In fact, using an operator-based distance can make the analysis more accurate and reliable than using distances which have no relationship with the genetic operators. In this paper we define a distance which is based on the standard one-point crossover. Given that the population strongly affects the neighborhood induced by the crossover, we first define a crossover-based distance between populations. Successively, we show that it is naturally possible to derive from this function a family of distances between individuals. Finally, we also introduce an algorithm to compute this distance efficiently.

The critical Casimir effect in films for generic non-symmetry-breaking boundary conditions

Systems described by an O(n) symmetrical ϕ4 Hamiltonian are considered in a d-dimensional film geometry at their bulk critical points. A detailed renormalization group (RG) study of the critical Casimir forces induced between the film's boundary planes , by thermal fluctuations is presented for the case where the O(n) symmetry remains unbroken by the surfaces. The boundary planes are assumed to cause short-range disturbances of the interactions that can be modelled by standard surface contributions ∝ϕ2 corresponding to subcritical or critical enhancement of the surface interactions. This translates into mesoscopic boundary conditions of the generic symmetry-preserving Robin type . RG-improved perturbation theory and Abel–Plana techniques are used to compute the L-dependent part fres of the reduced excess free energy per film area A → ∞ to two-loop order. When d < 4, it takes the scaling form fres ≈ D(c1LΦ/ν,c2LΦ/ν)/Ld−1 as L → ∞, where ci are scaling fields associated with the surface-enhancement variables c˚i, while Φ is a standard surface crossover exponent. The scaling function D(c1,c2) and its analogue for the Casimir force are determined via expansion in ϵ = 4 − d and extrapolated to d = 3 dimensions. In the special case c1 = c2 = 0, the expansion becomes fractional. Consistency with the known fractional expansions of D(0,0) and to order ϵ3/2 is achieved by appropriate reorganization of RG-improved perturbation theory. For appropriate choices of c1 and c2, the Casimir forces can have either sign. Furthermore, crossovers from attraction to repulsion and vice versa may occur as L increases.

Revised KAD tool to optimize F1 cars through a combined-elitarian genetic-fuzzy algorithm

The KAD (Knowledge Aided Design) tool is developed to predict the performance of an F1 car in different driving conditions and with different configurations. The regulations to put in trimming a car, also in the exasperated technology of the competitions, still demand a remarkable dose of luck and an elevated number of tests. It is then important to know a set of regulations close to the optimal trim before testing the car on the track. The difficult phase of this process is to evaluate the lap time. As a matter of fact driving style, track conditions and car behavior should be simulated. The optimisation of the fuzzy controller that simulates the pilot for an F1 racing car is difficult due to handling problems and velocity of response. For this purpose a specific Genetic Algorithm (GA) was conceived and tuned to work with a lumped mass model of an F1 racing car for the optimization of the fuzzy controller that simulates the pilot. A new mutation and a new crossover operator were defined to complement the standard crossover and mutation operators of the basic Holland’s GA. This was necessary in order to increase the overall performance of the fuzzy pilot. This approach was tested on an F1 car due to the huge amount of data available (Donnarumma, 1998; Moelenbein, 1989; Lee and Takagi, 1993).

The search for a spin crossover transition in small sizedπ-conjugated molecules: a Monte Carlo study

The spin crossover transition inπ-conjugated polymers is a complex phenomenon involving a balance betweenCoulomb interaction and collective lattice distortions. We explore sucha transition with a minimal electronic model comprising a Hubbard-U on-site repulsive potential and both electron–phonon and hyperfine interactions. The modelis then solved numerically for small molecules at finite temperature by Monte Carlo methods inthe search for the spin crossover. This is done at the mean field level in the Hubbard-U interaction at half filling. We demonstrate that for a certain region of the parameter spacethere is a spin crossover, where the system transits from a low-spin to a high-spin state asthe temperature increases. In close analogy to standard spin crossover in divalent magneticmolecules such a transition is entropy driven, with both the spin and the vibrationalcontributions to the entropy being relevant. Such a transition is practically unaffected bythe hyperfine interaction, which only plays a minor role in determining the electronicproperties.

Depth-control strategies for crossover in tree-based genetic programming

The standard subtree crossover operator in the tree-based genetic programming (GP) has been considered as problematic. In order to improve the standard subtree crossover, controlling depth of crossover points becomes a research topic. However, the existence of many different and inconsistent crossover depth-control schemes and the possibility of many other depth-control schemes make the identification of good depth-control schemes a challenging problem. This paper aims to investigate general heuristics for making good depth-control schemes for crossover in tree-based GP. It analyses the patterns of depth of crossover points in good predecessor programs of five GP systems that use the standard subtree crossover and four approximations of the optimal crossover operator on three problems in different domains. The analysis results show that an effective depth-control scheme is problem-dependent and evolutionary stage-dependent, and that good crossover events have a strong preference for roots and (less strongly) bottoms of parent program trees. The results also show that some ranges of depths between the roots and the bottoms are also preferred, suggesting that unequal-depth-selection-probability strategies are better than equal-depth-selection-probability strategies.

The n-of-1 clinical trial: the ultimate strategy for individualizing medicine?

N-of-1 or single subject clinical trials consider an individual patient as the sole unit of observation in a study investigating the efficacy or side-effect profiles of different interventions. The ultimate goal of an n-of-1 trial is to determine the optimal or best intervention for an individual patient using objective data-driven criteria. Such trials can leverage study design and statistical techniques associated with standard population-based clinical trials, including randomization, washout and crossover periods, as well as placebo controls. Despite their obvious appeal and wide use in educational settings, n-of-1 trials have been used sparingly in medical and general clinical settings. We briefly review the history, motivation and design of n-of-1 trials and emphasize the great utility of modern wireless medical monitoring devices in their execution. We ultimately argue that n-of-1 trials demand serious attention among the health research and clinical care communities given the contemporary focus on individualized medicine.

Disturbed Exploitation compact Differential Evolution for limited memory optimization problems

This paper proposes a novel and unconventional Memetic Computing approach for solving continuous optimization problems characterized by memory limitations. The proposed algorithm, unlike employing an explorative evolutionary framework and a set of local search algorithms, employs multiple exploitative search within the main framework and performs a multiple step global search by means of a randomized perturbation of the virtual population corresponding to a periodical randomization of the search for the exploitative operators. The proposed Memetic Computing approach is based on a populationless (compact) evolutionary framework which, instead of processing a population of solutions, handles its statistical model. This evolutionary framework is based on a Differential Evolution which cooperatively employs two exploitative search operators: the first is based on a standard Differential Evolution mutation and exponential crossover, and the second is the trigonometric mutation. These two search operators have an exploitative action on the algorithmic framework and thus contribute to the rapid convergence of the virtual population towards promising candidate solutions. The action of these search operators is counterbalanced by a periodical stochastic perturbation of the virtual population, which has the role of “disturbing” the excessively exploitative action of the framework and thus inhibits its premature convergence. The proposed algorithm, namely Disturbed Exploitation compact Differential Evolution, is a simple and memory-wise cheap structure that makes use of the Memetic Computing paradigm in order to solve complex optimization problems. The proposed approach has been tested on a set of various test problems and compared with state-of-the-art compact algorithms and with some modern population based meta-heuristics. Numerical results show that Disturbed Exploitation compact Differential Evolution significantly outperforms all the other compact algorithms present in literature and reaches a competitive performance with respect to modern population algorithms, including some memetic approaches and complex modern Differential Evolution based algorithms. In order to show the potential of the proposed approach in real-world applications, Disturbed Exploitation compact Differential Evolution has been implemented for performing the control of a space robot by simulating the implementation within the robot micro-controller. Numerical results show the superiority of the proposed algorithm with respect to other modern compact algorithms present in literature.

Genetic programming with one-point crossover and subtree mutation for effective problem solving and bloat control

Genetic programming (GP) is one of the most widely used paradigms of evolutionary computation due to its ability to automatically synthesize computer programs and mathematical expressions. However, because GP uses a variable length representation, the individuals within the evolving population tend to grow rapidly without a corresponding return in fitness improvement, a phenomenon known as bloat. In this paper, we present a simple bloat control strategy for standard tree-based GP that achieves a one order of magnitude reduction in bloat when compared with standard GP on benchmark tests, and practically eliminates bloat on two real-world problems. Our proposal is to substitute standard subtree crossover with the one-point crossover (OPX) developed by Poli and Langdon (Second online world conference on soft computing in engineering design and manufacturing, Springer, Berlin (1997)), while maintaining all other GP aspects standard, particularly subtree mutation. OPX was proposed for theoretical purposes related to GP schema theorems, however since it curtails exploration during the search it has never achieved widespread use. In our results, on the other hand, we are able to show that OPX can indeed perform an effective search if it is coupled with subtree mutation, thus combining the bloat control capabilities of OPX with the exploration provided by standard mutation.

Statistical Issues in Bioavailability/Bioequivalence Studies

For the approval of generic drug products, bioavailability/bioequivalence studies are often conducted to demonstrate that the drug absorption profiles in terms of the extent and rate of absorption of test products are bioequivalent to those of the innovative drug product. The bioavailability/bioequivalence studies are often conducted under a standard two-sequence, two-period (2x2) crossover design. Under the standard 2x2 crossover design, statistical methods are well established for the assessment of bioequivalence. However, it is a concern whether approved generic drug products can be used safely and interchangeably. In this article, drug interchangeability under a replicated crossover bioavailability/bioequivalence study is discussed. Several controversial statistical issues that are commonly encountered in the assessment of bioequivalence are discussed. In addition, some frequently asked questions during regulatory submissions are reviewed. Recommendations regarding possible resolutions are made whenever possible. Some concluding remarks on the feasibility of the application of current methods for bioequivalence to the assessment of biosimilarity of follow-on biologics are also presented.

Semantically-based crossover in genetic programming: application to real-valued symbolic regression

We investigate the effects of semantically-based crossover operators in genetic programming, applied to real-valued symbolic regression problems. We propose two new relations derived from the semantic distance between subtrees, known as semantic equivalence and semantic similarity. These relations are used to guide variants of the crossover operator, resulting in two new crossover operators--semantics aware crossover (SAC) and semantic similarity-based crossover (SSC). SAC, was introduced and previously studied, is added here for the purpose of comparison and analysis. SSC extends SAC by more closely controlling the semantic distance between subtrees to which crossover may be applied. The new operators were tested on some real-valued symbolic regression problems and compared with standard crossover (SC), context aware crossover (CAC), Soft Brood Selection (SBS), and No Same Mate (NSM) selection. The experimental results show on the problems examined that, with computational effort measured by the number of function node evaluations, only SSC and SBS were significantly better than SC, and SSC was often better than SBS. Further experiments were also conducted to analyse the perfomance sensitivity to the parameter settings for SSC. This analysis leads to a conclusion that SSC is more constructive and has higher locality than SAC, NSM and SC; we believe these are the main reasons for the improved performance of SSC.

Subset selection from multi-experiment data sets with application to milk fatty acid profiles

The development of routine analyses to allow for the handling of large amounts of samples and to avoid cost and time expensive analytical techniques is of high value. These routine analyses most often require calibration using the detailed analyses as reference values. A representative subset reflecting the complete range of the variables of interest is required for this purpose. In this paper this subset selection problem is tackled for multi-experiment data sets. Conventional techniques such as the Kennard and Stone algorithm and OptiSim are compared to a new approach based on Genetic Algorithms. The challenge here is to find an adequate objective function and to modify the standard crossover and mutation operators to keep the number of desired samples fixed. These techniques are applied on a data set containing the concentration of 45 fatty acids, determined by a simplified reference method, in 1033 milk samples, stemming from six different experiments. The objective is to select a subset of 100 samples in which each of the six different experiments is sufficiently represented. While there is no obvious way to generalize the conventional methods for multi-experiment data sets, this can quite easily be accomplished for Genetic Algorithms by modifying the objective function. Our results indicate that Genetic Algorithms are very capable of handling the subset selection problem for multi-experiment data sets.

A preliminary investigation into the effect of coffee on hypolagesia associated with transcutaneous electrical nerve stimulation

Transcutaneous electrical nerve stimulation (TENS) is a non-invasive, inexpensive analgesic technique used to relieve pain. It has been suggested that caffeine, an adenosine antagonist, may interfere with TENS action. This double-blind controlled pilot study investigated the effect of coffee on response to TENS in healthy human participants experiencing experimentally induced pain. Twelve participants (7 female, age range = 20-41 years) took part in two experiments separated by 24 h. Each experiment lasted 80 min and consisted of 3 x 15 min cycles: pre-TENS, during TENS predrink and during TENS postdrink [coffee (100 mg caffeine) or decaffeinated coffee randomized across experiments]. During each cycle, thresholds for electrical (EPT), mechanical (MPT) and cold pressor (CPT) pain were recorded. The statistical analysis modelled the responses for the coffee and decaffeinated coffee conditions during TENS (i.e. as a standard crossover) and detected no statistically significant effects between coffee and decaffeinated drinks for the natural logarithm (ln) transformed values of electrical pain threshold [ln EPT Coffee-ln EPT Decaffeinated coffee mean (standard error) = 0.0147 (0.2159)], mechanical pain threshold [ln MPT Coffee-ln MPT Decaffeinated coffee mean (standard error) = 0.1296 (0.0816)] and cold pain threshold [ln CPT Coffee-ln CPT Decaffeinated coffee mean (standard error) = 0.0793 (0.1139)]. We conclude that a single cup of coffee (100 mg caffeine) had no detectable effect on TENS outcome. Reasons why coffee did not produce a detectable effect on pain threshold are discussed.