%WBL 14 April 2011 (6 May) @proceedings(Beyer:2011:foga, title = {Foundations of Genetic Algorithms}, year = 2011, editor = {Hans-Georg Beyer and W.B. Langdon}, volume = {}, series = {}, address = {Schwarzenberg, Austria}, publisher_address = {}, month = {5-9 Jan}, organisation ={SigEvo}, publisher = {ACM}, note = {}, % email = {}, keywords = {}, ISBN13 = {978-1-4503-0633-1}, url = {http://portal.acm.org/citation.cfm?id=1967654}, size = {252 pages}, abstract = {}, notes = {ACM order number 910114}, ) @inproceedings(Jansen:2011:foga, title = {Analysis of evolutionary algorithms: from computational complexity analysis to algorithm engineering}, author = {Thomas Jansen and Christine Zarges}, booktitle = {Foundations of Genetic Algorithms}, year = 2011, editor = {Hans-Georg Beyer and W.B. Langdon}, pages = {1--14}, address = {Schwarzenberg, Austria}, month = {5-9 Jan}, organisation = {SigEvo}, publisher = {ACM}, note = {}, keywords = {}, ISBN13 = {978-1-4503-0633-1}, url = {}, size = {}, doi = {doi:10.1145/1967654.1967656}, abstract = {Analysing the computational complexity of evolutionary algorithms has become an accepted and important branch in evolutionary computation theory. This is usually done by analyzing the (expected) optimisation time measured by means of the number of function evaluations and describing its growth as a function of a measure for the size of the search space. Most often asymptotic results describing only the order of growth are derived. This corresponds to classical analysis of (randomised) algorithms in algorithmics. Recently, the emerging field of algorithm engineering has demonstrated that for practical purposes this analysis can be too coarse and more details of the algorithm and its implementation have to be taken into account in order to obtain results that are valid in practice. Using a very recent analysis of a simple evolutionary algorithm as starting point it is shown that the same holds for evolutionary algorithms. Considering this example it is demonstrated that counting function evaluations more precisely can lead to results contradicting actual run times. Motivated by these limitations of computational complexity analysis an algorithm engineering-like approach is presented.}, notes = {ACM order number 910114}, ) @inproceedings(Arnold:2011:foga, title = {On the behaviour of the (1,lambda)-es for a simple constrained problem}, author = {Dirk V. Arnold}, booktitle = {Foundations of Genetic Algorithms}, year = 2011, editor = {Hans-Georg Beyer and W.B. Langdon}, pages = {15--24}, address = {Schwarzenberg, Austria}, month = {5-9 Jan}, organisation = {SigEvo}, publisher = {ACM}, note = {}, keywords = {}, ISBN13 = {978-1-4503-0633-1}, url = {}, size = {}, doi = {doi:10.1145/1967654.1967657}, abstract = {We study the behaviour of the (1,lambda)-ES for a linear problem with a single linear constraint. The algorithm produces offspring until lambda feasible candidate solutions have been generated and selects the best of those as the next generation's parent. Integral expressions that describe the strategy's one-generation behaviour are developed and used in a simple zeroth order model for the steady state of the strategy. Implications for the performance of cumulative step size adaptation are discussed and a comparison with the (1+1)-ES is drawn.}, notes = {ACM order number 910114}, ) @inproceedings(Langdon:2011:foga, title = {Elementary bit string mutation landscapes}, author = {W. B. Langdon}, booktitle = {Foundations of Genetic Algorithms}, year = 2011, editor = {Hans-Georg Beyer and W.B. Langdon}, pages = {25--41}, address = {Schwarzenberg, Austria}, month = {5-9 Jan}, organisation = {SigEvo}, publisher = {ACM}, note = {}, keywords = {}, ISBN13 = {978-1-4503-0633-1}, url = {}, size = {}, doi = {doi:10.1145/1967654.1967658}, abstract = {Genetic Programming parity with only XOR is not elementary. GP parity can be represented as the sum of k/2+1 elementary landscapes. Statistics, including fitness distance correlation (FDC), of Parity's fitness landscape are calculated. Using Walsh analysis the eigen values and eigenvectors of the Laplacian of the two bit, three bit, n-bit and mutation only Genetic Algorithm fitness landscapes are given. Indeed all elementary bit string landscapes are related to the discrete Fourier functions. However most are rough (lambda/d approx 1). Also in many cases fitness autocorrelation falls rapidly with distance. GA runs support eigenvalue/graph degree (lambda/d) as a measure of the ruggedness of elementary landscapes for predicting problem difficulty. The elementary needle in a haystack (NIH) landscape is described.}, notes = {ACM order number 910114}, ) @inproceedings(Popovici:2011:foga, title = {On the practicality of optimal output mechanisms for co-optimization algorithms}, author = {Elena Popovici and Ezra Winston and Anthony Bucci}, booktitle = {Foundations of Genetic Algorithms}, year = 2011, editor = {Hans-Georg Beyer and W.B. Langdon}, pages = {43--59}, address = {Schwarzenberg, Austria}, month = {5-9 Jan}, organisation = {SigEvo}, publisher = {ACM}, note = {}, keywords = {}, ISBN13 = {978-1-4503-0633-1}, url = {}, size = {}, doi = {doi:10.1145/1967654.1967659}, abstract = {Co-optimisation problems involve one or more search spaces and a means of assessing interactions between entities in these spaces. Assessing a potential solution requires aggregating in some way the outcomes of a very large or infinite number of such interactions. This layer of complexity presents difficulties for algorithm design that are not encountered in ordinary optimisation. For example, what a co-optimization algorithm should output is not at all obvious. Theoretical research has shown that some output selection mechanisms yield better overall performance than others and described an optimal mechanism. This mechanism was shown to be strictly better than a greedy method in common use, but appeared prohibitive from a practical standpoint. In this paper we exhibit the optimal output mechanism for a particular class of co-optimization problems and a certain definition of better overall performance, and provide quantitative characterisations of domains for which this optimal mechanism becomes straightforward to implement. We conclude with a discussion of potential extensions of this work to other problem classes and other views on performance.}, notes = {ACM order number 910114}, ) @inproceedings(Coulom:2011:foga, title = {Handling expensive optimization with large noise}, author = {Remi Coulom and Philippe Rolet and Nataliya Sokolovska and Olivier Teytaud}, booktitle = {Foundations of Genetic Algorithms}, year = 2011, editor = {Hans-Georg Beyer and W.B. Langdon}, pages = {61--68}, address = {Schwarzenberg, Austria}, month = {5-9 Jan}, organisation = {SigEvo}, publisher = {ACM}, note = {}, keywords = {}, ISBN13 = {978-1-4503-0633-1}, url = {}, size = {}, doi = {doi:10.1145/1967654.1967660}, abstract = {We present lower and upper bounds on run times for expensive noisy optimisation problems. Runtimes are expressed in terms of number of fitness evaluations. Fitnesses considered are monotonic transformations of the sphere function. The analysis focuses on the common case of fitness functions quadratic in the distance to the optimum in the neighbourhood of this optimum - it is nonetheless also valid for any monotonic polynomial of degree p > 2. Upper bounds are derived via a bandit-based estimation of distribution algorithm that relies on Bernstein races called R-EDA. It is an evolutionary algorithm in the sense that it is based on selection, random mutations, with a distribution (updated at each iteration) for generating new individuals. It is known that the algorithm is consistent (i.e. it converges to the optimum asymptotically in the number of examples) even in some non-differentiable cases. Here we show that: (i) if the variance of the noise decreases to 0 around the optimum, it can perform well for quadratic transformations of the norm to the optimum, (ii) otherwise, a convergence rate is slower than the one exhibited empirically by an algorithm called Quadratic Logistic Regression (QLR) based on surrogate models - although QLR requires a probabilistic prior on the fitness class.}, notes = {ACM order number 910114}, ) @inproceedings(Durrett:2011:foga, title = {Computational complexity analysis of simple genetic programming on two problems modeling isolated program semantics}, author = {Greg Durrett and Frank Neumann and Una-May O'Reilly}, booktitle = {Foundations of Genetic Algorithms}, year = 2011, editor = {Hans-Georg Beyer and W.B. Langdon}, pages = {69--80}, address = {Schwarzenberg, Austria}, month = {5-9 Jan}, organisation = {SigEvo}, publisher = {ACM}, note = {}, keywords = {}, ISBN13 = {978-1-4503-0633-1}, url = {}, size = {}, doi = {doi:10.1145/1967654.1967661}, abstract = {Analysing the computational complexity of evolutionary algorithms (EAs) for binary search spaces has significantly informed our understanding of EAs in general. With this paper, we start the computational complexity analysis of genetic programming (GP). We set up several simplified GP algorithms and analyse them on two separable model problems, ORDER and MAJORITY, each of which captures a relevant facet of typical GP problems. Both analyses give first rigorous insights into aspects of GP design, highlighting in particular the impact of accepting or rejecting neutral moves and the importance of a local mutation operator.}, notes = {ACM order number 910114}, ) @inproceedings(Friedrich:2011:foga, title = {The logarithmic hypervolume indicator}, author = {Tobias Friedrich and Karl Bringmann and Thomas Voss and Christian Igel}, booktitle = {Foundations of Genetic Algorithms}, year = 2011, editor = {Hans-Georg Beyer and W.B. Langdon}, pages = {81--91}, address = {Schwarzenberg, Austria}, month = {5-9 Jan}, organisation = {SigEvo}, publisher = {ACM}, note = {}, keywords = {}, ISBN13 = {978-1-4503-0633-1}, url = {}, size = {}, doi = {doi:10.1145/1967654.1967662}, abstract = {It was recently proven that sets of points maximising the hypervolume indicator do not give a good multiplicative approximation of the Pareto front. We introduce a new "logarithmic hypervolume indicator" and prove that it achieves a close-to-optimal multiplicative approximation ratio. This is experimentally verified on several benchmark functions by comparing the approximation quality of the multi-objective covariance matrix evolution strategy (MO-CMA-ES) with the classic hypervolume indicator and the MO-CMA-ES with the logarithmic hypervolume indicator.}, notes = {ACM order number 910114}, ) @inproceedings(Sutton:2011:foga, title = {Approximating the distribution of fitness over hamming regions}, author = {Andrew M. Sutton and Darrell Whitley and Adele E. Howe}, booktitle = {Foundations of Genetic Algorithms}, year = 2011, editor = {Hans-Georg Beyer and W.B. Langdon}, pages = {93--103}, address = {Schwarzenberg, Austria}, month = {5-9 Jan}, organisation = {SigEvo}, publisher = {ACM}, note = {}, keywords = {}, ISBN13 = {978-1-4503-0633-1}, url = {}, size = {}, doi = {doi:10.1145/1967654.1967663}, abstract = {The distribution of fitness values across a set of states sharply influences the dynamics of evolutionary processes and heuristic search in combinatorial optimisation. In this paper we present a method for approximating the distribution of fitness values over Hamming regions by solving a linear programming problem that incorporates low order moments of the target function. These moments can be retrieved in polynomial time for select problems such as MAX-k-SAT using Walsh analysis. The method is applicable to any real function on binary strings that is epistatically bounded and discrete with asymptotic bounds on the cardinality of its codomain. We perform several studies on the ONE-MAX and MAX-k-SAT domains to assess the accuracy of the approximation and its dependence on various factors. We show that the approximation can accurately predict the number of states within a Hamming region that have an improving fitness value.}, notes = {ACM order number 910114}, ) @inproceedings(Kaden:2011:foga, title = {The role of selective pressure when solving symmetric functions in polynomial time}, author = {Lars Kaden and Nicole Weicker and Karsten Weicker}, booktitle = {Foundations of Genetic Algorithms}, year = 2011, editor = {Hans-Georg Beyer and W.B. Langdon}, pages = {105--117}, address = {Schwarzenberg, Austria}, month = {5-9 Jan}, organisation = {SigEvo}, publisher = {ACM}, note = {}, keywords = {}, ISBN13 = {978-1-4503-0633-1}, url = {}, size = {}, doi = {doi:10.1145/1967654.1967664}, abstract = {This paper is concerned with the question to which extent a change in the selective pressure might improve the run time of an optimisation algorithm considerably. The subject of this examination is the class of symmetric functions, i.e. OneMax with a subsequent application of a real valued function. We consider an improvement in runtime as considerable if an exponential run time becomes polynomial. The basis for this examination is a Markov chain analysis. An exact criterion for static selective pressure, telling which functions are solvable in polynomial time, is extended to a sufficient (but not necessary) criterion for changing selection pressure.}, notes = {ACM order number 910114}, ) @inproceedings(Doerr:2011:foga, title = {Runtime analysis of the (1+1) evolutionary algorithm on strings over finite alphabets}, author = {Benjamin Doerr and Daniel Johannsen and Martin Schmidt}, booktitle = {Foundations of Genetic Algorithms}, year = 2011, editor = {Hans-Georg Beyer and W.B. Langdon}, pages = {119--126}, address = {Schwarzenberg, Austria}, month = {5-9 Jan}, organisation = {SigEvo}, publisher = {ACM}, note = {}, keywords = {}, ISBN13 = {978-1-4503-0633-1}, url = {}, size = {}, doi = {doi:10.1145/1967654.1967665}, abstract = {In this work, we investigate a (1+1) Evolutionary Algorithm for optimizing functions over the space {0,...,r} n, where r is a positive integer. We show that for linear functions over {0,1,2}n, the expected runtime time of this algorithm is O(n log n). This result generalises an existing result on pseudo-Boolean functions and is derived using drift analysis. We also show that for large values of r, no upper bound for the run time of the (1+1) Evolutionary Algorithm for linear function on {0,...,r}n can be obtained with this approach nor with any other approach based on drift analysis with weight-independent linear potential functions.}, notes = {ACM order number 910114}, ) @inproceedings(Auger:2011:foga, title = {Analyzing the impact of mirrored sampling and sequential selection in elitist evolution strategies}, author = {Anne Auger and Dimo Brockhoff and Nikolaus Hansen}, booktitle = {Foundations of Genetic Algorithms}, year = 2011, editor = {Hans-Georg Beyer and W.B. Langdon}, pages = {127--138}, address = {Schwarzenberg, Austria}, month = {5-9 Jan}, organisation = {SigEvo}, publisher = {ACM}, note = {}, keywords = {}, ISBN13 = {978-1-4503-0633-1}, url = {}, size = {}, doi = {doi:10.1145/1967654.1967666}, abstract = {This paper presents a refined single parent evolution strategy that is derandomized with mirrored sampling and/or uses sequential selection. The paper analyses some of the elitist variants of this algorithm. We prove, on spherical functions with finite dimension, linear convergence of different strategies with scale-invariant step-size and provide expressions for the convergence rates as the expectation of some known random variables. In addition, we derive explicit asymptotic formulae for the convergence rate when the dimension of the search space goes to infinity. Convergence rates on the sphere reveal lower bounds for the convergence rate of the respective step-size adaptive strategies. We prove the surprising result that the (1+2)-ES with mirrored sampling converges at the same rate as the (1+1)-ES without and show that the tight lower bound for the (1+lambda-ES with mirrored sampling and sequential selection improves by 16% over the (1+1)-ES reaching an asymptotic value of about -0.235.}, notes = {ACM order number 910114}, ) @inproceedings(Sudholt:2011:foga, title = {Using Markov-chain mixing time estimates for the analysis of ant colony optimization}, author = {Dirk Sudholt}, booktitle = {Foundations of Genetic Algorithms}, year = 2011, editor = {Hans-Georg Beyer and W.B. Langdon}, pages = {139--150}, address = {Schwarzenberg, Austria}, month = {5-9 Jan}, organisation = {SigEvo}, publisher = {ACM}, note = {}, keywords = {}, ISBN13 = {978-1-4503-0633-1}, url = {}, size = {}, doi = {doi:10.1145/1967654.1967667}, abstract = {The Markov chain Monte Carlo paradigm has developed powerful and elegant techniques for estimating the time until a Markov chain approaches a stationary distribution. This time is known as mixing time. We introduce the reader into mixing time estimations via coupling arguments and use the mixing of pheromone models for analysing the expected optimisation time of ant colony optimization. We demonstrate the approach for plateaus in pseudo-Boolean optimisation and derive upper bounds for the time until a target set is found. We also describe how mixing times can be estimated for MMAS ant systems on shortest path problems.}, notes = {ACM order number 910114}, ) @inproceedings(Moraglio:2011:foga, title = {Abstract convex evolutionary search}, author = {Alberto Moraglio}, booktitle = {Foundations of Genetic Algorithms}, year = 2011, editor = {Hans-Georg Beyer and W.B. Langdon}, pages = {151--162}, address = {Schwarzenberg, Austria}, month = {5-9 Jan}, organisation = {SigEvo}, publisher = {ACM}, note = {}, keywords = {}, ISBN13 = {978-1-4503-0633-1}, url = {}, size = {}, doi = {doi:10.1145/1967654.1967668}, abstract = {Geometric crossover is a formal class of crossovers which includes many well-known recombination operators across representations. In this paper, we present a general result showing that all evolutionary algorithms using geometric crossover with no mutation perform the same form of convex search regardless of the underlying representation, the specific selection mechanism, the specific offspring distribution, the specific search space, and the problem at hand. We then start investigating a few representation/space-independent geometric conditions on the fitness landscape - various forms of generalised concavity - that when matched with the convex evolutionary search guarantee, to different extents, improvement of offspring over parents for any choice of parents. This is a first step towards showing that the convexity relation between search and landscape may play an important role towards explaining the performance of evolutionary algorithms in a general setting across representations.}, notes = {ACM order number 910114}, ) @inproceedings(Wagner:2011:foga, title = {Faster black-box algorithms through higher arity operators}, author = {Benjamin Doerr and Daniel Johannsen and Timo Kotzing and Per Kristian Lehre and Markus Wagner and Carola Winzen}, booktitle = {Foundations of Genetic Algorithms}, year = 2011, editor = {Hans-Georg Beyer and W.B. Langdon}, pages = {163--171}, address = {Schwarzenberg, Austria}, month = {5-9 Jan}, organisation = {SigEvo}, publisher = {ACM}, note = {}, keywords = {}, ISBN13 = {978-1-4503-0633-1}, url = {}, size = {}, doi = {doi:10.1145/1967654.1967669}, abstract = {We extend the work of Lehre and Witt (GECCO 2010) on the unbiased black-box model by considering higher arity variation operators. In particular, we show that already for binary operators the black-box complexity of LeadingOnes drops from Theta(n2) for unary operators to O(n log n). For OneMax, the Omega(n log n) unary black-box complexity drops to O(n) in the binary case. For k-ary operators, k lteq n, the OneMax-complexity further decreases to O(n / log k).}, notes = {ACM order number 910114}, ) @inproceedings(Cathabard:2011:foga, title = {Non-uniform mutation rates for problems with unknown solution lengths}, author = {Stephan Cathabard and Per Kristian Lehre and Xin Yao}, booktitle = {Foundations of Genetic Algorithms}, year = 2011, editor = {Hans-Georg Beyer and W.B. Langdon}, pages = {173--180}, address = {Schwarzenberg, Austria}, month = {5-9 Jan}, organisation = {SigEvo}, publisher = {ACM}, note = {}, keywords = {}, ISBN13 = {978-1-4503-0633-1}, url = {}, size = {}, doi = {doi:10.1145/1967654.1967670}, abstract = {Many practical optimisation problems allow candidate solutions of varying lengths, and where the length of the optimal solution is thereby a priori unknown. We suggest that non-uniform mutation rates can be beneficial when solving such problems. In particular, we consider a mutation operator that flips each bit with a probability that is inversely proportional to the bit position, rather than the bitstring length. The runtime of the (1+1) EA using this mutation operator is analysed rigorously on standard example functions. Furthermore, the behaviour of the new mutation operator is investigated empirically on a real world software engineering problem that has variable, and unknown solution lengths. The results show how the speedup that can be achieved with the new operator depends on the distribution of the solution lengths in the solution space. We consider a truncated geometric distribution, and show that the new operator can yield exponentially faster runtimes for some parameters of this distribution. The experimental results show that the new mutation operator leads to dramatically shorter run times on a class of instances of the software engineering problem that is conjectured to have short solutions on average.}, notes = {ACM order number 910114}, ) @inproceedings(Lassig:2011:foga, title = {Adaptive population models for offspring populations and parallel evolutionary algorithms}, author = {Jorg Lassig and Dirk Sudholt}, booktitle = {Foundations of Genetic Algorithms}, year = 2011, editor = {Hans-Georg Beyer and W.B. Langdon}, pages = {181--192}, address = {Schwarzenberg, Austria}, month = {5-9 Jan}, organisation = {SigEvo}, publisher = {ACM}, note = {}, keywords = {}, ISBN13 = {978-1-4503-0633-1}, url = {}, size = {}, doi = {doi:10.1145/1967654.1967671}, abstract = {We present two adaptive schemes for dynamically choosing the number of parallel instances in parallel evolutionary algorithms. This includes the choice of the offspring population size in a (1+lambda) EA as a special case. Our schemes are parameterless and they work in a black-box setting where no knowledge on the problem is available. Both schemes double the number of instances in case a generation ends without finding an improvement. In a successful generation, the first scheme resets the system to one instance, while the second scheme halves the number of instances. Both schemes provide near-optimal speed-ups in terms of the parallel time. We give upper bounds for the asymptotic sequential time (i.e., the total number of function evaluations) that are not larger than upper bounds for a corresponding non-parallel algorithm derived by the fitness-level method.}, notes = {ACM order number 910114}, ) @inproceedings(Wright:2011:foga, title = {On the movement of vertex fixed points in the simple GA}, author = {Alden H. Wright and Tomas Gedeon and J. Neal Richter}, booktitle = {Foundations of Genetic Algorithms}, year = 2011, editor = {Hans-Georg Beyer and W.B. Langdon}, pages = {193--207}, address = {Schwarzenberg, Austria}, month = {5-9 Jan}, organisation = {SigEvo}, publisher = {ACM}, note = {}, keywords = {}, ISBN13 = {978-1-4503-0633-1}, url = {}, size = {}, doi = {doi:10.1145/1967654.1967672}, abstract = {The Vose dynamical system model of the simple genetic algorithm models the behaviour of this algorithm for large population sizes and is the basis of the exact Markov chain model. Populations consisting of multiple copies of one individual correspond to vertices of the simplex. For zero mutation, these are fixed points of the dynamical system and absorbing states of the Markov chain. For proportional selection, the asymptotic stability of vertex fixed points is understood from previous work. We derive the eigenvalues of the differential at vertex fixed points of the dynamical system model for tournament selection. We show that as mutation increases from zero, hyperbolic asymptotically stable fixed points move into the simplex, and hyperbolic asymptotically unstable fixed points move outside of the simplex. We calculate the derivative of local path of the fixed point with respect to the mutation rate for proportional selection. Simulation analysis shows how fixed points bifurcate with larger changes in the mutation rate and changes in the crossover rate.}, notes = {ACM order number 910114}, ) @inproceedings(Kotzing:2011:foga, title = {Simple max-min ant systems and the optimization of linear pseudo-Boolean functions}, author = {Timo Kotzing and Frank Neumann and Dirk Sudholt and Markus Wagner}, booktitle = {Foundations of Genetic Algorithms}, year = 2011, editor = {Hans-Georg Beyer and W.B. Langdon}, pages = {209--218}, address = {Schwarzenberg, Austria}, month = {5-9 Jan}, organisation = {SigEvo}, publisher = {ACM}, note = {}, keywords = {}, ISBN13 = {978-1-4503-0633-1}, url = {}, size = {}, doi = {doi:10.1145/1967654.1967673}, abstract = {With this paper, we contribute to the understanding of ant colony optimisation (ACO) algorithms by formally analysing their runtime behaviour. We study simple MAX-MIN ant systems on the class of linear pseudo-Boolean functions defined on binary strings of length n. Our investigations point out how the progress according to function values is stored in the pheromones. We provide a general upper bound of O((n3 log n)rho) on the running time for two ACO variants on all linear functions, where rho determines the pheromone update strength. Furthermore, we show improved bounds for two well-known linear pseudo-Boolean functions called ONEMAX and BINVAL and give additional insights using an experimental study.}, notes = {ACM order number 910114}, ) @inproceedings(Bassett:2011:foga, title = {Using multivariate quantitative genetics theory to assist in EA customization}, author = {Jeffrey Kermes Bassett and Kenneth Alan {De Jong}}, booktitle = {Foundations of Genetic Algorithms}, year = 2011, editor = {Hans-Georg Beyer and W.B. Langdon}, pages = {219--229}, address = {Schwarzenberg, Austria}, month = {5-9 Jan}, organisation = {SigEvo}, publisher = {ACM}, note = {}, keywords = {}, ISBN13 = {978-1-4503-0633-1}, url = {}, size = {}, doi = {doi:10.1145/1967654.1967674}, abstract = {Customising and evolutionary algorithm (EA) for a new or unusual problem can seem relatively simple as long as one can devise an appropriate representation and reproductive operators to modify it. Unfortunately getting a customized EA to produce high quality results in a reasonable amount of time can be quite challenging. There is little guidance available to help practitioners deal with this issue. Most evolutionary computation (EC) theory is only applicable to specific representations, or assumes knowledge of the fitness function, such as the location of optima. We are developing an approach based on theory from the biology community to address this problem. Multivariate quantitative genetics theory characterises evolving populations as multivariate probability distributions of phenotypic traits. Some advantages it offers are a degree of independence from the underlying representation, and useful concepts such as phenotypic heritability. Re-working the quantitative genetics equations, we expose an additional term that we call "perturbation". We believe that perturbation and heritability provide quantitative measures of the exploration and exploitation, and that practitioners can use these to identify and diagnose imbalances in customised reproductive operators. To illustrate, we use these tools to diagnose problems with a standard recombination operator for a Pittsburgh approach classifier system. With this knowledge we develop a new, more balanced, recombination operator, and show that its use leads to significantly better results.}, notes = {ACM order number 910114}, ) @inproceedings(Malago:2011:foga, title = {Towards the geometry of estimation of distribution algorithms based on the exponential family}, author = {Luigi Malago and Matteo Matteucci and Giovanni Pistone}, booktitle = {Foundations of Genetic Algorithms}, year = 2011, editor = {Hans-Georg Beyer and W.B. Langdon}, pages = {230--242}, address = {Schwarzenberg, Austria}, month = {5-9 Jan}, organisation = {SigEvo}, publisher = {ACM}, note = {}, keywords = {}, ISBN13 = {978-1-4503-0633-1}, url = {}, size = {}, doi = {doi:10.1145/1967654.1967675}, abstract = {In this paper we present a geometrical framework for the analysis of Estimation of Distribution Algorithms (EDAs) based on the exponential family. From a theoretical point of view, an EDA can be modelled as a sequence of densities in a statistical model that converges towards distributions with reduced support. Under this framework, at each iteration the empirical mean of the fitness function decreases in probability, until convergence of the population. This is the context of stochastic relaxation, i.e., the idea of looking for the minima of a function by minimising its expected value over a set of probability densities. Our main interest is in the study of the gradient of the expected value of the function to be minimized, and in particular on how its landscape changes according to the fitness function and the statistical model used in the relaxation. After introducing some properties of the exponential family, such as the description of its topological closure and of its tangent space, we provide a characterisation of the stationary points of the relaxed problem, together with a study of the minimising sequences with reduced support. The analysis developed in the paper aims to provide a theoretical understanding of the behaviour of EDAs, and in particular their ability to converge to the global minimum of the fitness function. The theoretical results of this paper, beside providing a formal framework for the analysis of EDAs, lead to the definition of a new class algorithms for binary functions optimisation based on Stochastic Natural Gradient Descent (SNGD), where the estimation of the parameters of the distribution is replaced by the direct update of the model parameters by estimating the natural gradient of the expected value of the fitness function.}, notes = {ACM order number 910114}, ) @inproceedings(Beume:2011:foga, title = {Convergence rates of SMS-EMOA on continuous bi-objective problem classes}, author = {Nicola Beume and Marco Laumanns and Gunter Rudolph}, booktitle = {Foundations of Genetic Algorithms}, year = 2011, editor = {Hans-Georg Beyer and W.B. Langdon}, pages = {243--251}, address = {Schwarzenberg, Austria}, month = {5-9 Jan}, organisation = {SigEvo}, publisher = {ACM}, note = {}, keywords = {}, ISBN13 = {978-1-4503-0633-1}, url = {}, size = {}, doi = {doi:10.1145/1967654.1967676}, abstract = {Convergence rate analyses of evolutionary multi-objective optimization algorithms in continuous search space are yet rare. First results have been obtained for simple algorithms. Here, we provide concrete results of convergence rates for a state-of-the-art algorithm, namely the S-metric selection evolutionary multi-objective optimization algorithm (SMSEMOA). We show that the SMS-EMOA produces the same sequence of populations as certain single-objective evolutionary algorithms on arbitrary problem classes. Thereby we are able to transfer known convergence properties for classes of convex functions. We especially consider the SMS-EMOA with populations of parents and offspring greater than one and different concepts for the choice of the reference point used for the internal calculation of the dominated hypervolume within the selection operator.}, notes = {ACM order number 910114}, )