## Schedule (Day 1, Day 2, Day 3, Day 4)

### Schedule for Saturday (top)

 When Who What 9.30am Organisers Welcome 10am Timo Kötzing, Andrei Lissovoi, Carsten Witt (1+1) EA on Generalized Dynamic OneMax 11am Coffee Break 11.30am Johannes Lengler, Nick Spooner Fixed Budget Performance of the (1+1)-EA on Linear Functions 12.30pm Lunch Break 1.30pm Leslie Goldberg Invited Talk: Evolutionary Dynamics on Graphs 3pm Coffee Break 3.30pm Eric Scott, Kenneth De Jong Understanding Simple Asynchronous Evolutionary Algorithms

### Schedule for Sunday (top)

 When Who What 9.30am Sandra Astete-Morales, Marie-Liesse Cauwet, Olivier Teytaud Evolution Strategies with Additive Noise: A Convergence Rate Lower Bound 10.30am Coffee Break 11am Adam Prügel-Bennett, Jonathan Rowe, Jonathan Shapiro Run-Time Analysis of Population-Based Evolutionary Algorithm in Noisy Environments 1pm Excursion

### Schedule for Monday (top)

 When Who What 9.30am Duc-Cuong Dang, Per Kristian Lehre Efficient Optimisation of Noisy Fitness Functions with Population-based Evolutionary Algorithms 10.30am Coffee Break 11am Keki Burjorjee Implicit Concurrency in Evolutionary Computation 12pm Lunch Break 1pm Mathys C. Du Plessis, Andries P. Engelbrecht, Andre Calitz Self-Adapting the Brownian Radius in a Differential Evolution Algorithm for Dynamic Environments 2pm Renato Tinos, Darrell Whitley, Francisco Chicano Partition Crossover for Pseudo-Boolean Optimization 3pm Coffee Break 3.30pm Luigi Malagò, Giovanni Pistone Information Geometry of Gaussian Distributions in View of Stochastic Optimization 4.30pm Oswin Krause, Christian Igel A More Efficient Rank-one Covariance Matrix Update for Evolution Strategies 7pm Conference Dinner

### Schedule for Tuesday (top)

 When Who What 9.30am Marie-Liesse Cauwet, Shih-Yuan Chiu, Kuo-Min Lin, David Saint-Pierre, Fabien Teytaud, Olivier Teytaud, Shi-Jim Yen Parallel Evolutionary Algorithms Performing Pairwise Comparisons 10.30am Coffee Break 11am Alan Lockett Insights From Adversarial Fitness Functions 12pm Lunch Break 1pm Richard Mealing, Jonathan Shapiro Convergence of Strategies in Simple Co-Adapting Games 2pm Golnaz Badkobeh, Per Kristian Lehre, Dirk Sudholt Black-box Complexity of Parallel Search with Distributed Populations 3pm Coffee Break 3.30pm Thomas Jansen On the Black-Box Complexity of Example Functions: The Real Jump Function 4.30pm Organisers Close

## Talks (Day 1, Day 2, Day 3, Day 4)

### Talks on Saturday (top)

#### Saturday, 10am Timo Kötzing, Andrei Lissovoi, Carsten Witt: (1+1) EA on Generalized Dynamic OneMax

Evolutionary algorithms (EAs) perform well in settings involving uncertainty, including settings with stochastic or dynamic fitness functions. In this paper, we analyze the (1+1) EA on dynamically changing OneMax, as introduced by Droste (2003). We re-prove the known results on first hitting times using the modern tool of drift analysis. We extend these results to search spaces which allow for more than two values per dimension.

Furthermore, we make an anytime analysis as suggested by Jansen and Zarges (2014), analyzing how closely the (1+1) EA can track the dynamically moving optimum over time. We get tight bounds both for the case of bit strings, as well the case of more than two values per position. Surprisingly, in the latter setting, the expected quality of the search point maintained by the (1+1) EA does not depend on the number of values per dimension.

#### Saturday, 11.30am Johannes Lengler, Nick Spooner: Fixed Budget Performance of the (1+1)-EA on Linear Functions

We present a fixed budget analysis of the (1+1) evolutionary algorithm for general linear functions, considering both the quality of the solution after a predetermined ‘budget’ of fitness function evaluations (a priori) and the improvement in quality when the algorithm is given additional budget, given the quality of the current solution (a posteriori). Two methods are presented: one based on drift analysis, the other on the differential equation method and Chebyshev’s inequality. While the first method is superior for general linear functions, the second can be more precise for specific functions and provides concentration guarantees. As an example, we provide tight a posteriori fixed budget results for the function OneMax.

#### Saturday, 1.30pm Leslie Goldberg: Evolutionary Dynamics on Graphs

The Moran process models the spread of mutations in populations on graphs. This talk discusses the model, as adapted by Lieberman, Hauert and Nowak. I will describe what is known about fixation probabilities and about the expected absorption time of the process. The talk is based on joint work with Josep Diaz, David Richerby and Maria Serna and also by joint work with these authors and with George Mertzios and Paul Spirakis.

#### Saturday, 3.30pm Eric Scott, Kenneth De Jong: Understanding Simple Asynchronous Evolutionary Algorithms

Asynchronous evolutionary algorithms promise to eliminate idle time and improve the wall-clock time incurred while evolving solutions to large, complex, stochastic simulation models. The behavior of asynchronous algorithms is not well understood, however, and it’s not clear if and when the evolutionary trajectory they follow may be detrimental. We conduct a preliminary analysis of simple asynchronous EAs, finding that a bias toward individuals with fast evaluation times exists in some cases, but that this bias tends only to speed up convergence, not slow it down.

### Talks on Sunday (top)

#### Sunday, 9.30am Sandra Astete-Morales, Marie-Liesse Cauwet, Olivier Teytaud: Evolution Strategies with Additive Noise: A Convergence Rate Lower Bound

We consider the problem of optimizing functions corrupted with additive noise. It is known that evolutionary algorithms can reach a simple regret $O(1/\sqrt{n})$ within logarithmic factors, when n is the number of function evaluations. We show mathematically that this bound is tight, at least for a wide family of evolution strategies without large mutations.

#### Sunday, 11am Adam Prügel-Bennett, Jonathan Rowe, Jonathan Shapiro: Run-Time Analysis of Population-Based Evolutionary Algorithm in Noisy Environments

This paper analyses a generational evolutionary algorithm using only selection and uniform crossover. With a probability arbitrarily close to one the evolutionary algorithm is shown to solve OneMax in $O(n\log^2(n))$ function evaluations using a population of size $c n \log(n)$. We then show that this algorithm can solve OneMax with noise variance $n$ again in $O(n\log^2(n))$ function evaluations.

### Talks on Monday (top)

#### Monday, 9.30am Duc-Cuong Dang, Per Kristian Lehre: Efficient Optimisation of Noisy Fitness Functions with Population-based Evolutionary Algorithms

Population-based Evolutionary Algorithms (EA) can optimise pseudo-Boolean functions in expected polynomial time, even when only partial information about the problem is available. In this paper, we show that this result extends to optimisation of pseudo-Boolean problems with an additive noise term. Very general conditions on the noise term is derived, under which the EA optimises the noisy function in expected polynomial time. In the case of the OneMax and LeadingOnes problems, efficient optimisation is even possible when the variance of the noise distribution grows quickly with the problem size.

#### Monday, 11am Keki Burjorjee: Implicit Concurrency in Evolutionary Computation

We establish theoretical support for Implicit concurrent multivariate effect evaluation —implicit concurrency for short— a versatile computational learning efficiency thought to underlie general-purpose, non-local, noise-tolerant optimization in genetic algorithms. We demonstrate that implicit concurrency is indeed a form of efficient learning by showing that it can be used to obtain close-to-optimal bounds on the time and queries required to approximately correctly solve a constrained version ($k = 7$, $\eta = 1/5$) of a recognizable computational learning problem: learning parities with noisy membership queries. We argue that a genetic algorithm that treats the noisy membership query oracle as a fitness function can be straightforwardly used to approximately correctly learn the essential attributes in $O(\log^{1.585} n)$ queries and $O(n \log^{1.585} n)$ time, where $n$ is the total number of attributes. Our proof relies on an accessible symmetry argument and the use of statistical hypothesis testing to reject a global null hypothesis at the $10^{−100}$ level of significance. It is, to the best of our knowledge, the first relatively rigorous identification of efficient computational learning in a genetic algorithm on a non-trivial learning problem.

#### Monday, 1pm Mathys C. Du Plessis, Andries P. Engelbrecht, Andre Calitz: Self-Adapting the Brownian Radius in a Differential Evolution Algorithm for Dynamic Environments

Several algorithms aimed at dynamic optimisation problems have been developed. This paper reports on the incorporation of a self-adaptive Brownian radius into competitive differential evolution (CDE). Four variations of a novel technique to achieving the self-adaptation is suggested and motivated. An experimental investigation over a large number of benchmark instances is used to determine the most effective of the four variations. The new algorithm is compared to its base algorithm on an extensive set of benchmark problems and its performance analysed. Finally, the new algorithm is compared to other algorithms by means of reported results found in the literature. The results indicate that CDE is improved by the incorporation of the self-adaptive Brownian radius and that the new algorithm compares well with other algorithms.

#### Monday, 2pm Renato Tinos, Darrell Whitley, Francisco Chicano: Partition Crossover for Pseudo-Boolean Optimization

A partition recombination operator is introduced for all $k$-bounded pseudo-Boolean functions such as NK landscapes and MAX-$k$SAT. Under Partition crossover, the evaluation of the offspring can be directly obtained from partial evaluations of components found in the parents. Partition crossover explores the variable interaction graph of the pseudo-Boolean functions in order to partition the variables of the solution vector. Proofs are presented showing that if the differing variable assignments found in the two parents can be partitioned into $q$ non-interacting sets, Partition crossover can be used to find the best of $2^q$ possible offspring. This is done at $O(n)$ cost per recombination. Proofs are presented which show that parents that are locally optimal will always generate offspring that are locally optimal with respect to a (more restricted) hyperplane subspace. Empirical experiments show that parents that are locally optimal generate offspring that are locally optimal in the full search space more than 80 percent of the time. Experimental results show the efficiency of the proposed crossover when used in combination with a hybrid genetic algorithm.

#### Monday, 3.30pm Luigi Malagò, Giovanni Pistone: Information Geometry of Gaussian Distributions in View of Stochastic Optimization

We study the optimization of a continuous function by its stochastic relaxation, i.e., the optimization of the expected value of the function itself with respect to a density in a statistical model. We focus on gradient descent techniques applied to models from the exponential family and in particular on the multivariate Gaussian distribution. From the theory of the exponential family, we reparametrize the Gaussian distribution using natural and expectation parameters, and we derive formulas for natural gradients in both parameterizations. We discuss some advantages of the natural parameterization for the identification of sub-models in the Gaussian distribution based on conditional independence assumptions among variables. Gaussian distributions are widely used in stochastic optimization and in particular in model-based Evolutionary Computation, as in Estimation of Distribution Algorithms and Evolutionary Strategies. By studying natural gradient flows over Gaussian distributions our analysis and results directly apply to the study of CMA-ES and NES algorithms.

#### Monday, 4.30pm Oswin Krause, Christian Igel: A More Efficient Rank-one Covariance Matrix Update for Evolution Strategies

Learning covariance matrices of Gaussian distributions is at the heart of most variable-metric randomized algorithms for continuous optimization. If the search space dimensionality is high, updating the covariance or its factorization is computationally expensive. Therefore, we adopt an algorithm from numerical mathematics for rank-one updates of Cholesky factors. Our methods results in a quadratic time covariance matrix update scheme with minimal memory requirements. The numerically stable algorithm leads to triangular Cholesky factors. Systems of linear equations where the linear transformation is defined by a triangular matrix can be solved in quadratic time. This can be exploited to avoid the additional iterative update of the inverse Cholesky factor required in some covariance matrix adaptation algorithms proposed in the literature. When used together with the (1+1)-CMA-ES and the multi-objective CMA-ES, the new method leads to a memory reduction by a factor of almost four and a faster covariance matrix update. The numerical stability and runtime improvements are demonstrated on a set of benchmark functions.

### Talks on Tuesday (top)

#### Tuesday, 9.30am Marie-Liesse Cauwet, Shih-Yuan Chiu, Kuo-Min Lin, David Saint-Pierre, Fabien Teytaud, Olivier Teytaud, Shi-Jim Yen: Parallel Evolutionary Algorithms Performing Pairwise Comparisons

We study mathematically and experimentally the convergence rate of differential evolution and particle swarm optimization for simple unimodal functions. Due to parallelization concerns, the focus is on lower bounds on the runtime, i.e on upper bounds on the speed-up, as a function of the population sizes. Two cases are particularly relevant: population size of the order of magnitude of the dimension, and large population size. We use the branching factor as a tool for proving bounds, and get as upper bounds a linear speed-up for a population size of same order as the dimension, and a logarithmic speed-up for larger population sizes. We then propose parametrizations for differential evolution and particle swarm optimization that reach these bounds.

#### Tuesday, 11am Alan Lockett: Insights From Adversarial Fitness Functions

The performance of optimization is usually studied in specific settings where the fitness functions are highly constrained with static, stochastic or dynamic properties. This work examines what happens when the fitness function is a player engaged with the optimizer in an optimization game. Although the advantage of the fitness function is known through the No Free Lunch theorems, several deep and previously unexplored insights about the space of possible performance measurements arise as a consequence of studying these adversarial fitness function, including: 1) Every continuous and linear method of measuring performance can be identified with the optimization game for some adversarial fitness; 2) For any convex continuous performance criterion, there is some deterministic optimizer that performs best, even when the fitness function is stochastic or dynamic; 3) Every stochastic optimization method can be viewed as a probabilistic choice over countably many deterministic methods.

#### Tuesday, 1pm Richard Mealing, Jonathan Shapiro: Convergence of Strategies in Simple Co-Adapting Games

Simultaneously co-adapting agents in an uncooperative setting can result in a non-stationary environment where optimisation or learning is difficult and, where the agents strategies may not converge to solutions. This work looks at simple simultaneous-move games with two or three actions and, two or three players. Fictitious play is an old but popular algorithm that can converge to solutions, albeit slowly, in self-play in games like these. It models its opponents assuming that they use stationary strategies and, plays a best-response strategy to these models. We propose two new variants of fictitious play that remove this assumption, explicitly assuming that the opponents use dynamic strategies. The opponent’s strategy is predicted using a sequence prediction method in the first variant and, a change detection method in the second variant. Empirical results show that if our variants converge to solutions, then they converge faster than fictitious play. However, they do not always converge exactly to correct solutions. For change detection, this is a very small number of cases but, for sequence prediction there are many. The convergence of sequence prediction is improved by combining it with fictitious play.

#### Tuesday, 2pm Golnaz Badkobeh, Per Kristian Lehre, Dirk Sudholt: Black-box Complexity of Parallel Search with Distributed Populations

Many metaheuristics such as island models and cellular evolutionary algorithms use a network of distributed populations that communicate search points along a spatial communication topology. The idea is to slow down the spread of information, reducing the risk of "premature convergence", and sacrificing exploitation for an increased exploration.
We introduce the distributed black-box complexity as the minimum number of function evaluations every distributed black-box algorithm needs to optimise a given problem. It depends on the topology, the number of populations $\lambda$, and the problem size $n$. We give upper and lower bounds on the distributed black-box complexity for unary unbiased black-box algorithms on a class of unimodal functions in order to study the impact of communication topologies on performance. Our results confirm that rings and torus graphs can lead to higher black-box complexities, compared to unrestricted communication. We further determine cut-off points for the number of populations $\lambda$, above which no distributed black-box algorithm can achieve linear speedups.

#### Tuesday, 3.30pm Thomas Jansen: On the Black-Box Complexity of Example Functions: The Real Jump Function

Black-box complexity measures the difficulty of classes of functions with respect to optimisation by black-box algorithms. Comparing the black-box complexity with the worst case performance of a best know randomised search heuristics can help assessing if the randomised search heuristic is efficient or if there is room for improvement. When considering an example function it is necessary to extend it to a class of functions since single functions always have black-box complexity. Different kinds of extensions of single functions to function classes have been considered. In cases where the gap between the performance of the best randomised search heuristic and the black-box complexity is still large it can help to consider more restricted black-box complexity notions like unbiased black-box complexity. For the well-known Jump function both approaches have not been successful so far. We argue that the problem is not with the notion of black-box complexity but with the extension to a function class. We propose a different extension and show that for this extension there is a much better agreement even between the performance of an extremely simple evolutionary algorithm and the most general notion of black-box complexity.