Evolutionary algorithms (EAs) are general-purpose problem solvers that usually perform an unbiased search. This is reasonable and desirable in a black-box scenario. For combinatorial optimization problems, often more knowledge about the structure of optimal solutions is given, which can be leveraged by means of biased search operators. We consider the Minimum Spanning Tree (MST) problem in a single- and multi-objective version, and introduce a biased mutation, which puts more emphasis on the selection of edges of low rank in terms of low domination number. We present example graphs where the biased mutation can significantly speed up the expected runtime until (Pareto-)optimal solutions are found. On the other hand, we demonstrate that bias can lead to exponential runtime if heavy edges are necessarily part of an optimal solution. However, on general graphs in the single-objective setting, we show that a combined mutation operator which decides for unbiased or biased edge selection in each step with equal probability exhibits a polynomial upper bound -- as unbiased mutation -- in the worst case and benefits from bias if the circumstances are favorable.
This paper characterizes and discusses devolutionary genetic algorithms and evaluates their performances in solving the minimum labeling Steiner tree (MLST) problem. We define devolutionary algorithms as the process of reaching a feasible solution by devolving a population of super-optimal unfeasible solutions over time. We claim that distinguishing them from the widely used evolutionary algorithms is relevant. The most important distinction lies in the fact that in the former type of processes, the value function decreases over successive generation of solutions, thus providing a natural stopping condition for the computation process. We show how classical evolutionary concepts, such as crossing, mutation and fitness can be adapted to aim at reaching an optimal or close-to-optimal solution among the first generations of feasible solutions. We additionally introduce a novel integer linear programming formulation of the MLST problem and a valid constraint used for speeding up the devolutionary process. Finally, we conduct an experiment comparing the performances of devolutionary algorithms to those of state of the art approaches used for solving randomly generated instances of the MLST problem. Results of this experiment support the use of devolutionary algorithms for the MLST problem and their development for other NP-hard combinatorial optimization problems.
Runtime analysis aims at contributing to our understanding of evolutionary algorithms through mathematical analyses of their runtimes. In the context of discrete optimization problems, runtime analysis classically studies the time needed to find an optimal solution. However, both from a practical and from a theoretical viewpoint, more fine-grained performance measures are needed to gain a more detailed understanding of the main working principles and their resulting performance implications. Two complementary approaches have been suggested: fixed-budget analyses and fixed-target analyses. In this work, we conduct an in-depth study on the advantages and the limitations of fixed-target analyses. We show that, different from fixed-budget analyses, many classical methods from the runtime analysis of discrete evolutionary algorithms yield fixed-target results without greater effort. We use this to conduct a number of new fixed-target analyses. However, we also point out examples where an extension of existing runtime results to fixed-target results is highly non-trivial.
We consider the expected runtime of non-elitist evolutionary algorithms (EAs), when they are applied to a family of fitness functions with a plateau of second-best fitness in a Hamming ball of radius r around a unique global optimum. On one hand, using the level-based theorems, we obtain polynomial upper bounds on the expected runtime for some modes of non-elitist EA based on unbiased mutation and the bitwise mutation in particular. On the other hand, we show that the EA with fitness proportionate selection is inefficient if the bitwise mutation is used with the standard settings of mutation probability.
Classical benchmark problems utilize multiple transformation techniques to increase optimization difficulty, e.g., shift for anti centering effect and rotation for anti dimension sensitivity. Despite testing the transformation invariance, however, such operations do not really change the landscape's "shape", but rather than change the "view point". For instance, after rotated, ill conditional problems are turned around in terms of orientation but still keep proportional components, which, to some extent, does not create much obstacle in optimization. In this paper, inspired from image processing, we investigate a novel graphic conformal mapping transformation on benchmark problems to deform the function shape. The bending operation does not alter the function basic properties, e.g., a unimodal function can almost maintain its unimodality after bent, but can modify the shape of interested area in the search space. Experiments indicate the same optimizer spends more search budget and encounter more failures on the conformal bent functions than the rotated version. Several parameters of the proposed function are also analyzed to reveal performance sensitivity of the evolutionary algorithms.
The Dendritic Cell Algorithm (DCA) as one of the emerging evolutionary algorithms is based on the behavior of the specific immune agents; known as Dendritic Cells (DCs). DCA has several potentially beneficial features for binary classification problems. In this paper, we aim at providing a new version of this immune-inspired mechanism acts as a semi-supervised classifier which can be a defensive shield in network intrusion detection problem. Till now, no strategy or idea has already been adopted on the GetAntigen() function on detection phase, but randomly sampling entails the DCA to provide undesirable results in several cycles in each time. This leads to uncertainty. Whereas it must be accomplished by biological behaviors of DCs in tissues, we have proposed a novel strategy which exactly acts based on its immunological functionalities of dendritic cells. The proposed mechanism focuses on two items: First, to obviate the challenge of needing to have a preordered antigen set for computing danger signal, and the second, to provide a novel immune-inspired idea in order to non-random data sampling. A variable functional migration threshold is also computed cycle by cycle that shows necessity of the Migration threshold (MT) flexibility. A significant criterion so called capability of intrusion detection (CID) used for tests. All of the tests have been performed in a new benchmark dataset named UNSW-NB15. Experimental consequences demonstrate that the present schema dominates the standard DCA and has higher CID in comparison with other approaches found in literature.
The $(1+(\lambda,\lambda))$ genetic algorithm is a bright example of an evolutionary algorithm which was developed based on the insights from theoretical findings. This algorithm uses crossover, and it was shown to asymptotically outperform all mutation-based evolutionary algorithms even on simple problems like OneMax. Subsequently it was studied on a number of other problems, but all of these were pseudo-Boolean. We aim at improving this situation by proposing an adaptation of the $(1+(\lambda,\lambda))$ genetic algorithm to permutation-based problems. Such an adaptation is required, because permutations are noticeably different from bit strings in some key aspects, such as the number of possible mutations and their mutual dependence. We also present the first runtime analysis of this algorithm on a permutation-based problem called Ham whose properties resemble those of OneMax. On this problem, where the simple mutation-based algorithms have the running time of $\Theta(n^2 \log n)$ for problem size $n$, the $(1+(\lambda,\lambda))$ genetic algorithm finds the optimum in $O(n^2)$ fitness queries. We augment this analysis with experiments, which show that this algorithm is also fast in practice.
Segmentation partitions an image into different regions containing pixels with similar attributes. A standard non-contextual variant of Fuzzy C-means clustering algorithm (FCM), considering its simplicity is generally used in image segmentation. Using FCM has its disadvantages like it is dependent on the initial guess of the number of clusters and highly sensitive to noise. Satisfactory visual segments cannot be obtained using FCM. Particle Swarm Optimization (PSO) belongs to the class of evolutionary algorithms and has good convergence speed and fewer parameters compared to Genetic Algorithms (GAs). An optimized version of PSO can be combined with FCM to act as a proper initializer for the algorithm thereby reducing its sensitivity to initial guess. A hybrid PSO algorithm named Adaptive Particle Swarm Optimization (APSO) which improves in the calculation of various hyper parameters like inertia weight, learning factors over standard PSO, using insights from swarm behaviour, leading to improvement in cluster quality can be used. This paper presents a new image segmentation algorithm called Adaptive Particle Swarm Optimization and Fuzzy C-means Clustering Algorithm (APSOF), which is based on Adaptive Particle Swarm Optimization (APSO) and Fuzzy C-means clustering. Experimental results show that APSOF algorithm has edge over FCM in correctly identifying the optimum cluster centers, there by leading to accurate classification of the image pixels. Hence, APSOF algorithm has superior performance in comparison with classic Particle Swarm Optimization (PSO) and Fuzzy C-means clustering algorithm (FCM) for image segmentation.
Evolving diverse sets of high quality solutions has gained increasing interest in the evolutionary computation literature in recent years. With this paper, we contribute to this area of research by examining evolutionary diversity optimisation approaches for the classical Traveling Salesperson Problem (TSP). We study the impact of using different diversity measures for a given set of tours and the ability of evolutionary algorithms to obtain a diverse set of high quality solutions when adopting these measures. Our studies show that a large variety of diverse high quality tours can be achieved by using our approaches. Furthermore, we compare our approaches in terms of theoretical properties and the final set of tours obtained by the evolutionary diversity optimisation algorithm.
Neural Architecture Search (NAS), i.e., the automation of neural network design, has gained much popularity in recent years with increasingly complex search algorithms being proposed. Yet, solid comparisons with simple baselines are often missing. At the same time, recent retrospective studies have found many new algorithms to be no better than random search (RS). In this work we consider, for the first time, a simple Local Search (LS) algorithm for NAS. We particularly consider a multi-objective NAS formulation, with network accuracy and network complexity as two objectives, as understanding the trade-off between these two objectives is arguably the most interesting aspect of NAS. The proposed LS algorithm is compared with RS and two evolutionary algorithms (EAs), as these are often heralded as being ideal for multi-objective optimization. To promote reproducibility, we create and release two benchmark datasets, named MacroNAS-C10 and MacroNAS-C100, containing 200K saved network evaluations for two established image classification tasks, CIFAR-10 and CIFAR-100. Our benchmarks are designed to be complementary to existing benchmarks, especially in that they are better suited for multi-objective search. We additionally consider a version of the problem with a much larger architecture space. While we find and show that the considered algorithms explore the search space in fundamentally different ways, we also find that LS substantially outperforms RS and even performs nearly as good as state-of-the-art EAs. We believe that this provides strong evidence that LS is truly a competitive baseline for NAS against which new NAS algorithms should be benchmarked.
This paper intends to understand and to improve the working principle of decomposition-based multi-objective evolutionary algorithms. We review the design of the well-established Moea/d framework to support the smooth integration of different strategies for sub-problem selection, while emphasizing the role of the population size and of the number of offspring created at each generation. By conducting a comprehensive empirical analysis on a wide range of multi-and many-objective combinatorial NK landscapes, we provide new insights into the combined effect of those parameters on the anytime performance of the underlying search process. In particular, we show that even a simple random strategy selecting sub-problems at random outperforms existing sophisticated strategies. We also study the sensitivity of such strategies with respect to the ruggedness and the objective space dimension of the target problem.
Given a point in $m$-dimensional objective space, any $\varepsilon$-ball of a point can be partitioned into the incomparable, the dominated and dominating region. The ratio between the size of the incomparable region, and the dominated (and dominating) region decreases proportionally to $1/2^{m-1}$, i.e., the volume of the Pareto dominating orthant as compared to all other volumes. Due to this reason, it gets increasingly unlikely that dominating points can be found by random, isotropic mutations. As a remedy to stagnation of search in many objective optimization, in this paper, we suggest to enhance the Pareto dominance order by involving an obtuse convex dominance cone in the convergence phase of an evolutionary optimization algorithm. We propose edge-rotated cones as generalizations of Pareto dominance cones for which the opening angle can be controlled by a single parameter only. The approach is integrated in several state-of-the-art multi-objective evolutionary algorithms (MOEAs) and tested on benchmark problems with four, five, six and eight objectives. Computational experiments demonstrate the ability of these edge-rotated cones to improve the performance of MOEAs on many-objective optimization problems.
The $(1 + (\lambda,\lambda))$ genetic algorithm is a younger evolutionary algorithm trying to profit also from inferior solutions. Rigorous runtime analyses on unimodal fitness functions showed that it can indeed be faster than classical evolutionary algorithms, though on these simple problems the gains were only moderate. In this work, we conduct the first runtime analysis of this algorithm on a multimodal problem class, the jump functions benchmark. We show that with the right parameters, the \ollga optimizes any jump function with jump size $2 \le k \le n/4$ in expected time $O(n^{(k+1)/2} e^{O(k)} k^{-k/2})$, which significantly and already for constant~$k$ outperforms standard mutation-based algorithms with their $\Theta(n^k)$ runtime and standard crossover-based algorithms with their $\tilde{O}(n^{k-1})$ runtime guarantee. For the isolated problem of leaving the local optimum of jump functions, we determine provably optimal parameters that lead to a runtime of $(n/k)^{k/2} e^{\Theta(k)}$. This suggests some general advice on how to set the parameters of the \ollga, which might ease the further use of this algorithm.
Domination-based multi-objective (MO) evolutionary algorithms (EAs) are today arguably the most frequently used type of MOEA. These methods however stagnate when the majority of the population becomes non-dominated, preventing convergence to the Pareto set. Hypervolume-based MO optimization has shown promising results to overcome this. Direct use of the hypervolume however results in no selection pressure for dominated solutions. The recently introduced Sofomore framework overcomes this by solving multiple interleaved single-objective dynamic problems that iteratively improve a single approximation set, based on the uncrowded hypervolume improvement (UHVI). It thereby however loses many advantages of population-based MO optimization, such as handling multimodality. Here, we reformulate the UHVI as a quality measure for approximation sets, called the uncrowded hypervolume (UHV), which can be used to directly solve MO optimization problems with a single-objective optimizer. We use the state-of-the-art gene-pool optimal mixing evolutionary algorithm (GOMEA) that is capable of efficiently exploiting the intrinsically available grey-box properties of this problem. The resulting algorithm, UHV-GOMEA, is compared to Sofomore equipped with GOMEA, and the domination-based MO-GOMEA. In doing so, we investigate in which scenarios either domination-based or hypervolume-based methods are preferred. Finally, we construct a simple hybrid approach that combines MO-GOMEA with UHV-GOMEA and outperforms both.
Generative Adversarial Networks (GANs) are an adversarial model that achieved impressive results on generative tasks. In spite of the relevant results, GANs present some challenges regarding stability, making the training usually a hit-and-miss process. To overcome these challenges, several improvements were proposed to better handle the internal characteristics of the model, such as alternative loss functions or architectural changes on the neural networks used by the generator and the discriminator. Recent works proposed the use of evolutionary algorithms on GAN training, aiming to solve these challenges and to provide an automatic way to find good models. In this context, COEGAN proposes the use of coevolution and neuroevolution to orchestrate the training of GANs. However, previous experiments detected that some of the fitness functions used to guide the evolution are not ideal. In this work we propose the evaluation of a game-based fitness function to be used within the COEGAN method. Skill rating is a metric to quantify the skill of players in a game and has already been used to evaluate GANs. We extend this idea using the skill rating in an evolutionary algorithm to train GANs. The results show that skill rating can be used as fitness to guide the evolution in COEGAN without the dependence of an external evaluator.
Recently it has been proved that a simple algorithm configurator called ParamRLS can efficiently identify the optimal neighbourhood size to be used by stochastic local search to optimise two standard benchmark problem classes. In this paper we analyse the performance of algorithm configurators for tuning the more sophisticated global mutation operator used in standard evolutionary algorithms, which flips each of the $n$ bits independently with probability $\chi/n$ and the best value for $\chi$ has to be identified. We compare the performance of configurators when the best-found fitness values within the cutoff time $\kappa$ are used to compare configurations against the actual optimisation time for two standard benchmark problem classes, Ridge and LeadingOnes. We rigorously prove that all algorithm configurators that use optimisation time as performance metric require cutoff times that are at least as large as the expected optimisation time to identify the optimal configuration. Matters are considerably different if the fitness metric is used. To show this we prove that the simple ParamRLS-F configurator can identify the optimal mutation rates even when using cutoff times that are considerably smaller than the expected optimisation time of the best parameter value for both problem classes.
Recent theoretical research has shown that self-adjusting and self-adaptive mechanisms can provably outperform static settings in evolutionary algorithms for binary search spaces. However, the vast majority of these studies focuses on unimodal functions which do not require the algorithm to flip several bits simultaneously to make progress. In fact, existing self-adjusting algorithms are not designed to detect local optima and do not have any obvious benefit to cross large Hamming gaps. We suggest a mechanism called stagnation detection that can be added as a module to existing evolutionary algorithms (both with and without prior self-adjusting algorithms). Added to a simple (1+1) EA, we prove an expected runtime on the well-known Jump benchmark that corresponds to an asymptotically optimal parameter setting and outperforms other mechanisms for multimodal optimization like heavy-tailed mutation. We also investigate the module in the context of a self-adjusting (1+$\lambda$) EA and show that it combines the previous benefits of this algorithm on unimodal problems with more efficient multimodal optimization. To explore the limitations of the approach, we additionally present an example where both self-adjusting mechanisms, including stagnation detection, do not help to find a beneficial setting of the mutation rate. Finally, we investigate our module for stagnation detection experimentally.
The chance-constrained knapsack problem is a variant of the classical knapsack problem where each item has a weight distribution instead of a deterministic weight. The objective is to maximize the total profit of the selected items under the condition that the weight of the selected items only exceeds the given weight bound with a small probability of $\alpha$. In this paper, consider problem-specific single-objective and multi-objective approaches for the problem. We examine the use of heavy-tail mutations and introduce a problem-specific crossover operator to deal with the chance-constrained knapsack problem. Empirical results for single-objective evolutionary algorithms show the effectiveness of our operators compared to the use of classical operators. Moreover, we introduce a new effective multi-objective model for the chance-constrained knapsack problem. We use this model in combination with the problem-specific crossover operator in multi-objective evolutionary algorithms to solve the problem. Our experimental results show that this leads to significant performance improvements when using the approach in evolutionary multi-objective algorithms such as GSEMO and NSGA-II.
Divide-and-conquer-based (DC-based) evolutionary algorithms (EAs) have achieved notable success in dealing with large-scale optimization problems (LSOPs). However, the appealing performance of this type of algorithms generally requires a high-precision decomposition of the optimization problem, which is still a challenging task for existing decomposition methods. This study attempts to address the above issue from a different perspective and proposes an eigenspace divide-and-conquer (EDC) approach. Different from existing DC-based algorithms that perform decomposition and optimization in the original decision space, EDC first establishes an eigenspace by conducting singular value decomposition on a set of high-quality solutions selected from recent generations. Then it transforms the optimization problem into the eigenspace, and thus significantly weakens the dependencies among the corresponding eigenvariables. Accordingly, these eigenvariables can be efficiently grouped by a simple random strategy and each of the resulting subproblems can be addressed more easily by a traditional EA. To verify the efficiency of EDC, comprehensive experimental studies were conducted on two sets of benchmark functions. Experimental results indicate that EDC is robust to its parameters and has good scalability to the problem dimension. The comparison with several state-of-the-art algorithms further confirms that EDC is pretty competitive and performs better on complicated LSOPs.
Evolution gave rise to human and animal intelligence here on Earth. We argue that the path to developing artificial human-like-intelligence will pass through mimicking the evolutionary process in a nature-like simulation. In Nature, there are two processes driving the development of the brain: evolution and learning. Evolution acts slowly, across generations, and amongst other things, it defines what agents learn by changing their internal reward function. Learning acts fast, across one's lifetime, and it quickly updates agents' policy to maximise pleasure and minimise pain. The reward function is slowly aligned with the fitness function by evolution, however, as agents evolve the environment and its fitness function also change, increasing the misalignment between reward and fitness. It is extremely computationally expensive to replicate these two processes in simulation. This work proposes Evolution via Evolutionary Reward (EvER) that allows learning to single-handedly drive the search for policies with increasingly evolutionary fitness by ensuring the alignment of the reward function with the fitness function. In this search, EvER makes use of the whole state-action trajectories that agents go through their lifetime. In contrast, current evolutionary algorithms discard this information and consequently limit their potential efficiency at tackling sequential decision problems. We test our algorithm in two simple bio-inspired environments and show its superiority at generating more capable agents at surviving and reproducing their genes when compared with a state-of-the-art evolutionary algorithm.