During the COVID-19 pandemic and similar outbreaks in the future, drones can be set up to reduce human interaction for medical supplies delivery, which is crucial in times of pandemic. In this short paper, we introduce the use of two evolutionary algorithms for multi-objective optimization (MOO) and tuning the parameters of the PD controller of a drone to follow the 3D desired path.
Optimal Lens Design constitutes a fundamental, long-standing real-world optimization challenge. Potentially large number of optima, rich variety of critical points, as well as solid understanding of certain optimal designs per simple problem instances, provide altogether the motivation to address it as a niching challenge. This study applies established Niching-CMA-ES heuristic to tackle this design problem (6-dimensional Cooke triplet) in a simulation-based fashion. The outcome of employing Niching-CMA-ES `out-of-the-box' proves successful, and yet it performs best when assisted by a local searcher which accurately drives the search into optima. The obtained search-points are corroborated based upon concrete knowledge of this problem-instance, accompanied by gradient and Hessian calculations for validation. We extensively report on this computational campaign, which overall resulted in (i) the location of 19 out of 21 known minima within a single run, (ii) the discovery of 540 new optima. These are new minima similar in shape to 21 theoretical solutions, but some of them have better merit function value (unknown heretofore), (iii) the identification of numerous infeasibility pockets throughout the domain (also unknown heretofore). We conclude that niching mechanism is well-suited to address this problem domain, and hypothesize on the apparent multidimensional structures formed by the attained new solutions.
Drones are effective for reducing human activity and interactions by performing tasks such as exploring and inspecting new environments, monitoring resources and delivering packages. Drones need a controller to maintain stability and to reach their goal. The most well-known drone controllers are proportional-integral-derivative (PID) and proportional-derivative (PD) controllers. However, the controller parameters need to be tuned and optimized. In this paper, we introduce the use of two evolutionary algorithms, biogeography-based optimization~(BBO) and particle swarm optimization (PSO), for multi-objective optimization (MOO) to tune the parameters of the PD controller of a drone. The combination of MOO, BBO, and PSO results in various methods for optimization: vector evaluated BBO and PSO, denoted as VEBBO and VEPSO; and non-dominated sorting BBO and PSO, denoted as NSBBO and NSPSO. The multi-objective cost function is based on tracking errors for the four states of the system. Two criteria for evaluating the Pareto fronts of the optimization methods, normalized hypervolume and relative coverage, are used to compare performance. Results show that NSBBO generally performs better than the other methods.
In addition to their undisputed success in solving classical optimization problems, neuroevolutionary and population-based algorithms have become an alternative to standard reinforcement learning methods. However, evolutionary methods often lack the sample efficiency of standard value-based methods that leverage gathered state and value experience. If reinforcement learning for real-world problems with significant resource cost is considered, sample efficiency is essential. The enhancement of evolutionary algorithms with experience exploiting methods is thus desired and promises valuable insights. This work presents a hybrid algorithm that combines topology-changing neuroevolutionary optimization with value-based reinforcement learning. We illustrate how the behavior of policies can be used to create distance and loss functions, which benefit from stored experiences and calculated state values. They allow us to model behavior and perform a directed search in the behavior space by gradient-free evolutionary algorithms and surrogate-based optimization. For this purpose, we consolidate different methods to generate and optimize agent policies, creating a diverse population. We exemplify the performance of our algorithm on standard benchmarks and a purpose-built real-world problem. Our results indicate that combining methods can enhance the sample efficiency and learning speed for evolutionary approaches.
Over the past decades, more and more methods gain a giant development due to the development of technology. Evolutionary Algorithms are widely used as a heuristic method. However, the budget of computation increases exponentially when the dimensions increase. In this paper, we will use the dimensionality reduction method Principal component analysis (PCA) to reduce the dimension during the iteration of Covariance Matrix Adaptation Evolution Strategy (CMA-ES), which is a good Evolutionary Algorithm that is presented as the numeric type and useful for different kinds of problems. We assess the performance of our new methods in terms of convergence rate on multi-modal problems from the Black-Box Optimization Benchmarking (BBOB) problem set and we also use the framework COmparing Continuous Optimizers (COCO) to see how the new method going and compare it to the other algorithms.
Crossover and mutation are the two main operators that lead to new solutions in evolutionary approaches. In this article, a new method of performing the crossover phase is presented. The problem of choice is evolutionary decision tree construction. The method aims at finding such individuals that together complement each other. Hence we say that they are diversely specialized. We propose the way of calculating the so-called complementary fitness. In several empirical experiments, we evaluate the efficacy of the method proposed in four variants and compare it to a fitness-rank-based approach. One variant emerges clearly as the best approach, whereas the remaining ones are below the baseline.
This paper introduces MicroRCT, a novel open source simulator inspired by the theme park sandbox game RollerCoaster Tycoon. The goal in MicroRCT is to place rides and shops in an amusement park to maximize profit earned from park guests. Thus, the challenges for game AI include both selecting high-earning attractions and placing them in locations that are convenient to guests. In this paper, the MAP-Elites algorithm is used to generate a diversity of park layouts, exploring two theoretical questions about evolutionary algorithms and game design: 1) Is there a benefit to starting from a minimal starting point for evolution and complexifying incrementally? and 2) What are the effects of resource limitations on creativity and optimization? Results indicate that building from scratch with no costs results in the widest diversity of high-performing designs.
Jump functions are the {most-studied} non-unimodal benchmark in the theory of randomized search heuristics, in particular, evolutionary algorithms (EAs). They have significantly improved our understanding of how EAs escape from local optima. However, their particular structure -- to leave the local optimum one can only jump directly to the global optimum -- raises the question of how representative such results are. For this reason, we propose an extended class $\textsc{Jump}_{k,\delta}$ of jump functions that contain a valley of low fitness of width $\delta$ starting at distance $k$ from the global optimum. We prove that several previous results extend to this more general class: for all {$k \le \frac{n^{1/3}}{\ln{n}}$} and $\delta < k$, the optimal mutation rate for the $(1+1)$~EA is $\frac{\delta}{n}$, and the fast $(1+1)$~EA runs faster than the classical $(1+1)$~EA by a factor super-exponential in $\delta$. However, we also observe that some known results do not generalize: the randomized local search algorithm with stagnation detection, which is faster than the fast $(1+1)$~EA by a factor polynomial in $k$ on $\textsc{Jump}_k$, is slower by a factor polynomial in $n$ on some $\textsc{Jump}_{k,\delta}$ instances. Computationally, the new class allows experiments with wider fitness valleys, especially when they lie further away from the global optimum.
Social networks represent nowadays in many contexts the main source of information transmission and the way opinions and actions are influenced. For instance, generic advertisements are way less powerful than suggestions from our contacts. However, this process hugely depends on the influence of people who disseminate these suggestions. Therefore modern marketing often involves paying some targeted users, or influencers, for advertising products or ideas. Finding the set of nodes in a social network that lead to the highest information spread -- the so-called Influence Maximization (IM) problem -- is therefore a pressing question and as such it has recently attracted a great research interest. In particular, several approaches based on Evolutionary Algorithms (EAs) have been proposed, although they are known to scale poorly with the graph size. In this paper, we tackle this limitation in two ways. Firstly, we use approximate fitness functions to speed up the EA. Secondly, we include into the EA various graph-aware mechanisms, such as smart initialization, custom mutations and node filtering, to facilitate the EA convergence. Our experiments show that the proposed modifications allow to obtain a relevant runtime gain and also improve, in some cases, the spread results.
In recent years, Evolutionary Algorithms (EAs) have frequently been adopted to evolve instances for optimization problems that pose difficulties for one algorithm while being rather easy for a competitor and vice versa. Typically, this is achieved by either minimizing or maximizing the performance difference or ratio which serves as the fitness function. Repeating this process is useful to gain insights into strengths/weaknesses of certain algorithms or to build a set of instances with strong performance differences as a foundation for automatic per-instance algorithm selection or configuration. We contribute to this branch of research by proposing fitness-functions to evolve instances that show large performance differences for more than just two algorithms simultaneously. As a proof-of-principle, we evolve instances of the multi-component Traveling Thief Problem~(TTP) for three incomplete TTP-solvers. Our results point out that our strategies are promising, but unsurprisingly their success strongly relies on the algorithms' performance complementarity.
In practise, it is often desirable to provide the decision-maker with a rich set of diverse solutions of decent quality instead of just a single solution. In this paper we study evolutionary diversity optimization for the knapsack problem (KP). Our goal is to evolve a population of solutions that all have a profit of at least $(1-\varepsilon)\cdot OPT$, where OPT is the value of an optimal solution. Furthermore, they should differ in structure with respect to an entropy-based diversity measure. To this end we propose a simple $(\mu+1)$-EA with initial approximate solutions calculated by a well-known FPTAS for the KP. We investigate the effect of different standard mutation operators and introduce biased mutation and crossover which puts strong probability on flipping bits of low and/or high frequency within the population. An experimental study on different instances and settings shows that the proposed mutation operators in most cases perform slightly inferior in the long term, but show strong benefits if the number of function evaluations is severely limited.
Designing optimal soft modular robots is difficult, due to non-trivial interactions between morphology and controller. Evolutionary algorithms (EAs), combined with physical simulators, represent a valid tool to overcome this issue. In this work, we investigate algorithmic solutions to improve the Quality Diversity of co-evolved designs of Tensegrity Soft Modular Robots (TSMRs) for two robotic tasks, namely goal reaching and squeezing trough a narrow passage. To this aim, we use three different EAs, i.e., MAP-Elites and two custom algorithms: one based on Viability Evolution (ViE) and NEAT (ViE-NEAT), the other named Double Map MAP-Elites (DM-ME) and devised to seek diversity while co-evolving robot morphologies and neural network (NN)-based controllers. In detail, DM-ME extends MAP-Elites in that it uses two distinct feature maps, referring to morphologies and controllers respectively, and integrates a mechanism to automatically define the NN-related feature descriptor. Considering the fitness, in the goal-reaching task ViE-NEAT outperforms MAP-Elites and results equivalent to DM-ME. Instead, when considering diversity in terms of "illumination" of the feature space, DM-ME outperforms the other two algorithms on both tasks, providing a richer pool of possible robotic designs, whereas ViE-NEAT shows comparable performance to MAP-Elites on goal reaching, although it does not exploit any map.
In practical optimisation the dominant characteristics of the problem are often not known prior. Therefore, there is a need to develop general solvers as it is not always possible to tailor a specialised approach to each application. The hybrid form of Multi-Level Selection Genetic Algorithm (MLSGA) already shows good performance on range of problems due to its diversity-first approach, which is rare among Evolutionary Algorithms. To increase the generality of its performance this paper proposes a distinct set of co-evolutionary mechanisms, which defines co-evolution as competition between collectives rather than individuals. This distinctive approach to co-evolutionary provides less regular communication between sub-populations and different fitness definitions between individuals and collectives. This encourages the collectives to act more independently creating a unique sub-regional search, leading to the development of co-evolutionary MLSGA (cMLSGA). To test this methodology nine genetic algorithms are selected to generate several variants of cMLSGA, which incorporates these approaches at the individual level. The new mechanisms are tested on over 100 different functions and benchmarked against the 9 state-of-the-art competitors in order to find the best general solver. The results show that the diversity of co-evolutionary approaches is more important than their individual performances. This allows the selection of two competing algorithms that improve the generality of cMLSGA, without large loss of performance on any specific problem type. When compared to the state-of-the-art, the proposed methodology is the most universal and robust, leading to an algorithm more likely to solve complex problems with limited knowledge about the search space.
Evolutionary algorithms (EAs) are general-purpose optimization algorithms, inspired by natural evolution. Recent theoretical studies have shown that EAs can achieve good approximation guarantees for solving the problem classes of submodular optimization, which have a wide range of applications, such as maximum coverage, sparse regression, influence maximization, document summarization and sensor placement, just to name a few. Though they have provided some theoretical explanation for the general-purpose nature of EAs, the considered submodular objective functions are defined only over sets or multisets. To complement this line of research, this paper studies the problem class of maximizing monotone submodular functions over sequences, where the objective function depends on the order of items. We prove that for each kind of previously studied monotone submodular objective functions over sequences, i.e., prefix monotone submodular functions, weakly monotone and strongly submodular functions, and DAG monotone submodular functions, a simple multi-objective EA, i.e., GSEMO, can always reach or improve the best known approximation guarantee after running polynomial time in expectation. Note that these best-known approximation guarantees can be obtained only by different greedy-style algorithms before. Empirical studies on various applications, e.g., accomplishing tasks, maximizing information gain, search-and-tracking and recommender systems, show the excellent performance of the GSEMO.
Most evolutionary algorithms have multiple parameters and their values drastically affect the performance. Due to the often complicated interplay of the parameters, setting these values right for a particular problem (parameter tuning) is a challenging task. This task becomes even more complicated when the optimal parameter values change significantly during the run of the algorithm since then a dynamic parameter choice (parameter control) is necessary. In this work, we propose a lazy but effective solution, namely choosing all parameter values (where this makes sense) in each iteration randomly from a suitably scaled power-law distribution. To demonstrate the effectiveness of this approach, we perform runtime analyses of the $(1+(\lambda,\lambda))$ genetic algorithm with all three parameters chosen in this manner. We show that this algorithm on the one hand can imitate simple hill-climbers like the $(1+1)$ EA, giving the same asymptotic runtime on problems like OneMax, LeadingOnes, or Minimum Spanning Tree. On the other hand, this algorithm is also very efficient on jump functions, where the best static parameters are very different from those necessary to optimize simple problems. We prove a performance guarantee that is comparable to the best performance known for static parameters. For the most interesting case that the jump size $k$ is constant, we prove that our performance is asymptotically better than what can be obtained with any static parameter choice. We complement our theoretical results with a rigorous empirical study confirming what the asymptotic runtime results suggest.
Many real-world applications have the time-linkage property, and the only theoretical analysis is recently given by Zheng, et al. (TEVC 2021) on their proposed time-linkage OneMax problem, OneMax$_{(0,1^n)}$. However, only two elitist algorithms (1+1)EA and ($\mu$+1)EA are analyzed, and it is unknown whether the non-elitism mechanism could help to escape the local optima existed in OneMax$_{(0,1^n)}$. In general, there are few theoretical results on the benefits of the non-elitism in evolutionary algorithms. In this work, we analyze on the influence of the non-elitism via comparing the performance of the elitist (1+$\lambda$)EA and its non-elitist counterpart (1,$\lambda$)EA. We prove that with probability $1-o(1)$ (1+$\lambda$)EA will get stuck in the local optima and cannot find the global optimum, but with probability $1$, (1,$\lambda$)EA can reach the global optimum and its expected runtime is $O(n^{3+c}\log n)$ with $\lambda=c \log_{\frac{e}{e-1}} n$ for the constant $c\ge 1$. Noting that a smaller offspring size is helpful for escaping from the local optima, we further resort to the compact genetic algorithm where only two individuals are sampled to update the probabilistic model, and prove its expected runtime of $O(n^3\log n)$. Our computational experiments also verify the efficiency of the two non-elitist algorithms.
Evolutionary algorithms (EAs) are general-purpose optimisers that come with several parameters like the sizes of parent and offspring populations or the mutation rate. It is well known that the performance of EAs may depend drastically on these parameters. Recent theoretical studies have shown that self-adjusting parameter control mechanisms that tune parameters during the algorithm run can provably outperform the best static parameters in EAs on discrete problems. However, the majority of these studies concerned elitist EAs and we do not have a clear answer on whether the same mechanisms can be applied for non-elitist EAs. We study one of the best-known parameter control mechanisms, the one-fifth success rule, to control the offspring population size $\lambda$ in the non-elitist $(1,\lambda)$ EA. It is known that the $(1,\lambda)$ EA has a sharp threshold with respect to the choice of $\lambda$ where the expected runtime on the benchmark function OneMax changes from polynomial to exponential time. Hence, it is not clear whether parameter control mechanisms are able to find and maintain suitable values of $\lambda$. For OneMax we show that the answer crucially depends on the success rate $s$ (i.\,e.\ a one-$(s+1)$-th success rule). We prove that, if the success rate is appropriately small, the self-adjusting $(1,\lambda)$ EA optimises OneMax in $O(n)$ expected generations and $O(n \log n)$ expected evaluations, the best possible runtime for any unary unbiased black-box algorithm. A small success rate is crucial: we also show that if the success rate is too large, the algorithm has an exponential runtime on OneMax and other functions with similar characteristics.
A genetic algorithm (GA) is a search method that optimises a population of solutions by simulating natural evolution. Good solutions reproduce together to create better candidates. The standard GA assumes that any two solutions can mate. However, in nature and social contexts, social networks can condition the likelihood that two individuals mate. This impact of population network structure over GAs performance is unknown. Here we introduce the Networked Genetic Algorithm (NGA) to evaluate how various random and scale-free population networks influence the optimisation performance of GAs on benchmark functions. We show evidence of significant variations in performance of the NGA as the network varies. In addition, we find that the best-performing population networks, characterised by intermediate density and low average shortest path length, significantly outperform the standard complete network GA. These results may constitute a starting point for network tuning and network control: seeing the network structure of the population as a parameter that can be tuned to improve the performance of evolutionary algorithms, and offer more realistic modelling of social learning.
Object detection has been one of the most active topics in computer vision for the past years. Recent works have mainly focused on pushing the state-of-the-art in the general-purpose COCO benchmark. However, the use of such detection frameworks in specific applications such as autonomous driving is yet an area to be addressed. This study presents an enhanced 2D object detector based on Faster R-CNN that is better suited for the context of autonomous vehicles. Two main aspects are improved: the anchor generation procedure and the performance drop in minority classes. The default uniform anchor configuration is not suitable in this scenario due to the perspective projection of the vehicle cameras. Therefore, we propose a perspective-aware methodology that divides the image into key regions via clustering and uses evolutionary algorithms to optimize the base anchors for each of them. Furthermore, we add a module that enhances the precision of the second-stage header network by including the spatial information of the candidate regions proposed in the first stage. We also explore different re-weighting strategies to address the foreground-foreground class imbalance, showing that the use of a reduced version of focal loss can significantly improve the detection of difficult and underrepresented objects in two-stage detectors. Finally, we design an ensemble model to combine the strengths of the different learning strategies. Our proposal is evaluated with the Waymo Open Dataset, which is the most extensive and diverse up to date. The results demonstrate an average accuracy improvement of 6.13% mAP when using the best single model, and of 9.69% mAP with the ensemble. The proposed modifications over the Faster R-CNN do not increase computational cost and can easily be extended to optimize other anchor-based detection frameworks.
One of the first and easy to use techniques for proving run time bounds for evolutionary algorithms is the so-called method of fitness levels by Wegener. It uses a partition of the search space into a sequence of levels which are traversed by the algorithm in increasing order, possibly skipping levels. An easy, but often strong upper bound for the run time can then be derived by adding the reciprocals of the probabilities to leave the levels (or upper bounds for these). Unfortunately, a similarly effective method for proving lower bounds has not yet been established. The strongest such method, proposed by Sudholt (2013), requires a careful choice of the viscosity parameters $\gamma_{i,j}$, $0 \le i < j \le n$. In this paper we present two new variants of the method, one for upper and one for lower bounds. Besides the level leaving probabilities, they only rely on the probabilities that levels are visited at all. We show that these can be computed or estimated without greater difficulties and apply our method to reprove the following known results in an easy and natural way. (i) The precise run time of the (1+1) EA on \textsc{LeadingOnes}. (ii) A lower bound for the run time of the (1+1) EA on \textsc{OneMax}, tight apart from an $O(n)$ term. (iii) A lower bound for the run time of the (1+1) EA on long $k$-paths. We also prove a tighter lower bound for the run time of the (1+1) EA on jump functions by showing that, regardless of the jump size, only with probability $O(2^{-n})$ the algorithm can avoid to jump over the valley of low fitness.