Recent advances in Neural Architecture Search (NAS) such as one-shot NAS offer the ability to extract specialized hardware-aware sub-network configurations from a task-specific super-network. While considerable effort has been employed towards improving the first stage, namely, the training of the super-network, the search for derivative high-performing sub-networks is still under-explored. Popular methods decouple the super-network training from the sub-network search and use performance predictors to reduce the computational burden of searching on different hardware platforms. We propose a flexible search framework that automatically and efficiently finds optimal sub-networks that are optimized for different performance metrics and hardware configurations. Specifically, we show how evolutionary algorithms can be paired with lightly trained objective predictors in an iterative cycle to accelerate architecture search in a multi-objective setting for various modalities including machine translation and image classification.
As two popular schools of machine learning, online learning and evolutionary computations have become two important driving forces behind real-world decision making engines for applications in biomedicine, economics, and engineering fields. Although there are prior work that utilizes bandits to improve evolutionary algorithms' optimization process, it remains a field of blank on how evolutionary approach can help improve the sequential decision making tasks of online learning agents such as the multi-armed bandits. In this work, we propose the Genetic Thompson Sampling, a bandit algorithm that keeps a population of agents and update them with genetic principles such as elite selection, crossover and mutations. Empirical results in multi-armed bandit simulation environments and a practical epidemic control problem suggest that by incorporating the genetic algorithm into the bandit algorithm, our method significantly outperforms the baselines in nonstationary settings. Lastly, we introduce EvoBandit, a web-based interactive visualization to guide the readers through the entire learning process and perform lightweight evaluations on the fly. We hope to engage researchers into this growing field of research with this investigation.
Large-scale multiobjective optimization problems (LSMOPs) refer to optimization problems with multiple conflicting optimization objectives and hundreds or even thousands of decision variables. A key point in solving LSMOPs is how to balance exploration and exploitation so that the algorithm can search in a huge decision space efficiently. Large-scale multiobjective evolutionary algorithms consider the balance between exploration and exploitation from the individual's perspective. However, these algorithms ignore the significance of tackling this issue from the perspective of decision variables, which makes the algorithm lack the ability to search from different dimensions and limits the performance of the algorithm. In this paper, we propose a large-scale multiobjective optimization algorithm based on the attention mechanism, called (LMOAM). The attention mechanism will assign a unique weight to each decision variable, and LMOAM will use this weight to strike a balance between exploration and exploitation from the decision variable level. Nine different sets of LSMOP benchmarks are conducted to verify the algorithm proposed in this paper, and the experimental results validate the effectiveness of our design.
The Ornstein-Zernike equation is solved for the hard-sphere and square-well fluids using a diverse selection of closure relations; the attraction range of the square-well is chosen to be $\lambda=1.5.$ In particular, for both fluids we mainly focus on the solution based on a three-parameter version of the Verlet closure relation [Mol. Phys. 42, 1291-1302 (1981)]. To find the free parameters of the latter, an unconstrained optimization problem is defined as a condition of thermodynamic consistency based on the compressibility and solved using Evolutionary Algorithms. For the hard-sphere fluid, the results show good agreement when compared with mean-field equations of state and accurate computer simulation results; at high densities, i.e., close to the freezing transition, expected (small) deviations are seen. In the case of the square-well fluid, a good agreement is observed at low and high densities when compared with event-driven molecular dynamics computer simulations. For intermediate densities, the explored closure relations vary in terms of accuracy. Our findings suggest that a modification of the optimization problem to include, for example, additional thermodynamic consistency criteria could improve the results for the type of fluids here explored.
The incentive for using Evolutionary Algorithms (EAs) for the automated optimization and training of deep neural networks (DNNs), a process referred to as neuroevolution, has gained momentum in recent years. The configuration and training of these networks can be posed as optimization problems. Indeed, most of the recent works on neuroevolution have focused their attention on single-objective optimization. Moreover, from the little research that has been done at the intersection of neuroevolution and evolutionary multi-objective optimization (EMO), all the research that has been carried out has focused predominantly on the use of one type of DNN: convolutional neural networks (CNNs), using well-established standard benchmark problems such as MNIST. In this work, we make a leap in the understanding of these two areas (neuroevolution and EMO), regarded in this work as neuroevolutionary multi-objective, by using and studying a rich DNN composed of a CNN and Long-short Term Memory network. Moreover, we use a robust and challenging vehicle trajectory prediction problem. By using the well-known Non-dominated Sorting Genetic Algorithm-II, we study the effects of five different objectives, tested in categories of three, allowing us to show how these objectives have either a positive or detrimental effect in neuroevolution for trajectory prediction in autonomous vehicles.
This paper argues that generative art driven by conformance to a visual and/or semantic corpus lacks the necessary criteria to be considered creative. Among several issues identified in the literature, we focus on the fact that generative adversarial networks (GANs) that create a single image, in a vacuum, lack a concept of novelty regarding how their product differs from previously created ones. We envision that an algorithm that combines the novelty preservation mechanisms in evolutionary algorithms with the power of GANs can deliberately guide its creative process towards output that is both good and novel. In this paper, we use recent advances in image generation based on semantic prompts using OpenAI's CLIP model, interrupting the GAN's iterative process with short cycles of evolutionary divergent search. The results of evolution are then used to continue the GAN's iterative process; we hypothesise that this intervention will lead to more novel outputs. Testing our hypothesis using novelty search with local competition, a quality-diversity evolutionary algorithm that can increase visual diversity while maintaining quality in the form of adherence to the semantic prompt, we explore how different notions of visual diversity can affect both the process and the product of the algorithm. Results show that even a simplistic measure of visual diversity can help counter a drift towards similar images caused by the GAN. This first experiment opens a new direction for introducing higher intentionality and a more nuanced drive for GANs.
Benchmark suites are crucial for assessing the performance of evolutionary algorithms, but the constituent problems are often too complex to provide clear intuition about an algorithm's strengths and weaknesses. To address this gap, we introduce DOSSIER ("Diagnostic Overview of Selection Schemes In Evolutionary Runs"), a diagnostic suite initially composed of eight handcrafted metrics. These metrics are designed to empirically measure specific capacities for exploitation, exploration, and their interactions. We consider exploitation both with and without constraints, and we divide exploration into two aspects: diversity exploration (the ability to simultaneously explore multiple pathways) and valley-crossing exploration (the ability to cross wider and wider fitness valleys). We apply DOSSIER to six popular selection schemes: truncation, tournament, fitness sharing, lexicase, nondominated sorting, and novelty search. Our results confirm that simple schemes (e.g., tournament and truncation) emphasized exploitation. For more sophisticated schemes, however, our diagnostics revealed interesting dynamics. Lexicase selection performed moderately well across all diagnostics that did not incorporate valley crossing, but faltered dramatically whenever valleys were present, performing worse than even random search. Fitness sharing was the only scheme to effectively contend with valley crossing but it struggled with the other diagnostics. Our study highlights the utility of using diagnostics to gain nuanced insights into selection scheme characteristics, which can inform the design of new selection methods.
Standard evolutionary optimization algorithms assume that the evaluation of the objective and constraint functions is straightforward and computationally cheap. However, in many real-world optimization problems, these evaluations involve computationally expensive numerical simulations or physical experiments. Surrogate-assisted evolutionary algorithms (SAEAs) have recently gained increased attention for their performance in solving these types of problems. The main idea of SAEAs is the integration of an evolutionary algorithm with a selected surrogate model that approximates the computationally expensive function. In this paper, we propose a surrogate model based on a Lipschitz underestimation and use it to develop a differential evolution-based algorithm. The algorithm, called Lipschitz Surrogate-assisted Differential Evolution (LSADE), utilizes the Lipschitz-based surrogate model, along with a standard radial basis function surrogate model and a local search procedure. The experimental results on seven benchmark functions of dimensions 30, 50, 100, and 200 show that the proposed LSADE algorithm is competitive compared with the state-of-the-art algorithms under a limited computational budget, being especially effective for the very complicated benchmark functions in high dimensions.
Run time analysis of evolutionary algorithms recently makes significant progress in linking algorithm performance to algorithm parameters. However, settings that study the impact of problem parameters are rare. The recently proposed W-model provides a good framework for such analyses, generating pseudo-Boolean optimization problems with tunable properties. We initiate theoretical research of the W-model by studying how one of its properties -- neutrality -- influences the run time of random local search. Neutrality creates plateaus in the search space by first performing a majority vote for subsets of the solution candidate and then evaluating the smaller-dimensional string via a low-level fitness function. We prove upper bounds for the expected run time of random local search on this MAJORITY problem for its entire parameter spectrum. To this end, we provide a theorem, applicable to many optimization algorithms, that links the run time of MAJORITY with its symmetric version HASMAJORITY, where a sufficient majority is needed to optimize the subset. We also introduce a generalized version of classic drift theorems as well as a generalized version of Wald's equation, both of which we believe to be of independent interest.
Chemical plant design and optimisation have proven challenging due to the complexity of these real-world systems. The resulting complexity translates into high computational costs for these systems' mathematical formulations and simulation models. Research has illustrated the benefits of using machine learning surrogate models as substitutes for computationally expensive models during optimisation. This paper extends recent research into optimising chemical plant design and operation. The study further explores Surrogate Assisted Genetic Algorithms (SA-GA) in more complex variants of the original plant design and optimisation problems, such as the inclusion of parallel and feedback components. The novel extension to the original algorithm proposed in this study, Surrogate Assisted NSGA-\Romannum{2} (SA-NSGA), was tested on a popular literature case, the Pressure Swing Adsorption (PSA) system. We further provide extensive experimentation, comparing various meta-heuristic optimisation techniques and numerous machine learning models as surrogates. The results for both sets of systems illustrate the benefits of using Genetic Algorithms as an optimisation framework for complex chemical plant system design and optimisation for both single and multi-objective scenarios. We confirm that Random Forest surrogate assisted Evolutionary Algorithms can be scaled to increasingly complex chemical systems with parallel and feedback components. We further find that combining a Genetic Algorithm framework with Machine Learning Surrogate models as a substitute for long-running simulation models yields significant computational efficiency improvements, 1.7 - 1.84 times speedup for the increased complexity examples and a 2.7 times speedup for the Pressure Swing Adsorption system.
Decomposition-based multiobjective evolutionary algorithms (MOEAs) with clustering-based reference vector adaptation show good optimization performance for many-objective optimization problems (MaOPs). Especially, algorithms that employ a clustering algorithm with a topological structure (i.e., a network composed of nodes and edges) show superior optimization performance to other MOEAs for MaOPs with irregular Pareto optimal fronts (PFs). These algorithms, however, do not effectively utilize information of the topological structure in the search process. Moreover, the clustering algorithms typically used in conventional studies have limited clustering performance, inhibiting the ability to extract useful information for the search process. This paper proposes an adaptive reference vector-guided evolutionary algorithm using an adaptive resonance theory-based clustering with a topological structure. The proposed algorithm utilizes the information of the topological structure not only for reference vector adaptation but also for mating selection. The proposed algorithm is compared with 8 state-of-the-art MOEAs on 78 test problems. Experimental results reveal the outstanding optimization performance of the proposed algorithm over the others on MaOPs with various properties.
The stochastic nature of iterative optimization heuristics leads to inherently noisy performance measurements. Since these measurements are often gathered once and then used repeatedly, the number of collected samples will have a significant impact on the reliability of algorithm comparisons. We show that care should be taken when making decisions based on limited data. Particularly, we show that the number of runs used in many benchmarking studies, e.g., the default value of 15 suggested by the COCO environment, can be insufficient to reliably rank algorithms on well-known numerical optimization benchmarks. Additionally, methods for automated algorithm configuration are sensitive to insufficient sample sizes. This may result in the configurator choosing a `lucky' but poor-performing configuration despite exploring better ones. We show that relying on mean performance values, as many configurators do, can require a large number of runs to provide accurate comparisons between the considered configurations. Common statistical tests can greatly improve the situation in most cases but not always. We show examples of performance losses of more than 20%, even when using statistical races to dynamically adjust the number of runs, as done by irace. Our results underline the importance of appropriately considering the statistical distribution of performance values.
While the theoretical analysis of evolutionary algorithms (EAs) has made significant progress for pseudo-Boolean optimization problems in the last 25 years, only sporadic theoretical results exist on how EAs solve permutation-based problems. To overcome the lack of permutation-based benchmark problems, we propose a general way to transfer the classic pseudo-Boolean benchmarks into benchmarks defined on sets of permutations. We then conduct a rigorous runtime analysis of the permutation-based $(1+1)$ EA proposed by Scharnow, Tinnefeld, and Wegener (2004) on the analogues of the \textsc{LeadingOnes} and \textsc{Jump} benchmarks. The latter shows that, different from bit-strings, it is not only the Hamming distance that determines how difficult it is to mutate a permutation $\sigma$ into another one $\tau$, but also the precise cycle structure of $\sigma \tau^{-1}$. For this reason, we also regard the more symmetric scramble mutation operator. We observe that it not only leads to simpler proofs, but also reduces the runtime on jump functions with odd jump size by a factor of $\Theta(n)$. Finally, we show that a heavy-tailed version of the scramble operator, as in the bit-string case, leads to a speed-up of order $m^{\Theta(m)}$ on jump functions with jump size~$m$.%
Decomposition-based evolutionary algorithms have become fairly popular for many-objective optimization in recent years. However, the existing decomposition methods still are quite sensitive to the various shapes of frontiers of many-objective optimization problems (MaOPs). On the one hand, the cone decomposition methods such as the penalty-based boundary intersection (PBI) are incapable of acquiring uniform frontiers for MaOPs with very convex frontiers. On the other hand, the parallel reference lines of the parallel decomposition methods including the normal boundary intersection (NBI) might result in poor diversity because of under-sampling near the boundaries for MaOPs with concave frontiers. In this paper, a collaborative decomposition method is first proposed to integrate the advantages of parallel decomposition and cone decomposition to overcome their respective disadvantages. This method inherits the NBI-style Tchebycheff function as a convergence measure to heighten the convergence and uniformity of distribution of the PBI method. Moreover, this method also adaptively tunes the extent of rotating an NBI reference line towards a PBI reference line for every subproblem to enhance the diversity of distribution of the NBI method. Furthermore, a collaborative decomposition-based evolutionary algorithm (CoDEA) is presented for many-objective optimization. A collaborative decomposition-based environmental selection mechanism is primarily designed in CoDEA to rank all the individuals associated with the same PBI reference line in the boundary layer and pick out the best ranks. CoDEA is compared with several popular algorithms on 85 benchmark test instances. The experimental results show that CoDEA achieves high competitiveness benefiting from the collaborative decomposition maintaining a good balance among the convergence, uniformity, and diversity of distribution.
Recently, optimization has become an emerging tool for neuroscientists to study neural code. In the visual system, neurons respond to images with graded and noisy responses. Image patterns eliciting highest responses are diagnostic of the coding content of the neuron. To find these patterns, we have used black-box optimizers to search a 4096d image space, leading to the evolution of images that maximize neuronal responses. Although genetic algorithm (GA) has been commonly used, there haven't been any systematic investigations to reveal the best performing optimizer or the underlying principles necessary to improve them. Here, we conducted a large scale in silico benchmark of optimizers for activation maximization and found that Covariance Matrix Adaptation (CMA) excelled in its achieved activation. We compared CMA against GA and found that CMA surpassed the maximal activation of GA by 66% in silico and 44% in vivo. We analyzed the structure of Evolution trajectories and found that the key to success was not covariance matrix adaptation, but local search towards informative dimensions and an effective step size decay. Guided by these principles and the geometry of the image manifold, we developed SphereCMA optimizer which competed well against CMA, proving the validity of the identified principles. Code available at https://github.com/Animadversio/ActMax-Optimizer-Dev
Recent works showed that simple success-based rules for self-adjusting parameters in evolutionary algorithms (EAs) can match or outperform the best fixed parameters on discrete problems. Non-elitism in a (1,$\lambda$) EA combined with a self-adjusting offspring population size $\lambda$ outperforms common EAs on the multimodal Cliff problem. However, it was shown that this only holds if the success rate $s$ that governs self-adjustment is small enough. Otherwise, even on OneMax, the self-adjusting (1,$\lambda$) EA stagnates on an easy slope, where frequent successes drive down the offspring population size. We show that self-adjustment works as intended in the absence of easy slopes. We define everywhere hard functions, for which successes are never easy to find and show that the self-adjusting (1,$\lambda$) EA is robust with respect to the choice of success rates $s$. We give a general fitness-level upper bound on the number of evaluations and show that the expected number of generations is at most $O(d + \log(1/p_{\min}))$ where $d$ is the number of non-optimal fitness values and $p_{\min}$ is the smallest probability of finding an improvement from a non-optimal search point. We discuss implications for the everywhere hard function LeadingOnes and a new class OneMaxBlocks of everywhere hard functions with tunable difficulty.
Neural network pruning is a popular model compression method which can significantly reduce the computing cost with negligible loss of accuracy. Recently, filters are often pruned directly by designing proper criteria or using auxiliary modules to measure their importance, which, however, requires expertise and trial-and-error. Due to the advantage of automation, pruning by evolutionary algorithms (EAs) has attracted much attention, but the performance is limited for deep neural networks as the search space can be quite large. In this paper, we propose a new filter pruning algorithm CCEP by cooperative coevolution, which prunes the filters in each layer by EAs separately. That is, CCEP reduces the pruning space by a divide-and-conquer strategy. The experiments show that CCEP can achieve a competitive performance with the state-of-the-art pruning methods, e.g., prune ResNet56 for $63.42\%$ FLOPs on CIFAR10 with $-0.24\%$ accuracy drop, and ResNet50 for $44.56\%$ FLOPs on ImageNet with $0.07\%$ accuracy drop.
Evolutionary algorithms have been widely used for a range of stochastic optimization problems in order to address complex real-world optimization problems. We consider the knapsack problem where the profits involve uncertainties. Such a stochastic setting reflects important real-world scenarios where the profit that can be realized is uncertain. We introduce different ways of dealing with stochastic profits based on tail inequalities such as Chebyshev's inequality and Hoeffding bounds that allow to limit the impact of uncertainties. We examine simple evolutionary algorithms and the use of heavy tail mutation and a problem-specific crossover operator for optimizing uncertain profits. Our experimental investigations on different benchmarks instances show the results of different approaches based on tail inequalities as well as improvements achievable through heavy tail mutation and the problem specific crossover operator.
The compact genetic algorithm (cGA) is an non-elitist estimation of distribution algorithm which has shown to be able to deal with difficult multimodal fitness landscapes that are hard to solve by elitist algorithms. In this paper, we investigate the cGA on the CLIFF function for which it has been shown recently that non-elitist evolutionary algorithms and artificial immune systems optimize it in expected polynomial time. We point out that the cGA faces major difficulties when solving the CLIFF function and investigate its dynamics both experimentally and theoretically around the cliff. Our experimental results indicate that the cGA requires exponential time for all values of the update strength $K$. We show theoretically that, under sensible assumptions, there is a negative drift when sampling around the location of the cliff. Experiments further suggest that there is a phase transition for $K$ where the expected optimization time drops from $n^{\Theta(n)}$ to $2^{\Theta(n)}$.
This work concerns the evolutionary approaches to distributed stochastic black-box optimization, in which each worker can individually solve an approximation of the problem with nature-inspired algorithms. We propose a distributed evolution strategy (DES) algorithm grounded on a proper modification to evolution strategies, a family of classic evolutionary algorithms, as well as a careful combination with existing distributed frameworks. On smooth and nonconvex landscapes, DES has a convergence rate competitive to existing zeroth-order methods, and can exploit the sparsity, if applicable, to match the rate of first-order methods. The DES method uses a Gaussian probability model to guide the search and avoids the numerical issue resulted from finite-difference techniques in existing zeroth-order methods. The DES method is also fully adaptive to the problem landscape, as its convergence is guaranteed with any parameter setting. We further propose two alternative sampling schemes which significantly improve the sampling efficiency while leading to similar performance. Simulation studies on several machine learning problems suggest that the proposed methods show much promise in reducing the convergence time and improving the robustness to parameter settings.