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Various techniques for statistical analysis of the structure of fitness landscapes have been proposed. An important feature of these techniques is that they study the ruggedness of landscapes by measuring their correlation characteristics. This paper proposes a new information analysis of fitness landscapes. The underlying idea is to consider a fit...
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... Many landscape analysis techniques that measure local features are based on samples that are spatially correlated, i.e. sequences of neighbouring solutions, as opposed to a sample of independent solutions from the whole search space. Techniques that require such sequences of sampled solutions include correlation length for measuring ruggedness [38], entropic profiles of ruggedness and smoothness with respect to neutrality [35,36] -adapted as a single measure of ruggedness for continuous spaces [19], approximations of gradient [20], information content features [25], and measures of neutrality [34]. ...
Landscape analysis aims to characterise optimisation problems based on their objective (or fitness) function landscape properties. The problem search space is typically sampled, and various landscape features are estimated based on the samples. One particularly salient set of features is information content, which requires the samples to be sequences of neighbouring solutions, such that the local relationships between consecutive sample points are preserved. Generating such spatially correlated samples that also provide good search space coverage is challenging. It is therefore common to first obtain an unordered sample with good search space coverage, and then apply an ordering algorithm such as the nearest neighbour to minimise the distance between consecutive points in the sample. However, the nearest neighbour algorithm becomes computationally prohibitive in higher dimensions, thus there is a need for more efficient alternatives. In this study, Hilbert space-filling curves are proposed as a method to efficiently obtain high-quality ordered samples. Hilbert curves are a special case of fractal curves, and guarantee uniform coverage of a bounded search space while providing a spatially correlated sample. We study the effectiveness of Hilbert curves as samplers, and discover that they are capable of extracting salient features at a fraction of the computational cost compared to Latin hypercube sampling with post-factum ordering. Further, we investigate the use of Hilbert curves as an ordering strategy, and find that they order the sample significantly faster than the nearest neighbour ordering, without sacrificing the saliency of the extracted features.
... From this algorithm, we are interested in the regimes of high and low H(ϵ) 24,31 . The maximum IC (MIC) is defined as ...
... The other case of interest occurs when H(ϵ) ≤ η with η ≪ 1. This defines the sensitivity IC (SIC) 24,31 , ...
The parameters of the quantum circuit in a variational quantum algorithm induce a landscape that contains the relevant information regarding its optimization hardness. In this work, we investigate such landscapes through the lens of information content, a measure of the variability between points in parameter space. Our major contribution connects the information content to the average norm of the gradient, for which we provide robust analytical bounds on its estimators. This result holds for any (classical or quantum) variational landscape. We validate the analytical understating by numerically studying the scaling of the gradient in an instance of the barren plateau problem. In such instance, we are able to estimate the scaling pre-factors in the gradient. Our work provides a way to analyze variational quantum algorithms in a data-driven fashion well-suited for near-term quantum computers.
... Fitness landscapes of the set-point optimization problem can be expressed as a function of the following three components (Vassilev et al., 2000;Malan, 2014;Saleem et al., 2019): ...
... The presence of multiple and/or large neutral regions also challenges search algorithms, as such flat regions lack the information to direct a new search step. We refer to Vassilev et al. (2000); Malan (2014) for a detailed treatment on this topic. ...
... We consider the following two metrics to respectively estimate the landscape ruggedness and neutrality of the set-point optimization problem: first entropy metric (F E M) (Malan & Engelbrecht, 2009;Vassilev et al., 2000) and Proportion of Neutral structures (P N) (van Aardt et al., 2017). To this end, the solution space is sampled using a progressive random walk of n t −steps (Malan & Engelbrecht, 2014). ...
The present study proposes a multi-criteria framework that focuses on two conflicting objectives typically encountered in building energy management systems: energy consumption of the air handling units (AHU) and thermal comfort of the occupants. In particular, an adaptive control of set points to AHU controllers is crucial to balance these objectives. This study, therefore, formulates the selection of set points as an optimization problem wherein the objectives are to balance thermal comfort with energy consumption while accommodating the distinct preferences of the decision maker (DM). Two multi-criteria decision-making formulations are considered to aggregate the objectives per the DM’s preferences, i.e., conventional weight aggregation and \(\epsilon \)-constraint. Finally, an online particle swarm optimization is used to solve such aggregated formulations and adapt the set points in real time as per the prevailing ambient conditions. The performance of the proposed framework is assessed by considering an experimentally validated model of an AHU plant and the real-time weather data of Auckland, New Zealand. The results of this investigation show that the proposed framework can successfully optimize the energy performance of an AHU plant while meeting the thermal comfort requirements specified by the DM.
... Initially, some experts design some features to describe the landscape of the problem. The random wandering correlation function proposed by Weinberger [17] and the method of Vassilev et al. [18] computed to analyze the variation between neighboring observations on the discrete problem landscape. Steer et al. [19] adapted the method of Vassilev et al. on the continuous problem. ...
The No Free Lunch theorem tells us that no algorithm can beat other algorithms on all types of problems. The algorithm selection structure is proposed to select the most suitable algorithm from a set of algorithms for an unknown optimization problem. In this paper, an innovative algorithm selection approach called the CNN-HT two-stage algorithm selection framework is introduced. In the first stage, a Convolutional Neural Network (CNN) is employed to classify problems. In the second stage, the Hypothesis Testing (HT) technique is used to suggest the best-performing algorithm based on the statistical analysis of the performance metric of algorithms that address various problem categories. To provide a more general structure for the classification model, we adopt Exploratory Landscape Analysis (ELA) features of the problem as the input and utilize feature selection techniques to reduce the redundant ones. In problem classification, our proposed algorithm selection framework achieves an average accuracy of 96% for the classification of unknown black-box problems, and it improves to 98.8% after feature selection. This shows that our proposed classification method can accurately classify BBOB problems into 24 classes of problems and thus can correctly recommend algorithms accordingly. The performance of CNN-HT is compared with a single optimization algorithm on a continuous black-box optimization problem set, and the average ranking of CNN-HT is superior, demonstrating its effectiveness.
... Information content (IC) of a variational landscape is a measure of the variability thereof (e.g. direction between two neighboring points) [24]. Features of the landscape can be associated with values of the IC, e.g. ...
... The empirical IC H( ) computed from step 5 of the algorithm in Section II B peaks at the maximum IC (MIC) [24,25], ...
... The proof can be found in Appendix A 4. The point where H( ) ≤ η is defined as sensitivity IC (SIC) [24,25], ...
The parameters of the quantum circuit in a variational quantum algorithm induce a landscape that contains useful information to solve the task. In this work we investigate such landscape through the lens of information content which measures the variability between points in the parameter space. Our major contribution connects the information content to the average norm of the gradient, where we provide robust analytical bounds on its estimators. This result holds for any (classical or quantum) variational landscape. We validate this by numerically studying the scaling of the gradient in an instance of the barren plateau problem. With our analytical understanding we are able to the scaling pre-factors in the gradient of this problem. Our work opens a new way to investigate the limits of variational quantum algorithms in a data-driven fashion with near-term quantum computers.
... Prior to each decision method call, the modality (as a measure of ruggedness) of the local problem of each agent was calculated. To complete this, we followed the method of [77]. First, we generated a series of fitness values by using a random path of the solution candidates on the fitness landscape. ...
Cartesian genetic programming is a popular version of classical genetic programming, and it has now demonstrated a very good performance in solving various use cases. Originally, programs evolved by using a centralized optimization approach. Recently, an algorithmic level decomposition of program evolution has been introduced that can be solved by a multi-agent system in a fully distributed manner. A heuristic for distributed combinatorial problem-solving was adapted to evolve these programs. The applicability of the approach and the effectiveness of the used multi-agent protocol as well as of the evolved genetic programs for the case of full enumeration in local agent decisions has already been successfully demonstrated. Symbolic regression, n-parity, and classification problems were used for this purpose. As is typical of decentralized systems, agents have to solve local sub-problems for decision-making and for determining the best local contribution to solving program evolution. So far, only a full enumeration of the solution candidates has been used, which is not sufficient for larger problem sizes. We extend this approach by using CMA-ES as an algorithm for local decisions. The superior performance of CMA-ES is demonstrated using Koza’s computational effort statistic when compared with the original approach. In addition, the distributed modality of the local optimization is scrutinized by a fitness landscape analysis.
... Some of them may describe the landscape features in qualitative ways, while the others in quantitative ways. For example, based on the concept of information entropy, the information characteristics analysis [39] can tell which fitness landscape is more rugged between two problems. However, for a single problem, it cannot determine whether the problem has a rugged fitness landscape, since there is lack of a clear metric to quantify the landscape features. ...
As an effective optimization tool, artificial bee colony (ABC) algorithm has attracted increasing attention in recent years. However, ABC still shows unsatisfactory performance in solving complex optimization problems. Although many ABC variants have been developed, the structural features been rarely considered, which have a significant effect on algorithm performance. Therefore, a novel ABC variant, called FLABC, is proposed by designing an online fitness landscape analysis technique. In this technique, the population is considered as a sample of, and the idea of dispersion metric is used to identify the landscape features. According to the identified features, the solution search equations with distinct characteristics can be adaptively used, which helps adapt the search to the fitness landscape. In addition, FLABC has another two modifications, i.e., the dynamic multiple subpopulations and modified scout bee phase. In the experiments, FLABC is verified on two well-known test suites (CEC2013 and CEC2015) and two real-world optimization problems. Seven well-established ABC variants and five non-ABC variants are included in the performance comparison, and the results verify that FLABC has very competitive performance, especially on the functions with rugged fitness landscapes.
... Additional information is required to gain a detailed understanding of the landscape. Vassilev et al. [20] propose a set of entropy (or information) measures to define the topography of a fitness landscape by analyzing random walks over the landscape. The analysis of a random walk of steps on a landscape ℒ produces a sequence of fitness values { } =0 , which holds features about the landscape structure. ...
... The string ( ) can be viewed as a sequence of pairs of characters, +1 I.e., a substring of length 2. The value of should be chosen less than * , the information stability. The information measures proposed by Vassilev et al. [20] are described in the following subsections. The salient advantage of Information FLA is that it is based upon random walks, and the exhaustive analysis of the whole search space is not required. ...
... Hence, a larger basin of attraction leads to a smaller degree of isolation and vice versa. Furthermore, evolutionary search may present different levels of difficulty for landscapes with equal number of optima [20]. ...
... • Information Content: The 5 sequence-based features of this set rely on an enhanced version of the information content method from the combinatorial domain [19,20]. ...
Exploratory Landscape Analysis is a powerful technique for numerically characterizing landscapes of single-objective continuous optimization problems. Landscape insights are crucial both for problem understanding as well as for assessing benchmark set diversity and composition. Despite the irrefutable usefulness of these features, they suffer from their own ailments and downsides. Hence, in this work we provide a collection of different approaches to characterize optimization landscapes. Similar to conventional landscape features, we require a small initial sample. However, instead of computing features based on that sample, we develop alternative representations of the original sample. These range from point clouds to 2D images and, therefore, are entirely feature-free. We demonstrate and validate our devised methods on the BBOB testbed and predict, with the help of Deep Learning, the high-level, expert-based landscape properties such as the degree of multimodality and the existence of funnel structures. The quality of our approaches is on par with methods relying on the traditional landscape features. Thereby, we provide an exciting new perspective on every research area which utilizes problem information such as problem understanding and algorithm design as well as automated algorithm configuration and selection.
... Primary works in this area have been focused on elementary landscape features such as ruggedness where these features have been described by different methods like correlation length, correlation and auto-correlation functions (Stadler, 1996;Weinberger, 1990), and other description methods like information content (Vassilev et al., 2000). In comparison to high-level descriptions of landscapes based on expert knowledge, a wide variety of low-level features have been introduced by different research groups that can characterize the landscapes with some computer-generated features. ...
The performance of optimization algorithms significantly depends on the landscape of the problems. It is known that there is no single algorithm that outperforms others on problems with different fitness landscapes. One of the issues in metaheuristic algorithms is keeping the balance between exploration and exploitation. The features extracted from analysis of fitness landscapes can be used to select the suitable algorithm for the given problem. However, these features are usually expensive and extracted prior to the optimization process which leads to a single algorithm to be selected. In this work, we propose an intelligent switch mechanism that enjoys an efficient non-convex ratio (ENCR) feature extracted online during the optimization to switch between two choices of algorithms, each favoring a type of landscape in terms of modality. For this work, two case studies including a pair of Harris hawks optimizer (HHO) and differential evolution (DE) and another pair of multiverse optimizer (MVO) and moth-flame optimizer (MFO) are selected among several algorithms to evaluate the performance of this framework. The proposed one-way and two-way switch algorithms take advantage of the merits of the two base algorithms to reach better final solutions and higher convergence rates in the majority of case studies. The overall comparison and ranking of the algorithms, including a random switch baseline, demonstrates the superiority of the intelligent switch mechanisms over the baselines.
