Fig 1 - uploaded by Thomas Bäck
Content may be subject to copyright.
Source publication
Methods are developed to numerically analyze an evolutionary algorithm (EA) that applies mutation and selection on a bit-string representation to find the optimum for a bimodal unitation function called a trap function. This research bridges part of the gap between the existing convergence velocity analysis of strictly unimodal functions and global...
Citations
... On the other hand, empirical convergence analysis is mostly done on the basis of solutions obtained in different iterations for a single trial of the algorithm. Majority of evaluation techniques focus on solution quality of EOAs, which include non-parametric approaches [1], parametric approaches [2], [3], statistical tests [4], Bootstrapping [5], [6], Drift analysis [7], Exploratory Landscape Analysis (ELA) [8], theoretic analysis [9], [10] and visual analysis approaches [11]- [15] etc. Whereas, convergence analysis in general is done through visual inspection A. Biswas of graphical presentation of solutions obtained in different iterations sequentially [16]- [22]. Although many approaches have been developed, parametric and non-parametric approaches are widely used for analyzing solution quality of EOAs. ...
The performance of individual evolutionary optimization algorithms is mostly measured in terms of statistics such as mean, median and standard deviation etc., computed over the best solutions obtained with few trails of the algorithm. To compare the performance of two algorithms, the values of these statistics are compared instead of comparing the solutions directly. This kind of comparison lacks direct comparison of solutions obtained with different algorithms. For instance, the comparison of best solutions (or worst solution) of two algorithms simply not possible. Moreover, ranking of algorithms is mostly done in terms of solution quality only, despite the fact that the convergence of algorithm is also an important factor. In this paper, a direct comparison approach is proposed to analyze the performance of evolutionary optimization algorithms. A direct comparison matrix called \emph{Prasatul Matrix} is prepared, which accounts direct comparison outcome of best solutions obtained with two algorithms for a specific number of trials. Five different performance measures are designed based on the prasatul matrix to evaluate the performance of algorithms in terms of Optimality and Comparability of solutions. These scores are utilized to develop a score-driven approach for comparing performance of multiple algorithms as well as for ranking both in the grounds of solution quality and convergence analysis. Proposed approach is analyzed with six evolutionary optimization algorithms on 25 benchmark functions. A non-parametric statistical analysis, namely Wilcoxon paired sum-rank test is also performed to verify the outcomes of proposed direct comparison approach.
... As the agent has no prior knowledge of the environment or its location within it, restricting the search space to 3 × 5 would provide additional information and bias the problem. is created; agents can explore without penalty, and there is no indication of proximity to the optimal solution. However, when a cost to movement is introduced (c = 1), Figure 3b shows that a trap function is created in the landscape (Nijssen & Bäck, 2003). This means that agents receive a lower fitness as they get closer to the optimum, making it difficult for 350 evolution to find. ...
... The first set of experiments explore the effect that a cost to movement has on evolution, using a 1+1 evolutionary algorithm (EA). The 1+1 EA has been shown to be simple yet effective for simple search problems (Droste et al., 2002;Nijssen & Bäck, 2003), which makes 355 it an appropriate choice for agent evolution in the RC-due to its small search space. As the population size is 1, the EA described in Section 3.2 is adapted such that the single agent in the population will only be replaced if the fitness of the offspring is greater than, or equal to, its own fitness; the EA would in fact instead be a random walk if the offspring always replaced the single agent in the population. ...
Understanding how evolutionary agents behave in complex environments is a challenging problem. Agents can be faced with complex fitness landscapes derived from multi-stage tasks, interaction with others, and limited environmental feedback. Agents that evolve to overcome these can sometimes access greater fitness, as a result of factors such as cooperation and tool use. However, it is often difficult to explain why evolutionary agents behave in certain ways, and what specific elements of the environment or task may influence the ability of evolution to find goal-achieving behaviours; even seemingly simple environments or tasks may contain features that affect agent evolution in unexpected ways. We explore principled simplification of evolutionary agent-based models, as a possible route to aiding their explainability. Using the River Crossing Task (RCT) as a case study, we draw on analysis in the Minimal River Crossing (RC-) Task testbed, which was designed to simplify the original task while keeping its key features. Using this method, we present new analysis concerning when agents evolve to successfully complete the RCT. We demonstrate that the RC- environment can be used to understand the effect that a cost to movement has on agent evolution, and that these findings can be generalised back to the original RCT. Then, we present new insight into the use of principled simplification in understanding evolutionary agents. We find evidence that behaviour dependent on features that survive simplification, such as problem structure, are amenable to prediction; while predicting behaviour dependent on features that are typically reduced in simplification, such as scale, can be invalid.
... Francois and Lavergne (2001) has introduced a statistical methodology to choose efficient parameter settings. The analysis method of EOAs has further grown in several directions such as bootstrapping (Nijssen and Back 2003;Carrano et al. 2008), exploratory landscape analysis (ELA) (Mersmann et al. 2010) and drift analysis (He and Yao 2001). Mathematical approaches (Muhlenbein and Mahnig 2001;Yang 2011;Lockett 2013;He and Chen 2013) and visual analysis approach (Wu et al. 1999;Lutton and Fekete 2011) have drawn attention for evaluating EOAs in recent years. ...
This work introduces a novel methodology to perform the comparative analysis of evolutionary optimization algorithms. The methodology relies simply on linear regression and quantile?quantile plots. The methodology is extrapolated as the one-to-one comparison, one-to-many comparison and many-to-many comparison of solution quality and convergence rate. Most of the existing approaches utilize both solution quality and convergence rate to perform comparative analysis. However, many-to-many comparison, i.e., ranking of algorithms is done only in terms of solution quality. The proposed method is capable of ranking algorithms in terms of both solution quality and convergence rate. Method is analyzed with well-established algorithms and real data obtained from 25 benchmark functions.
... As stated above, the evolutionary algorithms run mainly in the browser. The problem run is a multimodal problem called l-trap, which has been used extensively as a benchmark for evolutionary algorithms [11,28]. This function counts the number of bits in a sequence of l and assigns the local maximum if it has got 0 bits and the global maximum to l bits. ...
From the era of big science we are back to the "do it yourself", where you do
not have any money to buy clusters or subscribe to grids but still have
algorithms that crave many computing nodes and need them to measure
scalability. Fortunately, this coincides with the era of big data, cloud
computing, and browsers that include JavaScript virtual machines. Those are the
reasons why this paper will focus on two different aspects of volunteer or
freeriding computing: first, the pragmatic: where to find those resources,
which ones can be used, what kind of support you have to give them; and then,
the theoretical: how evolutionary algorithms can be adapted to an environment
in which nodes come and go, have different computing capabilities and operate
in complete asynchrony of each other. We will examine the setup needed to
create a very simple distributed evolutionary algorithm using JavaScript and
then find a model of how users react to it by collecting data from several
experiments featuring different classical benchmark functions.
... al [8] has extended with specific to parameter based performance analysis. Analysis method for EOAs have further grown in several directions such as Bootstrapping [9], [10], Exploratory Landscape Analysis(ELA) [11] and drift analysis [12]. Mathematical approaches [14]- [16] and visual analysis approach [13] have drawn attention for evaluating EOAs in recent years. ...
Growing application of evolutionary optimization algorithms in the problems of different domain have led to analyze their efficiency and effectiveness rigorously. Various approaches have been proposed to algorithms for performance evaluation such as parametric, non-parametric or mathematical which lack direct involvement of results obtained. A visual comparative performance evaluation method has been proposed in this paper incorporating more direct participation of results. Proposed method has been studied in perspective of three types of comparisons one-to-one, one-to-many and many-to-many. Necessary interpretations for the method have been illustrated and examined with solutions obtained on several benchmark functions through well known evolutionary optimization algorithms.
... The modularity in such problems should, in principle, be exploitable if identified correctly and the strict separability better enables rigorous analytical results to be obtained; accordingly, this form of function has been used extensively in the literature (see [27], [29], [50]). One popular way of constructing such functions is to take an inseparable function (technically speaking, an exactly (1, n)-separable function) and concatenate n/k copies of this function defined over k bits each. ...
... The probability to have this in at least one of n 2 pairs is bounded above by n 2 · (1/n 3 ) = O(1/n). One extreme application of Corollary 1 is using the well known trap function (see [27], [50]) as the sub-function to create an exactly (n/k, k)-separable function. Since the probability to find the global optimum for a trap function as sub-function is 2 −k we obtain O 2 2k n log n as upper bound on the optimization time of an appropriately parameterized MACRO-H. ...
The intuitive idea that good solutions to small problems can be reassembled into good solutions to larger problems is widely familiar in many fields including evolutionary computation. This idea has motivated the building-block hypothesis and model-building optimization methods that aim to identify and exploit problem structure automatically. Recently, a small number of works make use of such ideas by learning problem structure and using this information in a particular manner: these works use the results of a simple search process in primitive units to identify structural correlations (such as modularity) in the problem that are then used to redefine the variational operators of the search process. This process is applied recursively such that search operates at successively higher scales of organization, hence multi-scale search. Here, we show for the first time that there is a simple class of (modular) problems that a multi-scale search algorithm can solve in polynomial time that requires super-polynomial time for other methods. We discuss strengths and limitations of the multi-scale search approach and note how it can be developed further.
... where the 3 parameters a, b, and z are such that [8] ...
... We also note that if we fix z 2 = the complex trap function becomes a simple trap one. Summing up, for both kinds of trap functions there are many possible choices for the parameters a, b and z, (with z 1 = z and z 2 = − z 1 for the complex trap function) [8]. Some values are shown in table 1 and we will use them for our experiments. ...
We present a new nature-inspired algorithm, mt-GA, which is a parallelized version of a simple GA, where subpopulations evolve independently from each other and on different threads. The overall goal is to develop a population-based algorithm capable to escape from local optima. In doing so, we used complex trap functions, and we provide experimental answers to some crucial implementation decision problems. The obtained results show the robustness and efficiency of the proposed algorithm, even when compared to well-known state-of-the art optimization algorithms based on the clonal selection principle.
... Strictly analysis of EA computation complexity is the proper approach for an EA theory. Convergence analysis deals with the problem of whether a GA can find the global optimum [38]. The limitation of the convergence theory is that it studies EA behavior when running time approaching infinity. ...
... More and more recent researches fall into the category of convergence complexity (convergence velocity [38]) analysis that can give results in finite time. Strict analysis of convergence complexity is much more difficult than convergence analysis. ...
There are vast amount researches in Evolutionary Algorithms (EA). We need an overview of the current state of EA research every few years. This paper reviews some of the interesting researches at the current state in both theory and application of EA. Works in EA performance improvements are introduced in the sense of balancing between convergence speed and diversity in the population. The combination of EA with other methods is highlighted as a prospective area that may give fertility results. Some smart applications are reviewed in this paper, for example, application in nuclear power plant. The authors point out some research highlights and drawbacks in the conclusion. Future research suggestions are also given.
... ). In general, the first two representations are more suited and easy to implement on numerical optimization problems; whereas, the third representation enjoys solving the combinatorial optimization problems with a greater ease and efficiency (Nijssen and Ba¨ck, 2003; Goldberg, 1989). Thus, to propose effective algorithms that would efficiently work in all the representations is a convoluted task. ...
This paper characterizes general optimization problems into four categories based on the solution representation schemes, as they have been the key to the design of various evolutionary algorithms (EAs). Four EAs have been designed for different formulations with the aim of utilizing similar and generalized strategies for all of them. Several modifications to the existing EAs have been proposed and studied. First, a new tradeoff function-based mutation has been proposed that takes advantages of Cauchy, Gaussian, random as well as chaotic mutations. In addition, a generalized learning rule has also been proposed to ensure more thorough and explorative search. A theoretical analysis has been performed to establish the convergence of the learning rule. A theoretical study has also been performed in order to investigate the various aspects of the search strategy employed by the new tradeoff-based mutations. A more logical parameter tuning has been done by introducing the concept of orthogonal arrays in the EA experimentation. The use of noise-based tuning ensures the robust parameter tuning that enables the EAs to perform remarkably well in the further experimentations. The performance of the proposed EAs has been analyzed for different problems of varying complexities. The results prove the supremacy of the proposed EAs over other well-established strategies given in the literature.
... . Finally Droste, et al. [42] [43] point out the importance of the algorithm to accept mutated strings with the same fitness (as well as improved) such that the algorithm may cross flat spots in the search domain. The (1+1,m) algorithm may be extended to more than one parent and children, and beyond for example variable static mutation rates for children [40]. ...
Strings of bits (bitstrings) are a common first-order representation in the design and preliminary investigation of computational intelligence algorithms given (1) the ease in mapping the strings to arbitrary domains (such as real numbers), and (2) in terms of mathematical analysis. This work considers the use of bitstrings in the context of the clonal expansion and antigenic selection in a general clonal selection algorithm, and provides a general review of mutation-based optimization (genetic algorithms) and bit-string matching (classifier systems and negative selection).
