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Modeling building-block interdependency
Abstract
The Building-Block Hypothesis appeals to the notion of problem decomposition slid the assembly of solutions from sub-solutions. Accordingly, there have been many varieties of GA test problems with a structure based on building-blocks. Many of these problems use deceptive fitness functions to model interdependency between the bits within a block. However. very few have any model of interdependency between building-blocks; those that do are not consistent in the type of interaction used intra-block and inter-block. This paper discusses the inadequacies of the various Lest problems in the literature and clarifies the concept of building-block interdependency. We formulate a principled model of hierarchical interdependency that can be applied through many levels in a consistent manner and introduce Hierarchical If-and-only-if (H-IFF) as a canonical example. We present some empirical results of GAs on H-IFF showing that if population diversity is maintained and linkage is tight then the GA is able to identify and manipulate building-blocks over many levels of assembly, as the Building-Block Hypothesis suggests.
... Crossover allows for exchanging information between individuals and shall lead to finding new solutions of a higher quality. The nature of practical problems allows assuming that the gene-dependencies exist, and various gene groups may be less or more dependent on each other [4]. Therefore, identifying the strength of the inter-gene dependencies and decomposing the underlying problem structure was shown crucial for theoretical [5] and practical problems [3,6]. ...
... In practical problems, usually, the expectation is that the gene groups will not be fully separable [4,22,23]. Note that stateof-the-art linkage learning techniques (e.g., DSM-based [2,7,8], 3LO [9], Differential Grouping [14][15][16]) do not assume the existence of fully separable gene groups. ...
... In some optimization problems, many dependency levels may exist. The example of such problem is the Hierarchical-If-And-Only-If (HIFF) [4,5,9]. In HIFF problems, the first level of dependency may look like the problem is built from many separable gene groups (i.e., the problem seems like it has an additively separable nature [27]). ...
... Such molecule found in one of the parallels can be used to substitute all or a part of the other parallel populations. Other known parallelization and/or more complex mutation schemes (macromutations in hill-climbing) can also be used (eg, [121,122]). The results of this article tell us that such an experimental design will demonstrate its effectiveness at sufficiently small population sizes. ...
... The mutation scheme according to [130,131] proved to be the most effective for RR. Further, Watson with coauthors [121,122] tested HC routines that use the macromutation hill-climber (MMHC) on their RR function extensions, so they should also be tested on BioRS functions. ...
... After the fundamental publications on RR functions, their alternative versions were proposed, which were believed to show better performance of GA, within the framework of the theory of schemata and BBs, in comparison with other heuristic approaches [126]. We are mainly interested in the trap functions, as well as those functions where interactions between blocks were considered and analyzed [121]. The most resounding conclusion from the analysis of such functions is the importance of crossover and crossover-like functions for the effective solution of this kind of hard problems [33,[124][125][126][127][128]. ...
Evolutionary computing (EC) is an area of computer sciences and applied mathematics covering heuristic optimization algorithms inspired by evolution in Nature. EC extensively study all the variety of methods which were originally based on the principles of selectionism. As a result, many new algorithms and approaches, significantly more efficient than classical selectionist schemes, were found. This is especially true for some families of special problems. There are strong arguments to believe that EC approaches are quite suitable for modeling and numerical analysis of those methods of synthetic biology and biotechnology that are known as in vitro evolution. Therefore, it is natural to expect that the new algorithms and approaches developed in EC can be effectively applied in experiments on the directed evolution of biological macromolecules. According to the John Holland’s Schema theorem, the effective evolutionary search in genetic algorithms (GA) is provided by identifying short schemata of high fitness which in the further search recombine into the larger building blocks (BBs) with higher and higher fitness. The multimodularity of functional biological macromolecules and the preservation of already found modules in the evolutionary search have a clear analogy with the BBs in EC. It seems reasonable to try to transfer and introduce the methods of EC, preserving BBs and essentially accelerating the search, into experiments on in vitro evolution. We extend the key instrument of the Holland’s theory, the Royal Roads fitness function, to problems of the in vitro evolution (Biological Royal Staircase, BioRS, functions). The specific version of BioRS developed in this publication arises from the realities of experimental evolutionary search for (DNA-) RNA-devices (aptazymes). Our numerical tests showed that for problems with the BioRS functions, simple heuristic algorithms, which turned out to be very effective for preserving BBs in GA, can be very effective in in vitro evolution approaches. We are convinced that such algorithms can be implemented in modern methods of in vitro evolution to achieve significant savings in time and resources and a significant increase in the efficiency of evolutionary search.
... One limitation for classic MOEAs (including NSGA-II) is that new solutions are generated using fully randomized recombination (crossover) operators [22,26]. For example, the single-point and the multi-point crossovers randomly cut the chromosomes and exchange the genetic materials between two parent solutions, potentially breaking "promising" patterns. ...
... The latest advances in the evolutionary computation literature showed that a more effective search could be performed by identifying and preserving linkage structures, i.e., groups of genes (problem variables) that should be replicated altogether into the offspring. Linkage learning [26] is a broad umbrella of methods to infer linkage structures and exploit this knowledge within more "competent" variation operators [16]. ...
... While linkage learning has been shown to be effective for single-objective numerical problems [16,22,26], we argue that it can also have huge potential for multi-objective test case selection. In this context, a solution is a binary vector where each bit i indicates whether the i-th test case is selected or not for regression testing. ...
Test Case Selection (TCS) aims to select a subset of the test suite to run for regression testing. The selection is typically based on past coverage and execution cost data. Researchers have successfully used multi-objective evolutionary algorithms (MOEAs), such as NSGA-II and its variants, to solve this problem. These MOEAs use traditional crossover operators to create new candidate solutions through genetic recombination. Recent studies in numerical optimization have shown that better recombinations can be made using machine learning, in particular link-age learning. Inspired by these recent advances in this field, we propose a new variant of NSGA-II, called L2-NSGA, that uses linkage learning to optimize test case selection. In particular, we use an unsupervised clustering algorithm to infer promising patterns among the solutions (subset of test suites). Then, these patterns are used in the next iterations of L2-NSGA to create solutions that preserve these inferred patterns. Our results show that our customizations make NSGA-II more effective for test case selection. The test suite sub-sets generated by L2-NSGA are less expensive and detect more faults than those generated by MOEAs used in the literature for regression testing.
... To a problem to be decomposable, there must be none interaction between any two variables and each variable should be separately treated [94]. According to Watson [115], included in the term decomposable is the notion of identifiable component parts, and a set of correlated variables is not decomposable. Often in multivariate calibration there are considerable linear dependency among decision variables from spectral data [6,66]. ...
... In this sense, our first hypothesis arises and claims that spectral data in multivariate calibration may be considered as a non-completely decomposable problem. In a non-completely decomposable problem, some variables are closely correlated to other variables and therefore should be maintained in the same subset [115]. In this case, variable selection procedure in multivariate calibration may not be accordingly treated as a decomposable problem due to the constant presence of multicollinearity in the dataset (see Section 2.2). ...
... The BBs hypothesis appeals to the notion of problem decomposition and the assembly of solutions from sub-solutions. The method of forming solutions by first breaking down a problem into subproblems is a central tenet behind the BBs hypothesis [115]. ...
The procedure used to select a subset of suitable features in a given data set consists in
variable selection, which is important when the dataset contains large number of variables and many of them are redundant. Multivariate calibration combines variable selection with statistical techniques to build mathematical models which relate the data to a given property of interest in order to predict this property by selecting informative variables. In this context, variable selection techniques have been widely applied to the solution of several optimization problems. For instance, Genetic Algorithms (GAs) are easy to implement and consist in a population-based model that uses selection and recombination operators to generate new solutions. However, usually in multivariate calibration the dataset present a considerable correlation degree among variables and this provides an evidence about the problem not being properly decomposed. Moreover, some studies in literature have claimed genetic operators used by GAs can cause the building blocks (BBs) disruption of viable solutions. Therefore, this work aims to claim that selecting variables in multivariate calibration is a non-completely decomposable problem (hypothesis 1) as well as that recombination operators affects the non-decomposability assumption (hypothesis 2). Additionally, we are proposing two heuristics, one local search-based operator and two versions of an Epistasis-based Feature Selection Algorithm (EbFSA) to improve model prediction performance and avoid BBs disruption. Based on the performed inquiry and experimental results, we are able to endorse the viability of our hypotheses and demonstrate EbFSA can overcome some traditional algorithms.
... When the operator is turned off or replaced by a random recombination, the algorithm is not able to find the global optima of any benchmark problem tested. The problems adopted here illustrate several aspects which have been recently considered as tricky for EDAs, such as deception [11], symmetry [9], hierarchy [12], global multimodality [3] and the presence of overlapping building blocks [13]. The structured fashion of those and other classes of problems makes them hard for low-order and even for high-order EDAs. ...
... This Section shows an exploration in the parameter space using three representative test problems: shuffled HIFF [12], concatenated trap-5 [11] and graph bisection [3]. The experiment aims to find default values for some parameters of ϕ-PBIL. ...
... This section discusses and revises the benchmark problems used in the empirical evaluation Section. The reader is referred to [3] [12][11] [13] for a more detailed description of the problems. ...
The adoption of probabilistic models for selected individuals is a powerful approach for evolutionary computation. Probabilistic models based on high-order statistics have been used by estimation of distribution algorithms (EDAs), resulting better effectiveness when searching for global optima for hard optimization problems. This paper proposes a new framework for evolutionary algorithms, which combines a simple EDA based on order 1 statistics and a clustering technique in order to avoid the high computational cost required by higher order EDAs. The algorithm uses clustering to group genotypically similar solutions, relying that different clusters focus on different substructures and the combination of information from different clusters effectively combines substructures. The combination mechanism uses an information gain measure when deciding which cluster is more informative for any given gene position, during a pairwise cluster combination. Empirical evaluations effectively cover a comprehensive range of benchmark optimization problems.
... MOEAs that rely on Pareto ranking and problem decompositions have been shown to achieve good performance also compared to greedy algorithms and local solvers [53]. One limitation for classic MOEAs (including NSGA-II) is that new solutions are generated using fully randomized recombination (crossover) operators [45,49]. This could destroy potential promising patterns that can be created by MOEAs. ...
... This could destroy potential promising patterns that can be created by MOEAs. While linkage learning has been shown to be effective for single-objective numerical problems [38,45,49], we argue that it can also have huge potential for multi-objective test case selection. ...
... This mechanism is motivated by our belief that, in the presence of inaccurate energy functions, the generation of a diverse set of candidate conformations, that can potentially span multiple global and local energy-minima, can constitute a more robust approach (i.e. with better chances of achieving native-like structures) than to simply succeed in producing a single global minimum (the general tendency of evolutionary optimisation methods (Shir et al., 2010;Das et al., 2011)). This follows a similar approach of explicit diversity maintenance adopted in some works (Sastry et al., 2005;Goldberg et al., 1992) on dealing with deceptive 'trap' functions (Goldberg, 1987(Goldberg, , 1992, or other functions that tend to lead an optimiser away from the best configurations (Watson et al., 1998). ...
... This poses a problem to optimisation protocols which cannot overly rely on the relative rankings between different local optima, which (dependent on the protein) may be more or less 'deceptive' (Goldberg, 1987(Goldberg, , 1992. As explicit diversity preservation (niching) has been recognised to be essential in similar scenarios (Sastry et al., 2005;Goldberg et al., 1992;Watson et al., 1998), an alternative selection scheme, based on stochastic ranking (Runarsson and Yao, 2000), was integrated into the proposed RMA with the purpose of regulating selection pressure and enabling diversity maintenance. The results obtained indicate that this modification allows the RMA to display a more robust performance and improve upon Rosetta's performance in terms of the optimisation of both energy and correspondence to the native structure. ...
Computational approaches to de novo protein tertiary structure prediction, including those based on the preeminent 'fragment-assembly' technique, have failed to scale up fully to larger proteins (of the order of 100 residues and above). A number of limiting factors are thought to contribute to the scaling problem over and above the simple combinatorial explosion, but the key ones relate to the lack of exploration of properly diverse protein folds, and an acute form of 'deception' in the energy function whereby low-energy conformations do not reliably equate with native structures. In this paper, solutions to both of these problems are investigated through a multi-stage memetic algorithm incorporating the successful Rosetta method as a local search routine. It is found that specialised genetic operators significantly add to structural diversity and this translates well to reaching low energies. The use of a generalised stochastic ranking procedure for selection enables the memetic algorithm to handle and traverse deep energy wells that can be considered deceptive, which further adds to the ability of the algorithm to obtain a much-improved diversity of folds. The results should translate to a tangible improvement in the performance of protein structure prediction algorithms in blind experiments such as CASP, and potentially to a further step towards the more challenging problem of predicting the three-dimensional shape of large proteins.
... For our experiments on a static landscape we have selected the "hierarchical if and only if" fitness function. The hierarchical if and only if function was introduced by Watson et al. [46,47,48,49]. It was especially constructed to show what kind of problems a genetic algorithm with crossover is suit-able for. ...
... The solutions to this subproblem again need to be combined to solve the problem on the next step of the hierarchy. A genetic algorithm using mutation and crossover is especially suited to solve this problem provided that diversity is maintained [46]. ...
Evolutionary algorithms apply the process of variation, reproduction, and selection to look for an individual capable of solving the task at hand. In order to improve the evolvability of a population we propose to copy important characteristics of nature's search space. Desired characteristics for a genotype–phenotype mapping are described and several highly redundant genotype–phenotype mappings are analyzed in the context of a population-based search. We show that evolvability, defined as the ability of random variations to sometimes produce improvement, is influenced by the existence of neutral networks in genotype space. Redundant mappings allow the population to spread along the network of neutral mutations and the population is quickly able to recover after a change has occurred. The extent of the neutral networks affects the interconnectivity of the search space and thereby affects evolvability. © 2002 Wiley Periodicals, Inc.
... Equation 1 below, describes the fitness of a string of bits (corresponding to binary feature values, as above) using this construction. This function, which we call Hierarchical If-and-Only-If (HIFF), was first introduced in previous work as an alternative to functions such as 'The Royal Roads' and 'N-K landscapes', (see [15]). ...
... Here however, we are interested in the case where the decomposition structure is not known. We call this the 'Shuffled-HIFF' landscape [15] because this preferential bias is prevented by randomly re-ordering the position of features on the string such that their genetic linkage does not correspond to their epistatic structure (see [17]). In summary, this landscape exhibits local optima at all scales, which makes it very challenging to adaptation, and fundamental to the issues of saddle-crossing and scalable evolvability. ...
Several of the Major Transitions in natural evolution, such as the symbiogenic origin of eukaryotes from prokaryotes, share the feature that existing entities became the components of composite entities at a higher level of organisation. This composition of pre-adapted extant entities into a new whole is a fundamentally different source of variation from the gradual accumulation of small random variations, and it has some interesting consequences for issues of evolvability. In this paper we present a very abstract model of 'symbiotic composition' to explore its possible impact on evolvability. A particular adaptive landscape is used to exemplify a class where symbiotic composition has an adaptive advantage with respect to evolution under mutation and sexual recombination. Whilst innovation using conventional evolutionary algorithms becomes increasingly more difficult as evolution continues in this problem, innovation via symbiotic composition continues through successive hierarchical levels unimpeded.
... if(apply to(BestSequence, Prototype) is better than Prototype) 5 then Prototype ← apply to(BestSequence, Prototype) 6 until(POEMS termination condition) 7 ...
... H-IFF. A hierarchical-if-and-only-if function proposed in [6] is the representative of hierarchically decomposable problems. The hierarchical block structure of the function is a balanced binary tree. ...
Evolutionary algorithms have already been more or less successfully applied to a wide range of optimisation problems. Typically,
they are used to evolve a population of complete candidate solutions to a given problem, which can be further refined by some
problem-specific heuristic algorithm. In this paper, we introduce a new framework called Iterative Prototype Optimisation with Evolved Improvement Steps. This is a general optimisation framework, where an initial prototype solution is being improved iteration by iteration.
In each iteration, a sequence of actions/operations, which improves the current prototype the most, is found by an evolutionary
algorithm. The proposed algorithm has been tested on problems from two different optimisation problem domains – binary string
optimisation and the traveling salesman problem. Results show that the concept can be used to solve hard problems of big size
reliably achieving comparably good or better results than classical evolutionary algorithms and other selected methods.
... We have selected 5 functions with different characteristics: HIFF [16], EqualProducts [17], SixPeaks [17], Knapsack [18] and HTRAP [7]. In all algorithms we have used the same configuration, which has been taken from [12] in order to be able to fairly compare with the algorithm presented there where the function HIFF is also used. ...
... • HIFF The HIFF function (hierarchical if and only if) was defined in [16]. For this function, the input string must be an integer power of 2, and the power l is the number of levels. ...
This work studies the problem of premature convergence due to the lack of diversity in Estimation of Distributions Algorithms. This problem is quite important for these kind of algorithms since, even when using very complex probabilistic models, they can not solve certain optimization problems such as some deceptive, hierarchical or multimodal ones. There are several works in literature which propose different techniques to deal with premature convergence. In most cases, they arise as an adaptation of the techniques used with genetic algorithms, and use randomness to generate individuals. In our work, we study a new scheme which tries to preserve the population diversity. Instead of generating individuals randomly, it uses the information contained in the probability distribution learned from the population. In particular, a new probability distribution is obtained as a variation of the learned one so as to generate individuals with less probability to appear on the evolutionary process. This proposal has been validated experimentally with success with a set of different test functions.
... On this base, benchmark problems are proposed that share (or do not share) particular features observed based on real-world problems. Important examples of such benchmark tools may be the deceptive functions [2,3] and the Hierarchical-If-And-Only-If problems [38,39]. ...
Benchmarks are essential tools for the optimizer's development. Using them, we can check for what kind of problems a given optimizer is effective or not. Since the objective of the Evolutionary Computation field is to support the tools to solve hard, real-world problems, the benchmarks that resemble their features seem particularly valuable. Therefore, we propose a hop-based analysis of the optimization process. We apply this analysis to the NP-hard, large-scale real-world problem. Its results indicate the existence of some of the features of the well-known Leading Ones problem. To model these features well, we propose the Leading Blocks Problem (LBP), which is more general than Leading Ones and some of the benchmarks inspired by this problem. LBP allows for the assembly of new types of hard optimization problems that are not handled well by the considered state-of-the-art genetic algorithm (GA). Finally, the experiments reveal what kind of mechanisms must be proposed to improve GAs' effectiveness while solving LBP and the considered real-world problem.
... The separation of R 1 and R 2 produces a problem containing four global optima; each one containing thesame PS in all BBs, Interesting cases for MBOAs arise when a subset of loworder components can form high-order components, such as the case of hierarchical problem structure. Here we use the same hierarchical construction used in [52] as all MBOAs can overcome this characteristic when C is the identity map. This is because higher-order combinations can be efficiently identified by generating a distribution of solutions using the lower-level combinations. ...
We investigate the optimisation capabilities of an algorithm inspired by the Evolutionary Transitions in Individuality. In these transitions, the natural evolutionary process is repeatedly rescaled through successive levels of biological organisation. Each transition creates new higher-level evolutionary units that combine multiple units from the level below. We call the algorithm Deep Optimisation (DO) to recognise both its use of deep learning methods and the multi-level rescaling of biological evolutionary processes. The evolutionary model used in DO is a simple hill-climber, but, as higher-level representations are learned, the hill-climbing process is repeatedly rescaled to operate in successively higher-level representations. The transition process is based on a deep learning neural network (NN), specifically a deep auto-encoder. Our experiments with DO start with a study using the NP-hard problem, multiple knapsack (MKP). Comparing with state-of-the-art model-building optimisation algorithms (MBOAs), we show that DO finds better solutions to MKP instances and does so without using a problem-specific repair operator. A second, much more in-depth investigation uses a class of configurable problems to understand more precisely the distinct problem characteristics that DO can solve that other MBOAs cannot. Specifically, we observe a polynomial vs exponential scaling distinction where DO is the only algorithm to show polynomial scaling for all problems. We also demonstrate that some problem characteristics need a deep network in DO. In sum, our findings suggest that the use of deep learning principles have significant untapped potential in combinatorial optimisation. Moreover, we argue that natural evolution could be implementing something like DO, and the evolutionary transitions in individuality are the observable result.
... Linkage-learning refers to a large body of work in the evolutionary computation community that aims to infer linkage structures present in promising individuals [27]. Linkage structures are groups of "good" genes that contribute to the fitness of a given population. ...
With the ever-increasing use of web APIs in modern-day applications, it is becoming more important to test the system as a whole. In the last decade, tools and approaches have been proposed to automate the creation of system-level test cases for these APIs using evolutionary algorithms (EAs). One of the limiting factors of EAs is that the genetic operators (crossover and mutation) are fully randomized, potentially breaking promising patterns in the sequences of API requests discovered during the search. Breaking these patterns has a negative impact on the effectiveness of the test case generation process. To address this limitation, this paper proposes a new approach that uses agglomerative hierarchical clustering (AHC) to infer a linkage tree model, which captures, replicates, and preserves these patterns in new test cases. We evaluate our approach, called LT-MOSA, by performing an empirical study on 7 real-world benchmark applications w.r.t. branch coverage and real-fault detection capability. We also compare LT-MOSA with the two existing state-of-the-art white-box techniques (MIO, MOSA) for REST API testing. Our results show that LT-MOSA achieves a statistically significant increase in test target coverage (i.e., lines and branches) compared to MIO and MOSA in 4 and 5 out of 7 applications, respectively. Furthermore, LT-MOSA discovers 27 and 18 unique real-faults that are left undetected by MIO and MOSA, respectively.
... HTOP is specifically designed to provide clarity on how DO works with specific regards to the process of rescaling the variation operator to higher-order features and the necessity for a DNN to use a layerwise procedure. HTOP is inspired by Watson's Hierarchical If and only If (HIFF) problem (Watson, Hornby, and Pollack 1998) and uses the same recursive construction with an adaptation to cause deep structure. The generalised hierarchical construction is summarised here. ...
Deep Optimisation (DO) combines evolutionary search with Deep Neural Networks (DNNs) in a novel way - not for optimising a learning algorithm, but for finding a solution to an optimisation problem. Deep learning has been successfully applied to classification, regression, decision and generative tasks and in this paper we extend its application to solving optimisation problems. Model Building Optimisation Algorithms (MBOAs), a branch of evolutionary algorithms, have been successful in combining machine learning methods and evolutionary search but, until now, they have not utilised DNNs. DO is the first algorithm to use a DNN to learn and exploit the problem structure to adapt the variation operator (changing the neighbourhood structure of the search process). We demonstrate the performance of DO using two theoretical optimisation problems within the MAXSAT class. The Hierarchical Transformation Optimisation Problem (HTOP) has controllable deep structure that provides a clear evaluation of how DO works and why using a layerwise technique is essential for learning and exploiting problem structure. The Parity Modular Constraint Problem (MCparity) is a simplistic example of a problem containing higher-order dependencies (greater than pairwise) which DO can solve and state of the art MBOAs cannot. Further, we show that DO can exploit deep structure in TSP instances. Together these results show that there exists problems that DO can find and exploit deep problem structure that other algorithms cannot. Making this connection between DNNs and optimisation allows for the utilisation of advanced tools applicable to DNNs that current MBOAs are unable to use.
... Of particular interest is the block building modeling approach, which is a structured process to develop the final model by integrating the dynamics of several models, i.e. building blocks. (Watson et al., 1998) highlight arguments for the so-called "building-block hypothesis", which appeals to the notion of problem decomposition and the assembly of solutions from sub-solutions. ...
Governments have strongly recognized that critical infrastructures (CIs) play crucial roles in underpinning economy, security and societal welfare of countries. The proper functioning of energy, transportation, water plants, telecommunication, financial and other services, is vital for all communities. If a failed infrastructure is unable to deliver services and products to the others, damages may easily cascade into the larger system of interdependent CIs. Understanding such complex system-of-systems dynamics would help to prevent networked CIs from potential catastrophic cascading effects. However, existing security measures to protect a CI from threats and cyberattacks do not usually cross the organization’s boundaries.
This research proposes a block building modeling approach based on System Dynamics (SD) to improve the understanding of dynamics of disruptive events in interdependent CI systems. Unlike most of the previous works in modeling and simulation of interdependent CIs, this novel approach accounts for both dynamics within a CI and across CIs while investigating two relevant dimensions of system resilience: operational state and service level. Blocks of models are iteratively developed and assembled together to generate complex scenarios of disruption with the final purpose of simulation-based impact analysis, resilience assessment, policy and risk
scenario evaluation. The dynamic interdependency models offer a valuable and flexible tool for predictive analysis to support risk managers in assessing scenario of crisis as well as CI operators towards more effective investment decisions and collective response actions.
Principles of epidemic modeling are used to replicate diffusion and recovery dynamics of CI operations. Hence, SD is combined with a game-theoretic approach to understand “cyber-epidemics” triggered by strategic interactions between attacker and defender. Cyber attack-defense dynamics are modeled as a continuous game of timing to highlight that effectiveness of strategic moves strongly depends on “when to act”. The game-theoretic model is applied for the optimization of proactive and reactive defense scenarios. This application demonstrates how the dynamic interdependency models can be used to support strategic cybersecurity decisions within organizations. Promoting the use of information sharing to improve cybersecurity across
organizations, a further application of the dynamic interdependency model represents a relevant contribution to the design of a cyber incident early warning system for CI operators. In accordance with guidelines issued by the European Union Agency for Network and Information Security (ENISA) to identify critical assets and services, the
modeling is extended by a perspective of CI operators to demonstrate how it can be used to gain situational awareness in the context of European CIs.
... However, o en in multivariate calibration there are considerable linear dependencies among decision variables from spectral data [2,5]. According to Watson [12], a set of correlated variables is not decomposable. ...
Variable selection is a procedure used to choose a subset of features in order to extract information from them. It has been widely used in multivariate calibration together with statistical techniques to build a model from which it is possible to be interpreted by users. Genetic algorithms (GAs) have been successfully utilized as a variable selection method in multivariate calibration models. However, GAs solve a problem by trying different decompositions, and the variable selection problem usually can not be properly decomposed when there are considerable correlation among variables. Consequently, GAs tend to lead to a poor variable selection performance if the variables interdepence is strong. This work comes from a doctoral thesis, which is still in development and aims to (not only) demonstrate that selecting variables in multivariate calibration is a non-completely decomposable problem. Based on the preliminary results, we are able to claim the viability of our initial hypothesis.
... As a reference we also consider an MMA without any balancing at all which we denote as noB. We have considered three test functions, namely Deb's trap (TRAP) function [11] (concatenating 32 four-bit traps), Watson et al.'s Hierarchical-if-and-only-if (HIFF) function [43] (using 128 bits) and Goldberg et al.'s Massively Multimodal Deceptive Problem (MMDP) [14] (using 24 six-bit blocks). Tables 1-2. ...
Optimization algorithms deployed on unstable computational environments must be resilient to the volatility of computing nodes. Different fault-tolerance mechanisms have been proposed for this purpose. We focus on the use of island-based multimemetic algorithms, namely memetic algorithms which explicitly represent and evolve memes alongside solutions, endowed with self-scaling capabilities. These strategies dynamically resize populations in order to react to system fluctuations. In this context, we study the joint use of different self-healing strategies, aimed to compensating the harm that the loss of computing nodes produces. Firstly, we consider the use of probabilistic models in order to self-sample the current population when it has to be resized, thus minimizing distortions in the convergence of the population and the progress of the search. Then, we complement the previous approach with the use of rewiring strategies intended to keep a rich connectivity in the system along time. We perform an extensive empirical assessment of those strategies on three different problems, considering a simulated computational environment featuring diverse degrees of instability. It is shown that these self-healing strategies provide a performance improvement and interact synergistically with each other, in particular in scenarios with large volatility.
... Para três outros parâmetros, foram ajustados valores default através de investigação empírica, mostrada na figura 2. Adotamos três problemas-teste conhecidos na literatura: se e somente se hierárquico (HIFF) misturado (Watson et al., 1998), armadilha concatenada-5 (Pelikan et al., 1999) e particionamento de grafos (Peña et al., 2005), com tamanhos de instância 64, 50 e 42, correspondendo respectivamente às instâncias Pshuff64, Ptrapfive50 e Pcatring42 (a mesma que em Peña et al. (2005)). O número de ótimos globais varia entre as instâncias: Pcatring42 apresenta 6 ótimos globais, enquanto Ptrapfive50 possui um único e Pshuff64 possui 2. Os demais parâmetros foram, para esta avaliação, ajustados em valores que foram empiricamente verificados como sendo próximos aos mínimos necessários para a resolução de cada problema. ...
Classical evolutionary computation algorithms are not effective when solving gobally multimodal optimization prob-lems as convergence to a single optimum occurs. Later approaches often use some mechanism for maintaining population diversity as an auxiliary tool in the process. Those algorithms usually trust on sophisticated probabilistic models for capturing the problem structure. This paper presents an empirical evaluation of ϕ-PBIL, which is based on clustering as a diversity maintaining mech-anism, extracting relevant information about the problem structure directly from the clustering models. A new parameter set is obtained and a new empirical comparison between ϕ-PBIL and a competitor is carried out. It shows that ϕ-PBIL is more effective and substantially more efficient than a state-of-the-art algorithm for several instances of a benchmark combinatorial optimization problem. Resumo— Algoritmos clássicos de computação evolutiva não são efetivos em resolver problemas de otimização globalmente multimodais, devido a convergência para apenas um dos ótimos. Abordagens mais recentes recorrem a algum mecanismo de ma-nutenção da diversidade da população, como sendo uma ferramenta auxiliar do processo, confiando em modelos probabilísticos sofisticados para a identificação da estrutura do problema. Este artigo apresenta um novo estudo empírico do ϕ-PBIL, que é um algoritmo baseado em agrupamentos para manutenção da diversidade, extraindo informações relevantes sobre a estrutura do pro-blema a partir dos próprios modelos de agrupamento. Um novo conjunto de parâmetros é obtido aqui e uma nova comparação empírica entre o ϕ-PBIL e um concorrente é efetuada, onde fica evidente que, para diversas instâncias de um problema de otimiza-ção combinatória considerado benchmark, o ϕ-PBIL é mais efetivo e substancialmente mais eficiente que um algoritmo referência, considerado representante do estado da arte. Palavras-chave— Computação evolutiva, otimização, agrupamento.
... Tightly coupled component models are developed in a standard programming language using a set of modular programming libraries for different single-domain models and the resulting program is then compiled into a single executable. (For example: Leavesley et al. 1996;Dahmann 1997;Watson et al. 1998;Rizzoli et al. 1998;Reed et al. 1999;Krahl 2000;David et al. 2002;Voinov et al. 2004;Rahman et al. 2004;Kolbe at al. 2005;Ahuja et al. 2005;Müller 2009). Loosely coupled component models are developed by coupling various analysis and simulation programs at the data level. ...
This paper investigates the state-of-the-art with respect to simulation-based planning support systems in order to draw a set of requirements and best practices for an urban planning and design framework that enables multiple stakeholders with differing perspectives to systematically explore design options, leveraging the latest analysis and simulation techniques. From these requirements and best practices, the foundations and structure of such an urban planning and design framework are developed. A number of technological and methodological challenges are identified for future investigation.
... This may guide the search performed by EC algorithms to areas of individuals with certain "good" properties. Techniques of this kind are sometimes called linkage learning or building block learning (see Goldberg et al. [1991], van Kemenade [1996], Watson et al. [1998], and Harik [1999] as examples). Moreover, generalized recombination operators have been proposed in the literature, which incorporate the notion of "neighborhood search" into EC. ...
... We can simply expand the network shown inFigure 1 so that nodes are clustered into groups and sub-groups recursively. Alternatively, we may abstract the stability function into a simple binary function over strings of length N=2 P , where P is the number of hierarchical levels in the system (see Pollack 1998, and, for details). ...
Top-down hierarchical or recursive problem decomposition is a familiar and highly successful approach to design and optimization in engineering domains. However, top-down decomposition of a system or problem into more manageable parts requires a priori domain knowledge of what kinds of subsystems are feasible and what kinds of subsystem interfaces are manageable. To a large extent this depends on knowledge of existing components that have previously been identified as useful 'building-blocks' in the problem domain. In this paper we overview recent work that has developed an abstract model of automatic module discovery. In an abstract domain, our method discovers modules hierarchically in a bottom-up fashion that allows their re-use in subsequent higher-level structures. This method discovers modules without any a priori knowledge of the problem's modular structure. We outline our approach and results.
... In order to examine the capabilities of the algorithm in model evaluation, we have used two popular hierarchical problems introduced in this field [8 and 11]: RIFF and hTrap. HIFF is one of the first hierarchical problems that challenge ordinary genetic algorithms by deceiving any attempts that try to solve the problem as a single level problem [11]. Claimed to be the ultimate challenge by its introducers, hTrap is based on the m-k trap functions [8]. ...
Estimation of distribution algorithms, especially those using Bayesian network as their probabilistic model, have been able to solve many challenging optimization problems, including the class of hierarchical problems, competently. Since model-building constitute an important part of these algorithms, finding ways to improve the quality of the models built during optimization is very beneficial. This in turn requires mechanisms to evaluate the quality of the models, as each problem has a large space of possible models. The efforts in this field are mainly concentrated on single-level problems, due to complex structure of hierarchical problems which makes them hard to treat. In order to extend model analysis to hierarchical problems, a model evaluation algorithm is proposed in this paper which can be applied to different problems. The results of applying the algorithm to two common hierarchical problems are also mentioned and described.
... This may guide the search performed by EC algorithms to areas of individuals with certain "good" properties. Techniques of this kind are sometimes called linkage learning or building block learning (see Goldberg et al. [1991], van Kemenade [1996], Watson et al. [1998], and Harik [1999] as examples). Moreover, generalized recombination operators have been proposed in the literature, which incorporate the notion of "neighborhood search" into EC. ...
The field of metaheuristics for the application to combinatorial optimization problems is a rapidly growing field of research. This is due to the importance of combinatorial optimization problems for the scientific as well as the industrial world. We give a survey of the nowadays most important metaheuristics from a conceptual point of view. We outline the different components and concepts that are used in the different metaheuristics in order to analyze their similarities and differences. Two very important concepts in metaheuristics are intensification and diversification. These are the two forces that largely determine the behaviour of a metaheuristic. They are in some way contrary but also complementary to each other. We introduce a framework, that we call the I&D frame, in order to put different intensification and diversification components into relation with each other. Outlining the advantages and disadvantages of different metaheuristic approaches we conclude by pointing out the importance of hybridization of metaheuristics as well as the integration of metaheuristics and other methods for optimization.
... To illustrate the necessity of block processing, we define a problem structure constructing a two-level hierarchy as has been done for standard GAs and EDAs [36,28]. On the lower level, small-order Boolean functions are evaluated to provide the input to the higher level. ...
Michigan-style learning classifier systems (LCSs), such as the accuracy-based XCS system, evolve distributed problem solutions represented by a population of rules. Recently, it was shown that decomposable problems may require effective processing of subsets of problem attributes, which cannot be generally assured with standard crossover operators. A number of competent crossover operators capable of effective identification and processing of arbitrary subsets of variables or string positions were proposed for genetic and evolutionary algorithms. This paper effectively introduces two competent crossover operators to XCS by incorporating techniques from competent genetic algorithms (GAs): the extended compact GA (ECGA) and the Bayesian optimization algorithm (BOA). Instead of applying standard crossover operators, here a probabilistic model of the global population is built and sampled to generate offspring classifiers locally. Various offspring generation methods are introduced and evaluated. Results indicate that the performance of the proposed learning classifier systems XCS/ECGA and XCS/BOA is similar to that of XCS with informed crossover operators that is given all information about problem structure on input and exploits this knowledge using problem-specific crossover operators.
In this paper, we consider an NP-hard, real-world optimization problem from the field of computer networks. The problem refers to the network survivability and may be considered hard due to its scale. Such problems are usually successfully solved by various Genetic Algorithms (GAs). The recent advances in the development of Evolutionary Algorithms (EAs) dedicated to solving discrete-encoded problems show that GAs employing modern linkage learning techniques seem to have exceptional potential in proposing high-quality results. Many of such GAs are the state-of-the-art methods for various optimization problems, including various domain types and single- and multi-objective optimization problems. These GAs have also been shown effective in solving theoretical and practical problems. Thus, linkage learning development may lead to proposing GAs that are significantly more effective than their predecessors. Therefore, we develop the recently proposed linkage learning technique, namely the linkage learning based on local optimization (3LO) that is (to the best of our knowledge) based on fundamentally different ideas than all other linkage-based problem decomposition techniques. Due to these differences, 3LO has some exceptional features – it is proven that it will never commit some of the possible problem decomposition inconsistencies. However, 3LO was only proposed for binary-encoded problems. Therefore, to fill this gap and adjust 3LO to the considered problem, we propose linkage learning based on local optimization for discrete non-binary search spaces (3LO-nb). The obtained results show that 3LO-nb allows for reaching excellent results. Additionally, our proposition is generic, and its effectiveness may be verified on other non-binary discrete problems.
Complexity in water distribution systems (WDSs) poses a challenge for analysis and management of the systems. To reduce the complexity, the recent development of complex network science provides a system decomposition technique that converts a complex WDS with a large number of components into a simple system with a set of interconnected modules. Each module is a subsystem with stronger internal connections than external connections. Thus far, the topological features of the modular structure in WDS have been extensively studied but not the behavioural features, e.g. the hydraulic interdependencies among modules. Therefore, this paper aims to quantitatively measure and graphically visualize the module interdependency in WDSs, which helps understanding the behavioural complexity of WDSs and thus various WDS analyses, such as pipe maintenance, model calibration, rehabilitation, and District Metered Areas planning. Specifically, this study first identifies the WDS's modular structure then measures how changes in the state of one module (i.e. any single pipe failure or perturbed demand within each module) affect the state of another module. Modular interdependencies are summarized in an interdependency matrix and visualized by the digraph. Four real-world systems are analysed, and three of them shows low interdependencies among most of the modules and there are only a few critical modules whose status changes will substantially affect a number of other modules. Hence, highly interconnected topologies may not result in strong and complex module interdependency, which is a fact that simplifies several WDS analysis for practical applications as discussed in this paper.
Linkage learning techniques are a crucial part of many modern evolutionary methods dedicated to solving problems in discrete domains. Linkage information quality is decisive for the effectiveness of these methods. In this paper, we point on two possible linkage inaccuracy types. The missing linkage that occurs when some gene dependencies remain undiscovered, and the false linkage that takes place when linkage identifies gene dependencies that do not exist. To the best of our knowledge, all linkage learning techniques proposed so far are based on predictions, which can commit both of the mistake types. We propose a different approach. Instead of using statistical measures, or evolving the linkage, we check which genes are dependent on one another employing disturbances and the local search. We prove that the proposed technique will never report any false linkage. Thus, the proposed Linkage Learning based on Local Optimization (3LO) may miss some linkage but will never report a false one. The main objective of this paper is to show the potential brought by 3LO that is fundamentally different from other linkage learning techniques. Since the main disadvantage of the proposed technique is its computational cost, it does not seem suitable for some of the already known, effective evolutionary methods. To overcome this issue, we propose an evolutionary method that employs 3LO. The extensive experimental analysis performed on a large set of hard computational problems shows that the method using 3LO is found to be competitive with other state-of-the-art methods.
Successful and efficient use of evolutionary algorithms (EA) depends on the choice of the genotype, the problem representation (mapping from genotype to phenotype) and on the choice of search operators that are applied to the genotypes. These choices cannot be made independently of each other. The question whether a certain representation leads to better performing EAs than an alternative representation can only be answered when the operators applied are taken into consideration. The reverse is also true: deciding between alternative operators is only meaningful for a given representation.
In EA practice one can distinguish two complementary approaches. The first approach uses indirect representations where a solution is encoded in a standard data structure, such as strings, vectors, or discrete permutations, and standard off-the-shelf search operators are applied to these genotypes. This is for example the case in standard genetic algorithms, evolution strategies, and some genetic programming approaches like grammatical evolution or cartesian genetic programming. To evaluate the solution, the genotype needs to be mapped to the phenotype space. The proper choice of this genotype-phenotype mapping is important for the performance of the EA search process. The second approach, the direct representation, encodes solutions to the problem in its most 'natural' space and designs search operators to operate on this representation.
Research in the last few years has identified a number of key concepts to analyse the influence of representation-operator combinations on EA performance. Relevant properties of representations are locality and redundancy.
Locality is a result of the interplay between the search operator and the genotype-phenotype mapping. Representations are redundant if the number of phenotypes exceeds the number of possible genotypes. Redundant representations can lead to biased encodings if some phenotypes are on average represented by a larger number of genotypes or search operators favor some kind of phenotypes.
The tutorial gives a brief overview about existing guidelines for representation design, illustrates the different aspects of representations, gives a brief overview of models describing the different aspects, and illustrates the relevance of the aspects with practical examples.
Multimemetic algorithms (MMAs) are a subclass of memetic algorithms in which memes are explicitly attached to genotypes and evolve alongside them. We analyze the propagation of memes in MMAs with a spatial structure. For this purpose we propose an idealized selecto-Lamarckian model that only features selection and local improvement, and study under which conditions good, high-potential memes can proliferate. We compare population models with panmictic and toroidal grid topologies. We show that the increased takeover time induced by the latter is essential for improving the chances for good memes to express themselves in the population by improving their hosts, hence enhancing their survival rates. Experiments realized with an actual MMA on three different complex pseudo-Boolean functions are consistent with these findings, indicating that memes are more successful in a spatially structured MMA, rather than in a panmictic MMA, and that the performance of the former is significantly better than that of its panmictic counterpart
Analyzing evolutionary algorithms is often surprisingly difficult. It can be challenging even for very simple evolutionary algorithms on very simple functions. This is due to the fact that evolutionary algorithms are a class of randomized search heuristics mimicking natural evolution that have been designed to search effectively for good solutions in a vast search space without any thought about analysis. The directed random sampling of the search space they perform gives rise to complex and hard to analyze random processes that can be described as complex Markov chains as we have discussed in Sect. 3. 1. This motivates us to start our analysis with evolutionary algorithms that are as simple as possible and consider fitness functions that are as simple as possible. We do not claim that such evolutionary algorithms are actually applied in practice or that example problems bear much resemblance to real optimization problems.
Estimation of Distribution Algorithms (EDAs) require flexible probability
models that can be efficiently learned and sampled. Autoencoders (AE) are
generative stochastic networks with these desired properties. We integrate a
special type of AE, the Denoising Autoencoder (DAE), into an EDA and evaluate
the performance of DAE-EDA on several combinatorial optimization problems with
a single objective. We asses the number of fitness evaluations as well as the
required CPU times. We compare the results to the performance to the Bayesian
Optimization Algorithm (BOA) and RBM-EDA, another EDA which is based on a
generative neural network which has proven competitive with BOA. For the
considered problem instances, DAE-EDA is considerably faster than BOA and
RBM-EDA, sometimes by orders of magnitude. The number of fitness evaluations is
higher than for BOA, but competitive with RBM-EDA. These results show that DAEs
can be useful tools for problems with low but non-negligible fitness evaluation
costs.
At the end of the 2006 AGI Workshop, a number of presenters were invited to participate in a panel discussion on the theme “What Are the Bottlenecks, and How Soon to AGI?” This chapter presents a record of that dialogue, including audience participation, lightly edited by the presenters themselves for greater readability.
Selection pressure restrains the selection of individuals from the current population to produce a new population in the next generation. It gives individuals of higher quality a higher probability of being used to create the next generation so that evolutionary algorithms (EAs) can focus on promising regions in the search space. An evolutionary learning process is dynamic and requires different selection pressures at different learning stages in order to speed up convergence or avoid local optima. Therefore, it is desirable for selection mechanisms to be able to automatically tune selection pressure during evolution. Tournament selection is a popular selection method in EAs, especially genetic algorithms and genetic programming (GP). This paper focuses on tournament selection and shows that the standard tournament selection scheme is unaware of the dynamics in the evolutionary process and that the standard tournament selection scheme is unable to tune selection pressure automatically. This paper then presents a novel approach which integrates the knowledge of the fitness rank distribution (FRD) of a population into tournament selection. Through mathematical modeling, simulations, and experimental study in GP, this paper shows that the new approach is effective and using the knowledge of FRD is a promising way to modify the standard tournament selection method for tuning the selection pressure dynamically and automatically along evolution.
Nowadays, many engineering applications require the minimization of a cost function such as decreasing the delivery time or the used space, reducing the development effort, and so on. Not surprisingly, research in optimization is one of the most active fields of computer science. Metaheuristics are part of the state-of-the-art techniques for combinatorial optimization. But their success comes at the price of considerable efforts in design and development time. Can we go further and automate their preparation? Especially when time is limited, dedicated techniques are unknown or the tackled problem is not well understood? The Gestalt heuristic, a search based on meta-modeling, answers those questions. Our approach, inspired by Gestalt psychology, considers the problem representation as a key factor of the success of the metaheuristic search process. Thanks to the emergence of such representation abstraction, the metaheuristic is being assisted by constraining the search. This abstraction is mainly based on the aggregation of the representation variables. The metaheuristic operators then work with these new aggregates. By learning, the Gestalt heuristic continuously searches for the right level of abstraction. It turns out to be an engineering mechanism very much related with the intrinsic emergence concept. First, the paper introduces the approach in the practical context of combinatorial optimization. It describes one possible implementation with evolutionary algorithms. Then, several experimental studies and results are presented and discussed in order to test the suggested Gestalt heuristic implementation and its main characteristics. Finally, the heuristic is more conceptually discussed in the context of emergence.
Recent results in Search-Based Testing show that the relatively simple Alternating Variable hill climbing method outperforms Evolutionary Testing (ET) for many programs. For ET to perform well in covering an individual branch, a program must have a certain structure that gives rise to a fitness landscape that the crossover operator can exploit. This paper presents theoretical and empirical investigations into the types of program structure that result in such landscapes. The studies show that crossover lends itself to programs that process large data structures or have an internal state that is reached over a series of repeated function or method calls. The empirical study also investigates the type of crossover which works most efficiently for different program structures. It further compares the results obtained by ET with those obtained for different variants of hill climbing algorithm, which are found to be effective for many structures considered favourable to crossover, with the exception of structures with landscapes containing entrapping local optima.
Schemata theorem is based on the notion that similarities among the individuals of the population of a genetic algorithm are
related to the substructures present in the problem being solved. Similarities are currently taken into account in evolutionary
computation since the preservation of the diversity in the population is considered very important to allow the identification
of the problem structure, as much as to find and maintain several global optima. This work shows an empirical investigation
concerning the application of an algorithm which is based on learning from similarities among individuals. Those similarities
are shown to reveal information about the problem structure. Empirical evaluation and comparison show the effectiveness and
scalability of this new approach when solving multimodal optimization problems, including several instances of graph bisection
and a highly multimodal parity function.
This chapter explores the possibility that natural selection takes place in the brain. We review the theoretical and experimental
evidence for selectionist and competitive dynamics within the brain. We propose that in order to explain human problem-solving,
selectionist mechanisms demand extension to encompass the full Darwinian dynamic that arises from introducing replication
of neuronal units of selection. The algorithmic advantages of replication of representations that occur in natural selection
are not immediately obvious to the neuroscientist when compared with the kind of search normally proposed by instrumental
learning models, i.e. stochastic hill-climbing. Indeed, the notion of replicator dynamics in the brain remains controversial
and unproven. It starts from early thoughts on the evolution of ideas, and extends to behaviourist notions of selection of
state-action pairs, memetics, synaptic replicators, and hexagonal cortical replicators. Related but distinct concepts include
neural selectionism, and synfire chains. Our contribution here is to introduce three possible neuronal units of selection
and show how they relate to each other. First, we introduce the Adams synapse that can replicate (by quantal budding) and
mutate by attaching to nearby postsynaptic neurons rather than to the current postsynaptic neuron. More generally, we show
that Oja’s formulation of Hebbian learning is isomorphic to Eigen’s replicator equations, meaning that Hebbian learning can
be thought of as a special case of natural selection. Second, we introduce a synaptic group replicator, a pattern of synaptic
connectivity that can be copied to other neuronal groups. Third, we introduce an activity replicator that is a pattern of
bistable neuronal activities that can be copied between vectors of neurons. This last type of replicator is not composed of
the first two kinds, but may be dependent upon them. We suggest how these replicators may take part in diverse aspects of
cognition such as causal inference, human problem solving, and memory.
David Goldberg has defined a competent genetic algorithm as one which “can solve hard problems, quickly, accurately, and reliably.” Among other competent genetic algorithms that have been developed are the Bayesian optimization algorithm (BOA), the fast messy genetic algorithm (fmGA), and the linkage learning genetic algorithm (LLGA). These algorithms have been tested on problems of bounded difficulty
that are additive separable formed by deceptive subproblems of order not greater than k, where k < ℓ. BOA, fmGA, LLGA, and other competent genetic algorithms are stochastic, and thus, can only be assured of attaining optimality in a probabilistic sense. In this paper, we develop a deterministic algorithm that solves to optimality all linearly decomposable problems in a polynomial numberof function evaluations with respect to the maximum size of the subproblems,k. The algorithm presented does not rely on a population, does not recombine individuals or apply any other genetic operator. Furthermore, because it is deterministic, the number of function evaluations required to find the optimum can beknown in advance. The algorithm presented solves both the linkage and the optimization problems by finding the disjoint sets
of related variables and the optimal values of these variables at the same time. The fact that such an algorithm can be devised has important implications for the design of GA-hard problems, and the development and evaluation of genetic optimization algorithms.
The previous chapter has discussed how hierarchy can be used to reduce problem complexity in black-box optimization. Additionally, the chapter has identified the three important concepts that must be incorporated into black-box optimization methods based on selection and recombination to provide scalable solution for difficult hierarchical problems. Finally, the chapter proposed a number of artificial problems that can be used to test scalability of optimization methods that attempt to exploit hierarchy.
Most metaheuristics try to find a good balance between exploitation and exploration to achieve their goals. The exploration efficiency is highly dependent on the size and ruggedness of the search space. A metaheuristic such as the simple genetic algorithm (SGA) is not totally suited to traverse very large landscapes, especially deceptive ones. The approach proposed here improves the exploration of the SGA by adding a second search process through the way solutions are coded. We will designate by "observer" each possible coding that aims at reducing the search space. Information on the quality and adequacy of one possible observer is obtained by adopting this specific coding and testing how SGA benefits from this search space reduction. The new approach investigated here trains the observers for a specific time and then decides which of them is the most suitable to solve the whole problem. Concretely, a second evolutionary stage has been added to evolve observers for the SGA. These observers aim at reducing the size and smoothing the ruggedness of the search space through a simplification of the genotype. To test the proposed approach, we apply it to the classical hierarchical if-and-only-if (HIFF) problem and measure the efficiency of our approach in term of quality and time.
The performances (success) of a hill climber (RMHC) and a genetic algorithm (upGA) on a set of test problems with varied structural characteristics are compared to learn whether problem structural characteristic can be a feasible solution-independent indicator of when a problem will be more easily solved by a genetic algorithm than by hill climbing. Evidence supporting this hypothesis is found in this initial study. In particular, other factors (modularity, transitivity and fitness distribution) being equal, highly modular problems with broad right-skewed degree distributions are more easily solved by upGA than by RMHC. Suggestions are made for further research in this direction.
This paper proposes a new algorithm to identify and compose building blocks based on minimum mutual information criterion. Building blocks are interpreted as common subsequences between good individuals. The proposed algorithm can extract building blocks in population explicitly. The additively decomposable problems and hierarchical decomposable problems are used to validate the algorithm. The results are compared with Bayesian Optimization Algorithm, Hierarchical Bayesian Optimization Algorithm, and Chi-square Matrix. This proposed algorithm is simple, easy to tune and fast.
The hierarchical Bayesian optimization algorithm (hBOA) can solve nearly decomposable and hierarchical problems of bounded difficulty in a robust and scalable manner by building and sampling probabilistic models of promising solutions. This paper analyzes probabilistic models in hBOA on four important classes of test problems: concatenated traps, random additively decomposable problems, hierarchical traps and two-dimensional Ising spin glasses with periodic boundary conditions. We argue that although the probabilistic models in hBOA can encode complex probability distributions, analyzing these models is relatively straightforward and the results of such analyses may provide practitioners with useful information about their problems. The results show that the probabilistic models in hBOA closely correspond to the structure of the underlying optimization problem, the models do not change significantly in consequent iterations of BOA, and creating adequate probabilistic models by hand is not straightforward even with complete knowledge of the optimization problem.
Normalization transforms one parent genotype to be consistent with the other before crossover. In this paper, we explain how normalization alleviates the difficulties caused by nonsynonymously redundant encodings in genetic algorithms. We define the encodings with maximally nonsynonymous property and prove that the encodings induce uncorrelated search spaces. Extensive experiments for a number of problems show that normalization transforms the uncorrelated search spaces to correlated ones and leads to significant improvement in performance.
Mutation and crossover are the main search operators of different variants of evolutionary algorithms. Despite the many discussions on the importance of crossover nobody has proved rigorously for some explicitly defined fitness functions fn:{0,1}n→R that a genetic algorithm with crossover can optimize fn in expected polynomial time while all evolution strategies based only on mutation (and selection) need expected exponential time. Here such functions and proofs are presented for a genetic algorithm without any idealization. For some functions one-point crossover is appropriate while for others uniform crossover is the right choice.
Diversity preservation has shown to be very important for allowing the identification of the problem structure as much as for keeping several global optima during the process of evolutionary computation. The most important evolutionary algorithms currently available in the literature adopt diversity preservation techniques as supporting tools in the process, while they trust on more sophisticated models for the identification of the problem structure. This work evaluates a novel approach where a clustering algorithm plays a central role in the evolutionary process beyond maintaining the diversity. Empirical evaluation and comparison show the effectiveness of this new approach when solving multimodal optimization problems.
Hierarchical decomposition enhances the optimization power of genetic algorithms. It helps genetic algorithms to decompose problems which are not fully decomposable in one single level. To accomplish hierarchical decomposition, one must ensure (1) proper decomposition at each level, (2) preservation of alternative promising subsolutions, and (3) efficient representation of a subsolution as one single variable in the higher level. This paper proposes a chromosome compression scheme which represents subsolutions by the most expressive schemata. The pro- posed chromosome compression scheme is then combined with the dependency structure matrix genetic algorithm and the restricted tournament replacement to create a scalable optimization tool which optimizes problems via hierarchical decomposition. One important feature of the proposed method is that at the end of the run, the problem structure obtained from the pro- posed method is comprehensible to human researchers and is reusable for larger scale problems. The empirical result shows that the proposed method scales sub-quadratically on hierarchical problems and is able to capture the problem structures accurately.
In typical applications, genetic algorithms (GAs) process populations of potential problem solutions to evolve a single population member that specifies an "optimized" solution. The majority of GA analysis has focused on these optimization applications. In other applications (notably learning classifier systems and certain connectionist learning systems), a GA searches for a population of cooperative structures that jointly perform a computational task. This paper presents an analysis of this type of GA problem. The analysis considers a simplified genetics-based machine learning system: a model of an immune system. In this model, a GA must discover a set of pattern-matching antibodies that effectively match a set of antigen patterns. Analysis shows how a GA can automatically evolve and sustain a diverse, cooperative population. The cooperation emerges as a natural part of the antigen-antibody matching procedure. This emergent effect is shown to be similar to fitness sharing, ...