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This letter discusses the recent paper "Some technical remarks on the proof of the 'No Free Lunch' theorem." In that paper, some technical issues related to the formal proof of the no free lunch (NFL) theorem for search were given by Wolpert and Macready (1995 and 1997). As a result of a discussion among the authors, this letter explores the issues raised in that paper more thoroughly. This includes the presentation of a simpler version of the NFL proof in accord with a suggestion made explicitly by Köppen (2000) and implicitly by Wolpert and Macready (1997). It also includes the correction of an incorrect claim made by Köppen (2000) of a limitation of the NFL theorem. Finally, some thoughts on future research directions for research into algorithm performance are given. [ABSTRACT FROM AUTHOR]

RNA inverse folding problem is a bioinformatics problem where the objective is to find an RNA sequence that folds into a given target secondary structure. In this paper, we use evolutionary computation to solve a new and innovative multiobjective definition of this problem. In this new multiobjective definition of the problem, we have considered the similarity between target and predicted structures as a constraint, and three objective functions: 1) partition function (free energy of the ensemble); 2) ensemble diversity; and 3) nucleotides composition. The multiobjective metaheuristic to design RNA sequences (m2dRNAs) proposed in this paper is compared against other RNA inverse folding methods published in the literature, such as RNAinverse, RNA secondary structure designer, inverse folding of RNA, MODENA, NUPACK, fRNAkenstein, dynamics in sequence space optimization, RNAiFOLD, antaRNA, evolutionary RNA design, and Eterna players. After a comprehensive comparative study on two well-known benchmarks (Rfam and Eterna100), we conclude that m2dRNAs is capable of obtaining very promising results in terms of both quality of RNA designs and required runtime. The source code of m2dRNAs is available at http://arco.unex.es/arl/m2dRNAs-source_code.zip. [ABSTRACT FROM AUTHOR]

Engineering optimization problems usually involve computationally expensive simulations and many design variables. Solving such problems in an efficient manner is still a major challenge. In this paper, a generalized surrogate-assisted evolutionary algorithm is proposed to solve such high-dimensional expensive problems. The proposed algorithm is based on the optimization framework of the genetic algorithm (GA). This algorithm proposes to use a surrogate-based trust region local search method, a surrogate-guided GA (SGA) updating mechanism with a neighbor region partition strategy and a prescreening strategy based on the expected improvement infilling criterion of a simplified Kriging in the optimization process. The SGA updating mechanism is a special characteristic of the proposed algorithm. This mechanism makes a fusion between surrogates and the evolutionary algorithm. The neighbor region partition strategy effectively retains the diversity of the population. Moreover, multiple surrogates used in the SGA updating mechanism make the proposed algorithm optimize robustly. The proposed algorithm is validated by testing several high-dimensional numerical benchmark problems with dimensions varying from 30 to 100, and an overall comparison is made between the proposed algorithm and other optimization algorithms. The results show that the proposed algorithm is very efficient and promising for optimizing high-dimensional expensive problems. [ABSTRACT FROM AUTHOR]

Classification algorithms can suffer from performance degradation when the class distribution is unbalanced. This paper develops a two-step approach to evolving ensembles using genetic programming (GP) for unbalanced data. The first step uses multiobjective (MO) GP to evolve a Pareto-approximated front of GP classifiers to form the ensemble by trading-off the minority and the majority class against each other during learning. The MO component alleviates the reliance on sampling to artificially rebalance the data. The second step, which is the focus this paper, proposes a novel ensemble selection approach using GP to automatically find/choose the best individuals for the ensemble. This new GP approach combines multiple Pareto-approximated front members into a single composite genetic program solution to represent the (optimized) ensemble. This ensemble representation has two main advantages/novelties over traditional genetic algorithm (GA) approaches. First, by limiting the depth of the composite solution trees, we use selection pressure during evolution to find small highly-cooperative groups of individuals for the ensemble. This means that ensemble sizes are not fixed a priori (as in GA), but vary depending on the strength of the base learners. Second, we compare different function set operators in the composite solution trees to explore new ways to aggregate the member outputs and thus, control how the ensemble computes its output. We show that the proposed GP approach evolves smaller more diverse ensembles compared to an established ensemble selection algorithm, while still performing as well as, or better than the established approach. The evolved GP ensembles also perform well compared to other bagging and boosting approaches, particularly on tasks with high levels of class imbalance. [ABSTRACT FROM AUTHOR]

Recently, a number of high performance many-objective evolutionary algorithms with systematically generated weight vectors have been proposed in the literature. Those algorithms often show surprisingly good performance on widely used DTLZ and WFG test problems. The performance of those algorithms has continued to be improved. The aim of this paper is to show our concern that such a performance improvement race may lead to the overspecialization of developed algorithms for the frequently used many-objective test problems. In this paper, we first explain the DTLZ and WFG test problems. Next, we explain many-objective evolutionary algorithms characterized by the use of systematically generated weight vectors. Then we discuss the relation between the features of the test problems and the search mechanisms of weight vector-based algorithms such as multiobjective evolutionary algorithm based on decomposition (MOEA/D), nondominated sorting genetic algorithm III (NSGA-III), MOEA/dominance and decomposition (MOEA/DD), and $\theta $ -dominance based evolutionary algorithm ( $\theta$ -DEA). Through computational experiments, we demonstrate that a slight change in the problem formulations of DTLZ and WFG deteriorates the performance of those algorithms. After explaining the reason for the performance deterioration, we discuss the necessity of more general test problems and more flexible algorithms. [ABSTRACT FROM AUTHOR]

Convergence and diversity are interdependently handled during the evolutionary process by most existing many-objective evolutionary algorithms (MaOEAs). In such a design, the degraded performance of one would deteriorate the other, and only solutions with both are able to improve the performance of MaOEAs. Unfortunately, it is not easy to constantly maintain a population of solutions with both convergence and diversity. In this paper, an MaOEA based on two independent stages is proposed for effectively solving many-objective optimization problems (MaOPs), where the convergence and diversity are addressed in two independent and sequential stages. To achieve this, we first propose a nondominated dynamic weight aggregation method by using a genetic algorithm, which is capable of finding the Pareto-optimal solutions for MaOPs with concave, convex, linear and even mixed Pareto front shapes, and then these solutions are employed to learn the Pareto-optimal subspace for the convergence. Afterward, the diversity is addressed by solving a set of single-objective optimization problems with reference lines within the learned Pareto-optimal subspace. To evaluate the performance of the proposed algorithm, a series of experiments are conducted against six state-of-the-art MaOEAs on benchmark test problems. The results show the significantly improved performance of the proposed algorithm over the peer competitors. In addition, the proposed algorithm can focus directly on a chosen part of the objective space if the preference area is known beforehand. Furthermore, the proposed algorithm can also be used to effectively find the nadir points. [ABSTRACT FROM AUTHOR]

Among the different scientific domains where metaheuristics find applicability, bioinformatics represents a particularly challenging field due to the multiple complexity factors involved in the processing of biological data. In this context, the exploration of protein sequence data is remarkably increasing the temporal demands of such biological problems, thus motivating the interest in investigating new approaches that effectively combine bioinspired metaheuristics and parallelism. This paper addresses the reconstruction of ancestral relationships from amino acid sequences by using a multiobjective approach based on the shuffled frog-leaping optimization technique. Due to the inherent parallel nature of this approach, we define different parallel schemes aimed at exploiting the computing capabilities of modern cluster platforms. The experiments performed in five real datasets give account of the relevance of using parallelism-aware metaheuristic designs, as well as the need to consider both parallel performance and solution quality when tackling such difficult optimization scenarios. [ABSTRACT FROM AUTHOR]

Over the last 25 years, the multiple sequence alignment (MSA) problem has attracted the attention of biologists because it is one of the major techniques used in several areas of computational biology, such as homology searches, genomic annotation, protein structure prediction, gene regulation networks, or functional genomics. This problem implicates the alignment of more than two biological sequences, and is considered as a nondeterministic polynomial time optimization problem. In this paper, we find a number of different approaches for dealing with this biological sequence alignment problem. Basically, we distinguish six main groups: 1) exact methods; 2) progressive methods; 3) consistency-based methods; 4) iterative methods; 5) evolutionary algorithms; and 6) structure-based methods. In this paper, we propose the use of evolutionary computation and multiobjective optimization for solving this bioinformatics problem. A multiobjective version of a memetic metaheuristic is presented: hybrid multiobjective metaheuristics for MSA. In order to prove the effectiveness of the new proposal, we use three structure-based benchmarks created by using empirical data as input. The results obtained by our method are compared with well-known methods published in this paper, concluding that the new approach presents remarkable accuracy when dealing with sets of sequences with a low sequence similarity, the most frequent ones in real world. [ABSTRACT FROM AUTHOR]

This paper proposes a new multiobjective evolutionary algorithm for handling the problem of distribution network restoration after failures. The problem is formulated as a bi-objective optimization problem considering the total load restored and the time required for restoration. A new encoding scheme is proposed, in which the variables that encode the switch operation are separated into six groups, according to their roles in the faulty system configuration. Employing the idea of defining subspaces of a combinatorial space, those groups are used in order to define subpermutations within which the crossover and mutation operations are performed. In this way, the dimensionality of the search space becomes reduced, allowing a much more efficient search. The proposed encoding scheme also makes a single individual to encode several different solutions, leading to a further reduction of the search space dimensionality. Due to this peculiar feature of the encoding scheme, it becomes convenient to use an adaptation of the Strength Pareto Evolutionary Algorithm 2, in which the raw fitness is modified in order to allow the assignment of fitness to individuals that simultaneously encode several different solutions. The proposed algorithm was implemented such that good solutions are delivered within low processing times, of the order of some minutes for large real systems. [ABSTRACT FROM PUBLISHER]

The design of evolutionary algorithms has typically been focused on efficiently solving a single optimization problem at a time. Despite the implicit parallelism of population-based search, no attempt has yet been made to multitask, i.e., to solve multiple optimization problems simultaneously using a single population of evolving individuals. Accordingly, this paper introduces evolutionary multitasking as a new paradigm in the field of optimization and evolutionary computation. We first formalize the concept of evolutionary multitasking and then propose an algorithm to handle such problems. The methodology is inspired by biocultural models of multifactorial inheritance, which explain the transmission of complex developmental traits to offspring through the interactions of genetic and cultural factors. Furthermore, we develop a cross-domain optimization platform that allows one to solve diverse problems concurrently. The numerical experiments reveal several potential advantages of implicit genetic transfer in a multitasking environment. Most notably, we discover that the creation and transfer of refined genetic material can often lead to accelerated convergence for a variety of complex optimization functions. [ABSTRACT FROM PUBLISHER]

Financial ratios are key constituents of bankruptcy models. The bankruptcy prediction accuracy substantially improves when a limited number of ratios are used. From the literature, it has been found that human expertise has been applied to select financial ratios for bankruptcy models. Different experts tend to have different opinions and hence the bankruptcy prediction results depend upon their competency levels in that domain. Accordingly, there is a need for finding a systematic method or a tool to identify the influencing ratios. This paper develops a genetic bankrupt ratio analysis tool using a genetic algorithm to identify influencing ratios from different bankruptcy models and their influences in a quantitative form. The accuracy of values of influencing ratios is validated by comparing original threshold value of the bankruptcy models. The performance of influencing ratios has been compared with other feature selection techniques and the Altman model is considered to explain the effect of the influencing ratios. [ABSTRACT FROM PUBLISHER]

Artificial gene regulatory networks (GRNs) are biologically inspired dynamical systems used to control various kinds of agents, from the cells in developmental models to embodied robot swarms. Most recent work uses a genetic algorithm (GA) or an evolution strategy in order to optimize the network for a specific task. However, the empirical performances of these algorithms are unsatisfactory. This paper presents an algorithm that primarily exploits a network distance metric, which allows genetic similarity to be used for speciation and variation of GRNs. This algorithm, inspired by the successful neuroevolution of augmenting topologies algorithm’s use in evolving neural networks and compositional pattern-producing networks, is based on a specific initialization method, a crossover operator based on gene alignment, and speciation based upon GRN structures. We demonstrate the effectiveness of this new algorithm by comparing our approach both to a standard GA and to evolutionary programming on four different experiments from three distinct problem domains, where the proposed algorithm excels on all experiments. [ABSTRACT FROM AUTHOR]

The NK hybrid genetic algorithm (GA) for clustering is proposed in this paper. In order to evaluate the solutions, the hybrid algorithm uses the NK clustering validation criterion 2 (NKCV2). NKCV2 uses information about the disposition of ${N}$ small groups of objects. Each group is composed of ${K+1}$ objects of the dataset. Experimental results show that density-based regions can be identified by using NKCV2 with fixed small ${K}$. In NKCV2, the relationship between decision variables is known, which in turn allows us to apply gray box optimization. Mutation operators, a partition crossover (PX), and a local search strategy are proposed, all using information about the relationship between decision variables. In PX, the evaluation function is decomposed into ${q}$ independent components; PX then deterministically returns the best among ${2^{q}}$ possible offspring with computational complexity ${O(N)}$. The NK hybrid GA allows the detection of clusters with arbitrary shapes and the automatic estimation of the number of clusters. In the experiments, the NK hybrid GA produced very good results when compared to another GA approach and to state-of-art clustering algorithms. [ABSTRACT FROM AUTHOR]

Evolutionary paradigms have been successfully applied to neural network designs for two decades. Unfortunately, these methods cannot scale well to the modern deep neural networks due to the complicated architectures and large quantities of connection weights. In this paper, we propose a new method using genetic algorithms for evolving the architectures and connection weight initialization values of a deep convolutional neural network to address image classification problems. In the proposed algorithm, an efficient variable-length gene encoding strategy is designed to represent the different building blocks and the potentially optimal depth in convolutional neural networks. In addition, a new representation scheme is developed for effectively initializing connection weights of deep convolutional neural networks, which is expected to avoid networks getting stuck into local minimum that is typically a major issue in the backward gradient-based optimization. Furthermore, a novel fitness evaluation method is proposed to speed up the heuristic search with substantially less computational resource. The proposed algorithm is examined and compared with 22 existing algorithms on nine widely used image classification tasks, including the state-of-the-art methods. The experimental results demonstrate the remarkable superiority of the proposed algorithm over the state-of-the-art designs in terms of classification error rate and the number of parameters (weights). [ABSTRACT FROM AUTHOR]

It is our pleasure to introduce this special issue on the recent advances in the theoretical foundations of evolutionary computation (EC). While in the early days of this field, theoretical analyses inevitably focused on simplified models of evolutionary algorithms (EAs), the continuous progress made in the development of suitable mathematical techniques for the analysis now allows to derive proven statements regarding the performance of off-the-shelf metaheuristics, such as standard generational and steady-state genetic algorithms with no algorithmic simplifications. Comparisons between the performance of a given EA with the best possible one can also be made nowadays, allowing to assess whether a given algorithm may be improved upon or whether its performance is optimal for a given class of problems. Such understanding often provides insights for the design of new EAs which provably have better performance for given problems. We are glad that examples of results of this kind are present within this special issue. A total of 27 papers were submitted which were the subject of at least three independent reviews, and six manuscripts of the highest quality were selected for publication in the special issue. In the following, we provide a brief summary of these manuscripts. [ABSTRACT FROM AUTHOR]

Designing effective dispatching rules is an important factor for many manufacturing systems. However, this time-consuming process has been performed manually for a very long time. Recently, some machine learning approaches have been proposed to support this task. In this paper, we investigate the use of genetic programming for automatically discovering new dispatching rules for the single objective job shop scheduling problem (JSP). Different representations of the dispatching rules in the literature are newly proposed in this paper and are compared and analysed. Experimental results show that the representation that integrates system and machine attributes can improve the quality of the evolved rules. Analysis of the evolved rules also provides useful knowledge about how these rules can effectively solve JSP. [ABSTRACT FROM AUTHOR]

The first cooperative co-evolutionary algorithm (CCEA) was proposed by Potter and De Jong in 1994 and since then many CCEAs have been proposed and successfully applied to solving various complex optimization problems. In applying CCEAs, the complex optimization problem is decomposed into multiple subproblems, and each subproblem is solved with a separate subpopulation, evolved by an individual evolutionary algorithm (EA). Through cooperative co-evolution of multiple EA subpopulations, a complete problem solution is acquired by assembling the representative members from each subpopulation. The underlying divide-and-conquer and collaboration mechanisms enable CCEAs to tackle complex optimization problems efficiently, and hence CCEAs have been attracting wide attention in the EA community. This paper presents a comprehensive survey of these CCEAs, covering problem decomposition, collaborator selection, individual fitness evaluation, subproblem resource allocation, implementations, benchmark test problems, control parameters, theoretical analyses, and applications. The unsolved challenges and potential directions for their solutions are discussed. [ABSTRACT FROM AUTHOR]

Bilevel optimization refers to a challenging optimization problem which contains two levels of optimization problems. The task of bilevel optimization is to find the optimum of the upper-level problem, subject to the optimality of the corresponding lower-level problem. This nested nature introduces many difficulties such as nonconvexity and disconnectedness, and poses great challenges to traditional optimization methods. Using evolutionary algorithms in bilevel optimization has been demonstrated to be very promising in recent years. However, these algorithms suffer from low efficiency since they usually require a huge number of function evaluations. This paper proposes a bilevel covariance matrix adaptation evolution strategy to handle bilevel optimization problems. A search distribution sharing mechanism is designed so that we can extract a priori knowledge of the lower-level problem from the upper-level optimizer, which significantly reduces the number of function evaluations. We also propose a refinement-based elite preservation mechanism to trace the elite and avoid inaccurate solutions. Comparisons with five state-of-the-art algorithms on 22 benchmark problems and two real-world applications are carried out to test the performance of the proposed approach. The experimental results have shown the effectiveness of the proposed approach in keeping a good tradeoff between solution quality and computational efficiency. [ABSTRACT FROM AUTHOR]

In most real-world settings, designs are often gradually adapted and improved over time. Consequently, there exists knowledge from distinct (but possibly related) design exercises, which have either been previously completed or are currently in-progress, that may be leveraged to enhance the optimization performance of a particular target optimization task of interest. Further, it is observed that modern day design cycles are typically distributed in nature, and consist of multiple teams working on associated ideas in tandem. In such environments, vast amounts of related information can become available at various stages of the search process corresponding to some ongoing target optimization exercise. Successfully exploiting this knowledge is expected to be of significant value in many practical settings, where solving an optimization problem from scratch may be exorbitantly costly or time consuming. Accordingly, in this paper, we propose an adaptive knowledge reuse framework for surrogate-assisted multiobjective optimization of computationally expensive problems, based on the novel idea of multiproblem surrogates. This idea provides the capability to acquire and spontaneously transfer learned models across problems, facilitating efficient global optimization. The efficacy of our proposition is demonstrated on a series of synthetic benchmark functions, as well as two practical case studies. [ABSTRACT FROM AUTHOR]

This paper proposes a novel procedure for generating parametric scalable functions with diverse properties to strengthen numerical evaluation of niching methods. It combines three simple basic functions to form a composite multimodal function, in which the function parameter controls the number of global minima. The resultant composite function may show a variety of challenges in global optimization such as high condition, correlation, and presence of many undesirable local minima, as well as those peculiar to multimodal optimization, such as nonuniformly distributed global minima with dissimilar basin sizes. Moreover, the proposed procedure results in computationally inexpensive composite functions, when compared to those generated by available methods. This allows for benchmarking long-term success of niching methods on problems with many global minima. Six parametric benchmark functions are proposed in which the function parameter controls the number of global minima. Detailed analysis on distribution, basin shapes and sizes of the global minima is provided. One of the proposed test problems involve constraints, a matter which did not receive much attention in the past. These test functions are employed to compare some of the most successful niching methods in the literature. The numerical results disclose a drastic disparity between the performance of different niching methods on the composite functions and the existing test problems, demonstrating that the proposed composite functions simulate distinct challenges. Our findings highlight importance of the core search algorithm and challenge suitability of many niching strategies in more complicated landscapes and higher dimensions. [ABSTRACT FROM AUTHOR]

The zero-intelligence plus (ZIP) adaptive automated trading algorithm has been demonstrated to outperform human traders in experimental studies of continuous double auction (CDA) markets populated by mixtures of human and "software robot" traders. Previous papers have shown that values of the eight parameters governing behavior of ZIP traders can be automatically optimized using a genetic algorithm (GA), and that markets populated by GA-optimized traders perform better than those populated by ZIP traders with manually set parameter values. This paper introduces a more sophisticated version of the ZIP algorithm, called "ZIP60," which requires the values of 60 parameters to be set correctly. ZIP60 is shown here to produce significantly better results in comparison to the original ZIP algorithm (called "ZIP8" hereafter) when a GA is used to search the 60-dimensional parameter space. It is also demonstrated here that this works best when the GA itself has control over the dimensionality of the search-space, allowing evolution to guide the expansion of the search-space up from 8 parameters to 60 via intermediate steps. Principal component analysis of the best evolved ZIP60 parameter-sets establishes that no ZIP8 solutions are embedded in the 60-dimensional space. Moreover, some of the results and analysis presented here cast doubt on previously published ZIP8 results concerning the evolution of new "hybrid" auction mechanisms that appeared to be improvements on the CDA: it now seems likely that those results were actually consequences of the relative lack of sophistication in the original ZIP8 algorithm, because "hybrid" mechanisms occur much less frequently when ZIP60s are used. [ABSTRACT FROM AUTHOR]

This paper discusses a special technique, called conditionally matching rules (CMRs), for the representation of transition functions of cellular automata (CA) and its application to the evolutionary design of complex multistate CA. The problem of designing replicating loops in 2-D CA and the square calculation in 1-D CA will be treated as case studies. It will be shown that the evolutionary algorithm in combination with CMRs is able to successfully solve these tasks and provide some innovative results compared to existing solutions. In particular, a novel replication scheme will be presented that exhibits a higher replication speed in comparison with the existing replicating loops. As regards the square calculation, some results have been obtained that allow a substantial reduction of the number of steps of the cellular automaton against the currently known solution. The utilization of the CMRs in the proposed experiments represents the first case of a successful automatic evolutionary design of complex CA for solving nontrivial problems in which the existing conventional approaches have failed. [ABSTRACT FROM PUBLISHER]

Natural ecosystems exhibit complex dynamics of interacting species. Man-made ecosystems exhibit similar dynamics and, in the case of mobile app stores, can be said to perform optimization as developers seek to maximize app downloads. This work aims to understand stability and instability within app store dynamics and how it affects fitness. The investigation is carried out with AppEco, a model of the iOS App Store, which was extended for this paper and updated to model the store from 2008 to 2014. AppEco models apps containing features, developers who build the apps, users who download apps according to their preferences, and an app store that presents apps to the users. It also models developers who use commonly observed strategies to build their apps: innovator, milker, optimizer, copycat, and flexible (the ability to choose any strategy). Results show that despite the success of the copycat strategy, there is a clear stable state for low proportion of copycats in developer populations, mirroring results in theoretical biology for producer–scrounger systems. The results also show that the best fitness is achieved when the evolutionary optimizer (as producer) and copycat (as scrounger) strategies coexist together in stable proportions. [ABSTRACT FROM PUBLISHER]

State-of-the-art multiobjective evolutionary algorithms (MOEAs) treat all the decision variables as a whole to optimize performance. Inspired by the cooperative coevolution and linkage learning methods in the field of single objective optimization, it is interesting to decompose a difficult high-dimensional problem into a set of simpler and low-dimensional subproblems that are easier to solve. However, with no prior knowledge about the objective function, it is not clear how to decompose the objective function. Moreover, it is difficult to use such a decomposition method to solve multiobjective optimization problems (MOPs) because their objective functions are commonly conflicting with one another. That is to say, changing decision variables will generate incomparable solutions. This paper introduces interdependence variable analysis and control variable analysis to deal with the above two difficulties. Thereby, an MOEA based on decision variable analyses (DVAs) is proposed in this paper. Control variable analysis is used to recognize the conflicts among objective functions. More specifically, which variables affect the diversity of generated solutions and which variables play an important role in the convergence of population. Based on learned variable linkages, interdependence variable analysis decomposes decision variables into a set of low-dimensional subcomponents. The empirical studies show that DVA can improve the solution quality on most difficult MOPs. The code and supplementary material of the proposed algorithm are available at http://web.xidian.edu.cn/fliu/paper.html. [ABSTRACT FROM PUBLISHER]

Hyper-heuristics have recently emerged as a powerful approach to automate the design of heuristics for a number of different problems. Production scheduling is a particularly popular application area for which a number of different hyper-heuristics have been developed and are shown to be effective, efficient, easy to implement, and reusable in different shop conditions. In particular, they seem to be a promising way to tackle highly dynamic and stochastic scheduling problems, an aspect that is specifically emphasized in this survey. Despite their success and the substantial number of papers in this area, there is currently no systematic discussion of the design choices and critical issues involved in the process of developing such approaches. This paper strives to fill this gap by summarizing the state-of-the-art approaches, suggesting a taxonomy, and providing the interested researchers and practitioners with guidelines for the design of hyper-heuristics in production scheduling. This paper also identifies challenges and open questions and highlights various directions for future work. [ABSTRACT FROM PUBLISHER]

Meta-heuristic algorithms are often inspired by natural phenomena, including the evolution of species in Darwinian natural selection theory, ant behaviors in biology, flock behaviors of some birds, and annealing in metallurgy. Due to their great potential in solving difficult optimization problems, meta-heuristic algorithms have found their way into automobile engine design. There are different optimization problems arising in different areas of car engine management including calibration, control system, fault diagnosis, and modeling. In this paper we review the state-of-the-art applications of different meta-heuristic algorithms in engine management systems. The review covers a wide range of research, including the application of meta-heuristic algorithms in engine calibration, optimizing engine control systems, engine fault diagnosis, and optimizing different parts of engines and modeling. The meta-heuristic algorithms reviewed in this paper include evolutionary algorithms, evolution strategy, evolutionary programming, genetic programming, differential evolution, estimation of distribution algorithm, ant colony optimization, particle swarm optimization, memetic algorithms, and artificial immune system. [ABSTRACT FROM PUBLISHER]

The encoding or representation scheme in evolutionary algorithms is very important because it can greatly affect their performance. Most previous evolutionary algorithms for solving graph problems have traditionally used a vertex-based encoding in which each gene corresponds to a vertex. In this paper, addressing the well-known maximum cut problem, we introduce an edge-set encoding based on the spanning tree—a kind of edge-based encoding. In our encoding scheme, each gene corresponds to an edge subset derived from a spanning tree. In contrast to a traditional edge-based encoding in which each gene corresponds to only one edge, our encoding scheme has the advantage of representing only feasible solutions, so there is no need to apply a repair step. We present a genetic algorithm based on this new encoding. We have conducted various experiments on a large set of test graphs including commonly used benchmark graphs and have obtained performance improvement on sparse graphs, which frequently appear in real-world applications such as social networks and systems biology, in comparison with a scheme using a vertex-based encoding. [ABSTRACT FROM PUBLISHER]

Nonlinear equation systems may have multiple optimal solutions. The main task of solving nonlinear equation systems is to simultaneously locate these optimal solutions in a single run. When solving nonlinear equation systems by evolutionary algorithms, usually a nonlinear equation system should be transformed into a kind of optimization problem. At present, various transformation techniques have been proposed. This paper presents a simple and generic transformation technique based on multiobjective optimization for nonlinear equation systems. Unlike the previous work, our transformation technique transforms a nonlinear equation system into a biobjective optimization problem that can be decomposed into two parts. The advantages of our transformation technique are twofold: 1) all the optimal solutions of a nonlinear equation system are the Pareto optimal solutions of the transformed problem, which are mapped into diverse points in the objective space, and 2) multiobjective evolutionary algorithms can be directly applied to handle the transformed problem. In order to verify the effectiveness of our transformation technique, it has been integrated with nondominated sorting genetic algorithm II to solve nonlinear equation systems. The experimental results have demonstrated that, overall, our transformation technique outperforms another state-of-the-art multiobjective optimization based transformation technique and four single-objective optimization based approaches on a set of test instances. The influence of the types of Pareto front on the performance of our transformation technique has been investigated empirically. Moreover, the limitation of our transformation technique has also been identified and discussed in this paper. [ABSTRACT FROM AUTHOR]

In this paper, a new multiobjective optimization framework based on nondominated sorting and local search (NSLS) is introduced. The NSLS is based on iterations. At each iteration, given a population P , a simple local search method is used to get a better population P' , and then the nondominated sorting is adopted on P \cup P' to obtain a new population for the next iteration. Furthermore, the farthest-candidate approach is combined with the nondominated sorting to choose the new population for improving the diversity. Additionally, another version of NSLS (NSLS-C) is used for comparison, which replaces the farthest-candidate method with the crowded comparison mechanism presented in the nondominated sorting genetic algorithm II (NSGA-II). The proposed method (NSLS) is compared with NSLS-C and the other three classic algorithms: NSGA-II, MOEA/D-DE, and MODEA on a set of seventeen bi-objective and three tri-objective test problems. The experimental results indicate that the proposed NSLS is able to find a better spread of solutions and a better convergence to the true Pareto-optimal front compared to the other four algorithms. Furthermore, the sensitivity of NSLS is also experimentally investigated in this paper. [ABSTRACT FROM AUTHOR]

One of the major distinguishing features of the dynamic multiobjective optimization problems (DMOPs) is that optimization objectives will change over time, thus tracking the varying Pareto-optimal front becomes a challenge. One of the promising solutions is reusing “experiences” to construct a prediction model via statistical machine learning approaches. However, most existing methods neglect the nonindependent and identically distributed nature of data to construct the prediction model. In this paper, we propose an algorithmic framework, called transfer learning-based dynamic multiobjective evolutionary algorithm (EA), which integrates transfer learning and population-based EAs to solve the DMOPs. This approach exploits the transfer learning technique as a tool to generate an effective initial population pool via reusing past experience to speed up the evolutionary process, and at the same time any population-based multiobjective algorithms can benefit from this integration without any extensive modifications. To verify this idea, we incorporate the proposed approach into the development of three well-known EAs, nondominated sorting genetic algorithm II, multiobjective particle swarm optimization, and the regularity model-based multiobjective estimation of distribution algorithm. We employ 12 benchmark functions to test these algorithms as well as compare them with some chosen state-of-the-art designs. The experimental results confirm the effectiveness of the proposed design for DMOPs. [ABSTRACT FROM AUTHOR]

Determining the Nash equilibria (NEs) in a competitive electricity market is a challenging economic game problem. Although finding one equilibrium has been well studied, detecting multiple ones is more practical and difficult, with a few attempts to solve such discrete game problems. However, most of the real-life game problems, such an energy market is a continuous one containing infinite sets of strategy that can be adopted by each player. Therefore, in this paper, a co-evolutionary approach is proposed for detecting multiple NEs in a single run involving continuous games among ${N}$ -players. Five standard test functions and three IEEE energy market problems in three different scenarios are solved, and their results are compared with those obtained from state-of-the-art algorithms. The results clearly show the benefits of the proposed approach in terms of both the quality of solutions and efficiency. [ABSTRACT FROM AUTHOR]

In today’s world, the interconnections among objects in many domains are often modeled as networks, with nodes representing the objects and edges the existing relationships among them. A key feature of complex networks is the tendency of entities to group together to form communities. The detection of communities has been receiving a great deal of interest by researchers. In fact, the knowledge of how objects organize allows a better understanding of a network, and gives a deeper insight of interesting characteristics, that could not be caught if considering the network as a whole. In the last decade, evolutionary computation techniques have given a significant contribution in this context. The aim of this paper is to present the approaches based on evolutionary computation to uncover community structure. Especially, the representation schemes with the genetic operators apt for them are described, and the most popular fitness functions employed by the methods are discussed. The survey covers the most recent proposals optimizing either a single objective or multiple objectives for different types of network models, such as signed, dynamic, and multidimensional. [ABSTRACT FROM AUTHOR]

Interval many-objective optimization problems (IMaOPs), involving more than three objectives and at least one subjected to interval uncertainty, are ubiquitous in real-world applications. However, there have been very few effective methods for solving these problems. In this paper, we proposed a set-based genetic algorithm to effectively solve them. The original optimization problem was first transformed into a deterministic bi-objective problem, where new objectives are hyper-volume and imprecision. A set-based Pareto dominance relation was then defined to modify the fast nondominated sorting approach in NSGA-II. Additionally, set-based evolutionary schemes were suggested. Finally, our method was empirically evaluated on 39 benchmark IMaOPs as well as a car cab design problem and compared with two typical methods. The numerical results demonstrated the superiority of our method and indicated that a tradeoff approximate front between convergence and uncertainty can be produced. [ABSTRACT FROM PUBLISHER]

Virtual machine placement (VMP) and energy efficiency are significant topics in cloud computing research. In this paper, evolutionary computing is applied to VMP to minimize the number of active physical servers, so as to schedule underutilized servers to save energy. Inspired by the promising performance of the ant colony system (ACS) algorithm for combinatorial problems, an ACS-based approach is developed to achieve the VMP goal. Coupled with order exchange and migration (OEM) local search techniques, the resultant algorithm is termed an OEMACS. It effectively minimizes the number of active servers used for the assignment of virtual machines (VMs) from a global optimization perspective through a novel strategy for pheromone deposition which guides the artificial ants toward promising solutions that group candidate VMs together. The OEMACS is applied to a variety of VMP problems with differing VM sizes in cloud environments of homogenous and heterogeneous servers. The results show that the OEMACS generally outperforms conventional heuristic and other evolutionary-based approaches, especially on VMP with bottleneck resource characteristics, and offers significant savings of energy and more efficient use of different resources. [ABSTRACT FROM PUBLISHER]

Decomposition via scalarization is a basic concept for multiobjective optimization. The weighted sum (WS) method, a frequently used scalarizing method in decomposition-based evolutionary multiobjective (EMO) algorithms, has good features such as computationally easy and high search efficiency, compared to other scalarizing methods. However, it is often criticized by the loss of effect on nonconvex problems. This paper seeks to utilize advantages of the WS method, without suffering from its disadvantage, to solve many-objective problems. A novel decomposition-based EMO algorithm called multiobjective evolutionary algorithm based on decomposition LWS (MOEA/D-LWS) is proposed in which the WS method is applied in a local manner. That is, for each search direction, the optimal solution is selected only amongst its neighboring solutions. The neighborhood is defined using a hypercone. The apex angle of a hypervcone is determined automatically in a priori. The effectiveness of MOEA/D-LWS is demonstrated by comparing it against three variants of MOEA/D, i.e., MOEA/D using Chebyshev method, MOEA/D with an adaptive use of WS and Chebyshev method, MOEA/D with a simultaneous use of WS and Chebyshev method, and four state-of-the-art many-objective EMO algorithms, i.e., preference-inspired co-evolutionary algorithm, hypervolume-based evolutionary, \boldsymbol \theta -dominance-based algorithm, and SPEA2+SDE for the WFG benchmark problems with up to seven conflicting objectives. Experimental results show that MOEA/D-LWS outperforms the comparison algorithms for most of test problems, and is a competitive algorithm for many-objective optimization. [ABSTRACT FROM PUBLISHER]

Given a multivariate time series, possibly of high dimension, with unknown and time-varying joint distribution, it is of interest to be able to completely partition the time series into disjoint, contiguous subseries, each of which has different distributional or pattern attributes from the preceding and succeeding subseries. An additional feature of many time series is that they display self-affinity, so that subseries at one time scale are similar to subseries at another after application of an affine transformation. Such qualities are observed in time series from many disciplines, including biology, medicine, economics, finance, and computer science. This paper defines the relevant multiobjective combinatorial optimization problem with limited assumptions as a biobjective one, and a specialized evolutionary algorithm is presented which finds optimal self-affine time series partitionings with a minimum of choice parameters. The algorithm not only finds partitionings for all possible numbers of partitions given data constraints, but also for self-affinities between these partitionings and some fine-grained partitioning. The resulting set of Pareto-efficient solution sets provides a rich representation of the self-affine properties of a multivariate time series at different locations and time scales. [ABSTRACT FROM PUBLISHER]

In recent years, numerous studies have drawn the success of estimation of distribution algorithms (EDAs) to avoid the frequent breakage of building blocks of the conventional stochastic genetic operators-based evolutionary algorithms (EAs). In this paper, a novel graph-based EDA called probabilistic model building genetic network programming (PMBGNP) is proposed. Using the distinguished graph (network) structure of a graph-based EA called genetic network programming (GNP), PMBGNP ensures higher expression ability than the conventional EDAs to solve some specific problems. Furthermore, an extended algorithm called reinforced PMBGNP is proposed to combine PMBGNP and reinforcement learning to enhance the performance in terms of fitness values, search speed, and reliability. The proposed algorithms are applied to solve the problems of controlling the agents' behavior. Two problems are selected to demonstrate the effectiveness of the proposed algorithms, including the benchmark one, i.e., the Tileworld system, and a real mobile robot control. [ABSTRACT FROM PUBLISHER]

Practical optimization problems frequently include uncertainty about the quality measure, for example, due to noisy evaluations. Thus, they do not allow for a straightforward application of traditional optimization techniques. In these settings, randomized search heuristics such as evolutionary algorithms are a popular choice because they are often assumed to exhibit some kind of resistance to noise. Empirical evidence suggests that some algorithms, such as estimation of distribution algorithms (EDAs) are robust against a scaling of the noise intensity, even without resorting to explicit noise-handling techniques such as resampling. In this paper, we want to support such claims with mathematical rigor. We introduce the concept of graceful scaling in which the run time of an algorithm scales polynomially with noise intensity. We study a monotone fitness function over binary strings with additive noise taken from a Gaussian distribution. We show that myopic heuristics cannot efficiently optimize the function under arbitrarily intense noise without any explicit noise-handling. Furthermore, we prove that using a population does not help. Finally, we show that a simple EDA called the compact genetic algorithm can overcome the shortsightedness of mutation-only heuristics to scale gracefully with noise. We conjecture that recombinative genetic algorithms also have this property. [ABSTRACT FROM AUTHOR]

There are two main tasks involved in addressing a multiobjective optimization problem (MOP) by evolutionary multiobjective (EMO) algorithms: 1) make the population converge close to the Pareto-optimal front and 2) maintain adequate population diversity. However, most state-of-the-art EMO algorithms are designed based on the “convergence first and diversity second” principle. It has been observed that although these EMO algorithms have been successful in optimizing many real-world MOPs, they fail to solve certain problems that feature a severe imbalance between diversity preservation and achieving convergence. This paper characterizes an imbalanced MOP by clearly defining properties and indicating the reasons for the existing EMO algorithms’ difficulties in solving them. We then present 14 imbalanced problems, with and without constraints. Computational results using four existing EMO algorithms—elitist non-dominated sorting genetic algorithm (NSGA-II), multiobjective evolutionary algorithm based on decomposition (MOEA/D), strength Pareto evolutionary algorithm 2 (SPEA2), and S metric selection EMO algorithm (SMS-EMOA) and a proposed generalized vector-evaluated genetic algorithm are then presented. It is seen that these EMO algorithms cannot solve these imbalanced problems, but they are able to solve the problems when augmented by multiobjective to multiobjective (M2M), an approach that decomposes the population into several interacting subpopulations. These results and the successful application of the EMO methods with the M2M approach even on standard so-called balanced problems indicate the usefulness of using the M2M approach. [ABSTRACT FROM AUTHOR]

Factored evolutionary algorithms (FEAs) are a new class of evolutionary search-based optimization algorithms that have successfully been applied to various problems, such as training neural networks and performing abductive inference in graphical models. An FEA is unique in that it factors the objective function by creating overlapping subpopulations that optimize over a subset of variables of the function. In this paper, we give a formal definition of FEA algorithms and present empirical results related to their performance. One consideration in using an FEA is determining the appropriate factor architecture, which determines the set of variables each factor will optimize. For this reason, we present the results of experiments comparing the performance of different factor architectures on several standard applications for evolutionary algorithms. Additionally, we show that FEA’s performance is not restricted by the underlying optimization algorithm by creating FEA versions of hill climbing, particle swarm optimization, genetic algorithm, and differential evolution and comparing their performance to their single-population and cooperative coevolutionary counterparts. [ABSTRACT FROM AUTHOR]

The generalized quadratic multiple knapsack problem (GQMKP) extends the classical quadratic multiple knapsack problem with setups and knapsack preference of the items. The GQMKP can accommodate a number of real-life applications and is computationally difficult. In this paper, we demonstrate the interest of the memetic search approach for approximating the GQMKP by presenting a highly effective memetic algorithm (denoted by MAGQMK). The algorithm combines a backbone-based crossover operator (to generate offspring solutions) and a multineighborhood simulated annealing procedure (to find high quality local optima). To prevent premature convergence of the search, MAGQMK employs a quality-and-distance (QD) pool updating strategy. Extensive experiments on two sets of 96 benchmarks show a remarkable performance of the proposed approach. In particular, it discovers improved best solutions in 53 and matches the best known solutions for 39 other cases. A case study on a pseudo real-life problem demonstrates the efficacy of the proposed approach in practical situations. Additional analyses show the important contribution of the novel general-exchange neighborhood, the backbone-based crossover operator as well as the QD pool updating rule to the performance of the proposed algorithm. [ABSTRACT FROM PUBLISHER]

Railway timetable scheduling is a fundamental operational problem in the railway industry and has significant influence on the quality of service provided by the transport system. This paper explores the periodic railway timetable scheduling (PRTS) problem, with the objective to minimize the average waiting time of the transfer passengers. Unlike traditional PRTS models that only involve service lines with fixed cycles, this paper presents a more flexible model by allowing the cycle of service lines and the number of transfer passengers to vary with the time period. An enhanced differential evolution (DE) algorithm with dual populations, termed “dual-population DE” (DP-DE), was developed to solve the PRTS problem, yielding high-quality solutions. In the DP-DE, two populations cooperate during the evolution; the first focuses on global search by adopting parameter settings and operators that help maintain population diversity, while the second one focuses on speeding up convergence by adopting parameter settings and operators that are good for local fine tuning. A novel bidirectional migration operator is proposed to share the search experience between the two populations. The proposed DP-DE has been applied to optimize the timetable of the Guangzhou Metro system in Mainland China and six artificial periodic railway systems. Two conventional deterministic algorithms and seven highly regarded evolutionary algorithms are used for comparison. The comparison results reveal that the performance of DP-PE is very promising. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

To solve dynamic optimization problems, multiple population methods are used to enhance the population diversity for an algorithm with the aim of maintaining multiple populations in different subareas in the fitness landscape. Many experimental studies have shown that locating and tracking multiple relatively good optima rather than a single global optimum is an effective idea in dynamic environments. However, several challenges need to be addressed when multipopulation methods are applied, e.g., how to create multiple populations, how to maintain them in different subareas, and how to deal with the situation where changes cannot be detected or predicted. To address these issues, this paper investigates a hierarchical clustering method to locate and track multiple optima for dynamic optimization problems. To deal with undetectable dynamic environments, this paper applies the random immigrants method without change detection based on a mechanism that can automatically reduce redundant individuals in the search space throughout the run. These methods are implemented into several research areas, including particle swarm optimization, genetic algorithm, and differential evolution. An experimental study is conducted based on the moving peaks benchmark to test the performance with several other algorithms from the literature. The experimental results show the efficiency of the clustering method for locating and tracking multiple optima in comparison with other algorithms based on multipopulation methods on the moving peaks benchmark. [ABSTRACT FROM AUTHOR]

This paper presents a unique optimization method developed for landscape evolution problems. An existing hypothesis of the optimal channel network states that fluvial landscape evolution can be characterized as the procedure that follows minimum total energy expenditure. Previous studies have tested this hypothesis by solving an optimization problem, i.e., finding landscapes that satisfy the minimum total energy expenditure criterion, and showed that such optimized landscapes are similar to natural landscapes in many respects. These studies have approximated a 3-D landscape as a 2-D river network. While this network-based approach has greatly simplified the formulation of the optimization problem, this approximation limits the investigation of features such as longitudinal profiles, since their representation requires the gravitational direction-wise dimension. Here, an alternative technique is devised to fully handle the optimization of 3-D landforms over time. The proposed idea is to break down the time domain and to apply an optimization algorithm sequentially for discrete time steps. For the optimization part, a heuristic algorithm motivated from adaptation strategies of natural systems (here landscape formation) is used. This method is applied to a theoretical landscape with the condition that the balance between tectonic uplift and sediment lost is satisfied. It is found that landscapes of minimum total energy expenditure exhibit the Hack's law and the power-law in the exceedance probability distribution of drainage area, which are the characteristics found in natural river networks. However, they demonstrate no systematic pattern in longitudinal profiles. [ABSTRACT FROM PUBLISHER]

In this paper, the resource-constrained project scheduling problem with multiple execution modes for each activity is explored. This paper aims to find a schedule of activities such that the makespan of the schedule is minimized subject to the precedence and resource constraints. We present a two- " phase genetic local search algorithm that combines the genetic algorithm and the local search method to solve this problem. The first phase aims to search globally for promising areas, and the second phase aims to search more thoroughly in these promising areas. A set of elite solutions is collected during the first phase, and this set, which acts as the indication promising areas, is utilized to construct the initial population of the second phase. By suitable applications of the mutation with a large mutation rate, the restart of the genetic local search algorithm, and the collection of good solutions in the elite set, the strength of intensification and diversification can be properly adapted and the search ability retained in a long term. Computational experiments were conducted on the standard sets of project instances, and the experimental results revealed that the proposed algorithm was effective for both the short-term (with 5000 schedules being evaluated) and the long-term (with 50000 schedules being evaluated) search in solving this problem. [ABSTRACT FROM AUTHOR]

Student plagiarism is a major problem in universities worldwide. In this paper, we focus on plagiarism in answers to computer programming assignments, where students mix and/or modify one or more original solutions to obtain counterfeits. Although several software tools have been developed to help the tedious and time consuming task of detecting plagiarism, little has been done to assess their quality, because determining the real authorship of the whole submission corpus is practically impossible for markers. In this paper, we present a Grammar Evolution technique which generates benchmarks for testing plagiarism detection tools. Given a programming language, our technique generates set of original solutions to an assignment, together with a set of plagiarisms of the former set which mimic the basic plagiarism techniques performed by students. The authorship of the submission corpus is predefined by the user, providing a base for the assessment and further comparison of copy-catching tools. We give empirical evidence of the suitability of our approach by studying behavior of one advanced plagiarism detection tool (AC) on benchmarks coded in APL2, generated with our technique. [ABSTRACT FROM AUTHOR]

In this paper, an evolving least squares support vector machine (LSSVM) learning paradigm with a mixed kernel is proposed to explore stock market trends. In the proposed learning paradigm, a genetic algorithm (GA), one of the most popular evolutionary algorithms (EAs), is first used to select input features for LSSVM learning, i.e., evolution of input features. Then, another GA is used for parameters optimization of LSSVM, i.e., evolution of algorithmic parameters. Finally, the evolving LSSVM learning paradigm with best feature subset, optimal parameters, and a mixed kernel is used to predict stock market movement direction in terms of historical data series. For illustration and evaluation purposes, three important stock indices, S&P 500 Index, Dow Jones Industrial Average (DJIA) Index, and New York Stock Exchange (NYSE) Index, are used as testing targets. Experimental results obtained reveal that the proposed evolving LSSVM can produce some forecasting models that are easier to be interpreted by using a small number of predictive features and are more efficient than other parameter optimization methods. Furthermore, the produced forecasting model can significantly outperform other forecasting models listed in this paper in terms of the hit ratio. These findings imply that the proposed evolving LSSVM learning paradigm can be used as a promising approach to stock market tendency exploration. [ABSTRACT FROM AUTHOR]

Recent research on compact genetic algorithms (cGAs) has proposed a number of evolutionary search methods with reduced memory requirements. In cGAs, the evolution of populations is emulated by processing a probability vector with specific update rules. This paper considers the implementation of cGAs in microcontroller-based control platforms. In particular, to overcome some problems related to the binary encoding schemes adopted in most cGAs, this paper also proposes a new variant based on a real-valued solution coding. The presented variant achieves final solutions of the same quality as those found by binary cGAs, with a significantly reduced computational cost. The potential of the proposed approach is assessed by means of an extensive comparative study, which includes numerical results on benchmark functions, simulated and experimental microcon-troller design problems. [ABSTRACT FROM AUTHOR]

There are many applications where it is necessary to find an optimal spanning tree. For several of these, recent research has suggested the use of genetic algorithms (GAs). Historically, the Prüfer code has been one of the most popular representations for spanning trees, due largely to the bijective mapping between genotype and phenotype. However, it is has attracted much criticism for its low locality, a primary reason for its poor performance in GAs. Other representations such as direct encoding and network random keys have been shown to be far more effective. In 2001, an alternative called the Blob code was identified and adapted for use in GAs. It was shown to exhibit significantly higher locality than the Prüfer code. For a simple test problem, a GA using the Blob code was found to substantially outperform one using the Prüfer code. This paper suggests an alternative called the Dandelion code, which is more efficient and exhibits yet higher locality. Although both direct encoding and NetKeys are shown to give better results on the test problems used in this paper, the Dandelion code should be considered as a strong alternative, particularly for very large networks. [ABSTRACT FROM AUTHOR]