Self-regulated learning (SRL) skills are critical for effective learning and academic success. With the growing availability of trace data from students' online learning activities, researchers are increasingly leveraging this data to infer SRL processes. However, challenges remain regarding the validity of these inferences and their generalisability across diverse learning contexts. This study presents a structured approach to investigate these challenges by examining SRL behaviours in a multidisciplinary university cohort. The dataset includes 76 baseline survey responses, over 300 daily SRL survey submissions, and more than 6,000 sequences of recorded learning actions as trace data. Using mixed linear models and sequence mining, the analysis is grounded in SRL theory and evaluated through machine learning performance metrics. Our findings indicate consistent within-person patterns of SRL and online learning behaviours, supporting the concept of transferable, holistic skill development. Additionally, the results validate the trace-based detection of SRL engagement but highlight limitations in accurately detecting planning and reflection phases. These findings underscore the potential of automating SRL engagement detection while emphasising the need for multi-modal approaches to capture the full spectrum of SRL processes comprehensively.

This case study explores the online learning patterns of a cohort of first-year university students in two subjects: a compulsory science subject and an introductory programming subject, by analysing trace data from the Learning Management Systems (LMS). The methodology extends existing learning analytics techniques to incorporate temporal aspects of students’ learning, such as session duration and weekly online behaviours. By examining over 82,000 learning actions, the research unveils significant variations in students’ online learning strategies between subjects, offering deeper insights into these differences and their associated challenges. The study seeks to initiate broader discussions in learning analytics, emphasising the need to comprehend students’ diverse online learning experiences and encouraging further exploration in future research.

Constrained multiobjective optimization problems (CMOPs) are generally more challenging than unconstrained problems. This in part can be attributed to the infeasible region generated by the constraint functions, the interaction between constraints and objectives, or both. In this article, we explore the relationship between the performance of constrained multiobjective evolutionary algorithms (CMOEAs) and the instance characteristics of CMOP using instance space analysis (ISA). To do this, we extend recent work on Landscape Analysis features for characterizing CMOPs. Specifically, we introduce new features to describe the multiobjective-violation landscape, formed by the interaction between constraint violation and multiobjective fitness. The detailed evaluation of the algorithm footprints, spanning eight CMOP benchmark suites and 15 CMOEAs, demonstrates that ISA effectively captures the strength and weakness of the CMOEAs. We conclude that two characteristics, the isolation of nondominate set and the correlation between constraints and objectives evolvability, have the greatest impact on algorithm performance. However, the current benchmarks problems lack of diversity to represent the real-world problems and to fully reveal the efficacy of CMOEAs evaluated.

Dynamic multi-objective optimization problems (DMOPs) are widely accepted to be more challenging than stationary problems due to the time-dependent nature of the objective functions and/or constraints. Evaluation of purpose-built algorithms for DMOPs is often performed on narrow selections of dynamic instances with differing change magnitude and frequency or a limited selection of problems. In this paper, we focus on the reproducibility of simulation experiments for parameters of DMOPs. Our framework is based on an extension of PlatEMO, allowing for the reproduction of results and performance measurements across a range of dynamic settings and problems. A baseline schema for dynamic algorithm evaluation is introduced, which provides a mechanism to interrogate performance and optimization behaviours of well-known evolutionary algorithms that were not designed specifically for DMOPs. Importantly, by determining the maximum capability of non-dynamic multi-objective evolutionary algorithms, we can establish the minimum capability required of purpose-built dynamic algorithms to be useful. The simplest modifications to manage dynamic changes introduce diversity. Allowing non-dynamic algorithms to incorporate mutated/random solutions after change events determines the improvement possible with minor algorithm modifications. Future expansion to include current dynamic algorithms will enable reproduction of their results and verification of their abilities and performance across DMOP benchmark space.

Feature selection has been shown to be beneficial for many data mining and machine learning tasks, especially for big data analytics. Mutual Information (MI) is a well-known information-theoretic approach used to evaluate the relevance of feature subsets and class labels. However, estimating high-dimensional MI poses significant challenges. Consequently, a great deal of research has focused on using low-order MI approximations or computing a lower bound on MI called Variational Information (VI). These methods often require certain assumptions made on the probability distributions of features such that these distributions are realistic yet tractable to compute. In this paper, we reveal two sets of distribution assumptions underlying many MI and VI based methods: Feature Independence Distribution and Geometric Mean Distribution. We systematically analyze their strengths and weaknesses and propose a logical extension called Arithmetic Mean Distribution, which leads to an unbiased and normalised estimation of probability densities. We conduct detailed empirical studies across a suite of 29 real-world classification problems and illustrate improved prediction accuracy of our methods based on the identification of more informative features, thus providing support for our theoretical findings.

Machine learning techniques have been developed to learn from complete data. When missing values exist in a dataset, the incomplete data should be preprocessed separately by removing data points with missing values or imputation. In this paper, we propose an online approach to handle missing values while a classification model is learnt. To reach this goal, we develop a multi-objective optimization model with two objective functions for imputation and model selection. We also propose three formulations for imputation objective function. We use an evolutionary algorithm based on NSGA II to find the optimal solutions as the Pareto solutions. We investigate the reliability and robustness of the proposed model using experiments by defining several scenarios in dealing with missing values and classification. We also describe how the proposed model can contribute to medical informatics. We compare the performance of three different formulations via experimental results. The proposed model results get validated by comparing with a comparable literature.

Dynamic multi-objective optimization problems are very common in many real-world applications. Such problems are often characterized by time varying objectives, constraints or parameters. Consideration of dynamics is typically limited to a single dynamic time scale; a restriction on the realistic description of real-world scenarios. In this paper, we investigate the effects of asynchrony on algorithm performance for two and three objective benchmark optimization problems with two independent time variables. The independent update of these time variables is parameterized on a logarithmic scale between slow-relative change, synchronous change and fast-relative changes. To evaluate the effect of the asynchronous modes, six established multi-objective optimization algorithms, tailored specifically for dynamic problems, were used to solve the problems. The hybrid-based methods achieve significantly better hypervolume and generational distance measurements when compared to random re-initialization, diversity focused and population prediction methods. Interestingly, for selected values of the change-frequency parameter, the best operating ranges of the algorithms differ. The benefits of mutation over replacement in diversity schemes are observed. Future application to power, economic and chemical scenarios are proposed.

In complex social-ecological systems, multiple agents with diverse objectives take actions that affect the long-term dynamics of the system. Common pool resources are a subset of such systems, where property rights are typically poorly defined and dynamics are unknown a priori, creating a social dilemma reflected by the well-known `tragedy of the commons.' In this paper, we investigated the efficacy of deep reinforcement learning in a multi-agent setting of a common pool resource system. We used an abstract mathematical model of the system, represented as a partially-observable general-sum Markov game. In the first set of experiments, the independent agents used a deep Q-Network with discrete action spaces to guide decision-making. However, significant shortcomings were evident. Consequently, in a second set of experiments, a Deep Deterministic Policy Gradient learning model with continuous state and action spaces guided agent learning. Simulation results show that agents performed significantly better in terms of both sustainability and economic goals when using the second deep learning model. Despite the fact that agents do not have perfect foresight nor understanding of the implications of their `harvesting' efforts, deep reinforcement learning can be used effectively to `learn in the commons'.

Cooperative co-evolution (CC) is an effective framework that can be used to solve large-scale optimization problems. It typically divides a problem into components and uses one optimizer to solve the components in a round-robin fashion. However the relative contribution of each component to the overall fitness value may vary. Furthermore, using one optimizer may not be sufficient when solving a wide range of components with different characteristics. In this paper, we propose a novel CC framework which can select an appropriate optimizer to solve a component based on its contribution to the fitness improvement. In each evolutionary cycle, the candidate optimizer and component that make the greatest contribution to the fitness improvement are selected for evolving. We evaluated the efficacy of the proposed CC with Optimizer Selection (CCOS) algorithm using large-scale benchmark problems. The numerical experiments showed that CCOS outperformed the CC model without optimizer selection ability. When compared against several other state-of-the-art algorithms, CCOS generated competitive solution quality.

Problem decomposition plays an essential role in the success of cooperative co-evolution (CC), when used for solving large-scale optimization problems. The recently proposed recursive differential grouping (RDG) method has been shown to be very efficient, especially in terms of time complexity. However, it requires an appropriate parameter setting to estimate a threshold value in order to determine if two subsets of decision variables interact or not. Furthermore, using one global threshold value may be insufficient to identify variable interactions in components with different contribution to the fitness value. Inspired by the different grouping 2 (DG2) method, in this paper, we adaptively estimates a threshold value based on computational round-off errors for RDG. We derive an upper bound of the round-off errors, which is shown to be sufficient when identifying variable interactions across a wide range of large-scale benchmark problems. Comprehensive numerical experimental results showed that the proposed RDG2 method achieved higher decomposition accuracy than RDG and DG2. When embedded into a CC framework, it achieved statistically equal or significantly better solution quality than RDG and DG2, when used to solve the benchmark problems.

Trust and trustworthiness are of great importance in social and human systems, especially when considering managerial and economic decision-making. In this paper, we investigate the emergent dynamics of an evolutionary game-theoretic model-the N-player evolutionary trust game-consisting of three types of players: 1) an investor; 2) a trustee who is trustworthy; and 3) a trustee who is untrustworthy. Here, we limit the interactions between players to local neighborhoods defined by a specific spatial topology or social network. Players are able to adjust their game-playing strategies using an evolutionary update rule based on the payoffs obtained by their neighbors. Through comprehensive simulation experiments, we find that trust can be promoted when players interact on a social network despite a substantial number of untrustworthy individuals in the initial population. These results differ from findings reported for an unstructured population of the same game, where the existence of a single untrustworthy individual would eliminate trust completely. We compare the dynamics of the model with different social network densities and structures (e.g., from regular lattices to scale-free and random networks). We observe that the levels of trust vary under different network structures, and the level is correlated with how “difficult” the game is. When game conditions are easy (i.e., low temptation to defect and/or almost no initial untrustworthy trustees), homogeneous networks with higher densities can promote higher levels of trust. However, when the game becomes harder, heterogeneous social networks with lower densities are able to promote higher levels of trust and global net wealth.

Cooperative co-evolution (CC) is an evolutionary computation framework that can be used to solve high-dimensional optimization problems via a “divide-and-conquer” mechanism. However, the main challenge when using this framework lies in problem decomposition. That is, deciding how to allocate decision variables to a particular subproblem, especially interacting decision variables. Existing decomposition methods are typically computationally expensive. In this paper, we propose a new decomposition method, which we call recursive differential grouping (RDG), by considering the interaction between decision variables based on nonlinearity detection. RDG recursively examines the interaction between a selected decision variable and the remaining variables, placing all interacting decision variables into the same subproblem. We use analytical methods to show that RDG can be used to efficiently decompose a problem, without explicitly examining all pairwise variable interactions. We evaluated the efficacy of the RDG method using large scale benchmark optimization problems. Numerical simulation experiments showed that RDG greatly improved the efficiency of problem decomposition in terms of time complexity. Significantly, when RDG was embedded in a CC framework, the optimization results were better than results from seven other decomposition methods.

The Theory of Mind provides a framework for an agent to predict the actions of adversaries by building an abstract model of their strategies using recursive nested beliefs. In this paper, we extend a recently introduced technique for opponent modeling based on Theory of Mind reasoning. Our extended multi-agent Theory of Mind model explicitly considers multiple opponents simultaneously. We introduce a stereotyping mechanism, which segments the agent population into sub-groups of agents with similar behavior. Here, sub-group profiles guide decision making in place of individual agent profiles. We evaluate our model using a multi-player stochastic game, which presents agents with the challenge of unknown adversaries in a partially-observable environment. Simulation results demonstrate that the model performs well under uncertainty and that stereotyping allows larger groups of agents to be modeled robustly. The findings strengthen results showing that Theory of Mind modeling is useful in many artificial intelligence applications.

Interactions between decision variables typically make an optimization problem challenging for an evolutionary algorithm (EA) to solve. Exploratory landscape analysis (ELA) techniques can be used to quantify the level of variable interactions in an optimization problem. However, many studies using ELA techniques to investigate interactions have been limited to combinatorial problems, with very few studies focused on continuous variables. In this paper, we propose a novel ELA measure to quantify the level of variable interactions in continuous optimization problems. We evaluated the efficacy of this measure using a suite of benchmark problems, consisting of 24 multidimensional continuous optimization functions with differing levels of variable interactions. Significantly, the results reveal that our measure is robust and can accurately identify variable interactions. We show that the solution quality found by an EA is correlated with the level of variable interaction in a given problem. Finally, we present the results from simulation experiments illustrating that when our measure is embedded into an algorithm design framework, the enhanced algorithm achieves equal or better results on the benchmark functions.

Since there is no single best performing algorithm for all problems, an algorithm portfolio would leverage the strengths of complementary algorithms to achieve the best performance. In this paper, we present and evaluate a new technique for designing algorithm portfolios for continuous black-box optimization problems, based on social choice and voting theory concepts. Our technique, which we call ICARUS, models the portfolio design task as an election, in which each problem `votes' for a subset of preferred algorithms guided by a performance metric such as the number of fitness evaluations. The resulting `uncovered set' of algorithms forms the portfolio. We demonstrate the efficacy of ICARUS using a suite of state-of-the-art evolutionary algorithms and benchmark continuous optimization problems. Our analysis confirms that ICARUS creates an algorithm portfolio where the expected performance is superior to a manually constructed portfolio.

Cooperative co-evolution is a framework that can be used to effectively solve large scale optimization problems. This approach employs a divide and conquer strategy, which decomposes the problem into sub-components that are optimized separately. However, solution quality relies heavily on the decomposition method used. Ideally, the interacting decision variables should be assigned to the same sub-component and the interdependency between sub-components should be kept to a minimum. Differential grouping, a recently proposed method, has high decomposition accuracy across a suite of benchmark functions. However, we show that differential grouping can only identify decision variables that interact directly. Subsequently, we propose an extension of differential grouping that is able to correctly identify decision variables that also interact indirectly. Empirical studies show that our extended differential grouping method achieves perfect decomposition on all of the benchmark functions investigated. Significantly, when our decomposition method is embedded in the cooperative co-evolution framework, it achieves comparable or better solution quality than the differential grouping method.

This paper presents a novel generalised indirect reciprocity approach for promoting cooperation in social dilemma games. Here, players decide upon an action to play in the game based on public information (or “external cues”) rather than individual-specific information. The public information is constantly updated according to the underlying learning model. Comprehensive simulation experiments using the N-player Prisoner's Dilemma (PD) and Snowdrift (SD) games show that generalised indirect reciprocity promotes high levels of cooperation across a wide range of conditions. This is despite the fact that the make-up of player groups is continually changing. As expected, the extent of cooperative behaviour observed in the “constraint-relaxed” N-player SD game is significantly higher than the N-player PD game. Our proposed generalised indirect reciprocity model may shed light on the conundrum of cooperation between anonymous individuals.

Data-driven analysis methods, such as the information content of a fitness sequence, characterize a discrete fitness landscape by quantifying its smoothness, ruggedness, or neutrality. However, enhancements to the information content method are required when dealing with continuous fitness landscapes. One typically employed adaptation is to sample the fitness landscape using random walks with variable step size. However, this adaptation has significant limitations: random walks may produce biased samples, and uncertainty is added because the distance between observations is not accounted for. In this paper, we introduce a robust information content-based method for continuous fitness landscapes, which addresses these limitations. Our method generates four measures related to the landscape features. Numerical simulations are used to evaluate the efficacy of the proposed method. We calculate the Pearson correlation coefficient between the new measures and other well-known exploratory landscape analysis measures. Significant differences on the measures between benchmark functions are subsequently identified. We then demonstrate the practical relevance of the new measures using them as class predictors on a machine learning model, which classifies the benchmark functions into five groups. Classification accuracy greater than 90% was obtained, with computational costs bounded between 1% and 10% of the maximum function evaluation budget. The results demonstrate that our method provides relevant information, at a low cost in terms of function evaluations.

Reactive path planning to avoid collisions with moving obstacles enables more robust agent systems. However, many solutions assume that moving objects are passive; that is, they do not consider that the moving objects are themselves re-planning to avoid collisions, and thus may change their trajectory. In this paper we present a model, Anticipatory Stigmergic Collision Avoidance (ASCA) for reciprocal collision avoidance using anticipatory stigmergy. Unlike standard stigmergy, in which agents leave pheromones to indicate a trace of previous actions, anticipatory stigmergy deposits pheromones on intended future paths. By sharing their intended future paths with each other at regular intervals, agents can re-plan to attempt to avoid collisions. We experimentally evaluate ASCA over three scenarios, and compare with a state of art approach, Reciprocal Velocity Obstacles (RVO). Our evaluation showed that ASCA is consistently more robust in noisy environments in which transmitted information can be lost or degraded. Further, using ASCA without noise results in fewer collisions than RVO when agents are in formation, but more collisions when formed randomly.

In task environments with large state and action spaces, the use of temporal and state abstraction can potentially improve the decision making performance of agents. However, existing approaches within a reinforcement learning framework typically ide

XCS - the extended Classifier System - combines an evolutionary algorithm with reinforcement learning to evolve a population of condition-action rules (classifiers). Typically, population-based approaches are slow and increasing the problem size (in terms of the number of features/samples) poses a real threat to the suitability of XCS for real-world applications. Thus, reducing the execution time without losing accuracy is highly desirable. Profiling of the execution of off-the-shelf XCS implementations suggests that the rule matching process is the most computational demanding step. A solution to this is parallelization, i.e., using parallel processing techniques to speed up the matching process (and thus the entire XCS learning process). There are many ways to achieve that, using Graphic Processing Units (GPUs) is one option. Originally, GPUs were designed to conduct a sequence of graphics operations in a massively parallel fashion. Today, GPUs can be used for all sorts of general purpose calculations that are normally handled by the CPU. In this paper, we propose a hybrid rule matching process using both CPU and GPU simultaneously for a maximum performance gain. Our experimental results indicate that this approach does speed up the XCS learning process, and that the GPU is the dominant powerful computing resource in the model.

We study the evolution of cooperation in a population of agents playing the N-player Prisoner's Dilemma game via stigmergic interactions. Here, agent decision making is guided by a shared pheromone table. Actions are played at each time step and a trace (or signal) corresponding to the rewards received is recorded in this shared table. Subsequent actions are then determined probabilistically using the shared information. Comprehensive Monte Carlo simulation experiments show that the stigmergy-based mechanism is able to promote cooperation despite the fact that the make-up of the interacting groups is continually changing. A direct comparison with a genetic algorithm-based N-player model confirms that the extent of cooperative behaviour achieved is significantly higher across a wide range of cost-to-benefit ratios. In the concluding remarks, we highlight the real-world implications of stigmergic interactions.

The characterization of optimization problems over continuous parameter spaces plays an important role in optimization. A form of “fitness landscape” analysis is often carried out to describe the problem space in terms of modality, smoothness and variable separability. The outcomes of this analysis can then be used as a measure of problem difficulty and to predict the behaviour of a given algorithm. However, the metric value estimates of the landscape characterization are dependent upon the representation scheme adopted and the sampling method used. Consequently, the development of a complete classification of problem structure and complexity has proven to be challenging. In this paper, we continue this line of research. We present a methodology for the characterization of two dimensional numerical optimization problems. In our approach, data extracted during the search process is analyzed and the dependency of the results to the nominated sampling method are corrected. We show via computational simulations that the calculated metric values using our approach are consistent with the results from random experiments. As such, this study provides a first step towards the on-line calculation of fitness landscape characterization metrics and the development of empirical performance models of search algorithms. Advances in these areas would provide answers to the algorithm selection and portfolio configuration problems.

A community in a network is a set of nodes with a larger density of intra-community links than inter-community links. Tracking communities in a network via a community life-cycle model can reveal patterns on how the network evolve. Previous models of community life-cycle provided a first step towards analyzing how communities change over time. We introduce an extended life-cycle model having the minimum community size as a parameter. Our model is capable of uncovering anomaly in community evolution and dynamics such as communities with stable or stagnant size. We apply our model to track, and uncover trends in, the evolution of communities of genetic programming researchers. The lifespan of a community measures how long it has lived. The distribution of lifespan in the network of genetic programming researchers is shown to be modeled as an exponential-law, a phenomenon yet to be explored in other empirical networks. We show that our parameter of minimum community size can significantly affect how communities grow over time. The parameter is fine-tuned to detect anomaly in community evolution.

Mechanisms promoting the evolution of cooperation in two players and two strategies (22) evolutionary games have been investigated in great detail over the past decades. Understanding the effects of repeated interactions in multiplayer spatial games, however, is a formidable challenge. In this paper, we present a multiplayer evolutionary game model in which agents play iterative games in spatial populations. -player versions of the well-known Prisoner's Dilemma and the Snowdrift games are used as the basis of the investigation. These games were chosen as they have emerged as the most promising mathematical metaphors for studying cooperative phenomena. Here, we have adopted an experimental approach to study the emergent behavior, exploring different parameter configurations via numerical simulations. Key model parameters include the cost-to-benefit ratio, the size of groups, the number of repeated encounters, and the interaction topology. Our simulation results reveal that, while the introduction of iterated interactions does promote higher levels of cooperative behavior across a wide range of parameter settings, the cost-to-benefit ratio and group size are important factors in determining the appropriate length of beneficial repeated interactions. In particular, increasing the number of iterated interactions may have a detrimental effect when the cost-to-benefit ratio and group size are small.

The evolution of strategies in iterated multi-player social dilemma games is studied on small-world networks. Two different games with varying reward values - the N-player Iterated Prisoner's Dilemma (N-IPD) and the N-player Iterated Snowdrift game (N-ISD) - form the basis of this study. Here, the agents playing the game are mapped to the nodes of different network architectures, ranging from regular lattices to small-world networks and random graphs. In a given game instance, the focal agent participates in an iterative game with N-1 other agents drawn from its local neighbourhood. We use a genetic algorithm with synchronous updating to evolve agent strategies. Extensive Monte Carlo simulation experiments show that for smaller cost-to-benefit ratios, the extent of cooperation in both games decreases as the probability of re-wiring increases. For higher cost-to-benefit ratios, when the re-wiring probability is small we observe an increase in the level of cooperation in the N-IPD population, but not the N-ISD population. This suggests that the small-world network structure with small re-wiring probabilities can both promote and maintain higher levels of cooperation when the game becomes more challenging.

XCS is an accuracy-based machine learning technique, which combines reinforcement learning and evolutionary algorithms to evolve a set of classifiers (or rules) for pattern classification tasks. In this paper, we investigate the effects of alternative feature space partitioning techniques in a multiple population island-based parallel XCS. Here, each of the isolated populations evolve rules based on a subset of the features. The behavior of the multiple population model is carefully analyzed and compared with the original XCS using the Boolean logic multiplexer problem as a test case. Simulation results show that our multiple population XCS produced better performance and better generalization than the single population XCS model, especially when the problem increased in size. A caveat, however, is that the effectiveness of the model was dependent upon the feature space partitioning strategy used.

The problem of evolving and maintaining cooperation in both ecological and artificial multi-agent systems has intrigued scientists for decades. In this paper, we present an evolutionary game model that combines direct and spatial reciprocity to investigate the effectiveness of two different learning mechanisms used to promote cooperative behaviour in a social dilemma game - the N-player Iterated Prisoner's Dilemma (NIPD). Unlike the two-player game, in the NIPD the action of a player typically results in a non Pareto-optimal outcome for all other players within a social group given the relative costs and benefits associated with particular actions. Consequently, promoting system-wide cooperation is extremely difficult. We use comprehensive Monte Carlo simulation experiments to show that evolutionary-based strategy adaptation and update leads to significantly higher levels of cooperation in the NIPD when compared to social learning via cultural imitation. This finding suggests that when designing decentralised multi-agent systems, evolutionary adaptation mechanisms should be incorporated into the model where efficient collective actions are required.

This paper presents a critical analysis of the Pareto-Following Variation Operator (PFVO) when used as an approximation method for Multiobjective Evolutionary Algorithms (MOEA). In previous work, we have described the development and implementation of the PFVO. The simulation results reported indicated that when the PFVO was integrated with NSGA-II there was a significant increase in the convergence speed of the algorithm. In this study, we extend this work. We claim that when the PFVO is combined with any MOEA that uses a non-dominated sorting routine before selection, it will lead to faster convergence and high quality solutions. Numerical results are presented for two base algorithms: SPEA-II and RM-MEDA to support are claim. We also describe enhancements to the approximation method that were introduced so that the enhanced algorithm was able to track the Pareto-optimal front in the right direction.

Abstract Most algorithms developed for scheduling applications on global Grids focus on a single Quality of Service (QoS) parameter such as execution time, cost or total data transmission time. However, if we consider more than one QoS parameter (e.g. execution cost and time, which may be in conflict) then the problem becomes more challenging. To handle such scenarios, it is convenient to use heuristics rather than a deterministic algorithm. In this paper, we have proposed a workflow execution planning approach using Multiobjective Differential Evolution (MODE). Our goal was to generate a set of trade‐off schedules according to two user specified QoS requirements (time and cost), which will offer more flexibility to users when estimating their QoS requirements. We have compared our results with a well‐known baseline algorithm ‘Pareto‐archived Evolutionary Strategy (PAES)’. Simulation results show that the modified MODE is able to find significantly better spread of compromise solutions compared with that of PAES. Copyright © 2009 John Wiley & Sons, Ltd.

Recently, there has been increased interest in combining work from the complex networks domain with evolutionary computation to solve challenging search and optimization problems. Typically, individuals in the evolving population occupy a node in a graph (or network) and are only allowed to mate with individuals within their local neighbourhood. The use of specific graph topologies have been shown to alter the population dynamics, which in turn impacts on the ability of the algorithm to find (near)-optimal solutions for a given problem. In this paper, we continue this line of research. Here, we have analyzed the impact of clustering on the performance of graph-based evolutionary models. We have constructed a range of alternative graphs to act as scaffolding for the evolving population by systematically rewiring some of the edges/links in a regular lattice. Significantly, we have kept the mean node degree constant in all graphs. Two different problems defined on a binary string with regulated levels of epistasis - the NK Landscape problem and the hierarchical if and only if (H-IFF) problem - were used to examine the efficacy of our model. Simulation results show that the clustering coefficient of the underlying graph has a significant impact on the ability of a graph-based evolutionary algorithm to solve a given problem.

Tracking the Pareto-front in a dynamic multi-objective optimization problem (MOP) is a challenging task. Evolutionary algorithms are a representative meta-heuristic capable of meeting this challenge. Typically, the stochastic variation operators used in an evolutionary algorithm work in decision (or design) variable space, thus there are no guarantees that the new individuals produced are non-dominated and/or are unique in the population. In this paper, we introduce a novel variation operator that manipulates the values in both objective space and design variable space in such a way that it can avoid re-exploration of dominated solutions. The proposed operator, inspired by the theory of dynamic system identification, is based on integral transformation. Here, we approximate the next expected Pareto-front, and from this expected front, we generate corresponding correct decision variables. We show empirically that our algorithm can approximate the Pareto-optimal set for given static benchmark MOP’s and that it can track changes in the Pareto-front for particular dynamic MOP’s.

One of the major difficulties when applying Multiobjective Evolutionary Algorithms (MOEA) to real world problems is the large number of objective function evaluations. Approximate (or surrogate) methods offer the possibility of reducing the number of evaluations, without reducing solution quality. Artificial Neural Network (ANN) based models are one approach that have been used to approximate the future front from the current available fronts with acceptable accuracy levels. However, the associated computational costs limit their effectiveness. In this work, we introduce a simple approach that has comparatively smaller computational cost and we have developed this model as a variation operator that can be used in any kind of multiobjective optimizer. When designing this model, we have considered the whole search procedure as a dynamic system that takes available objective values in current front as input and generates approximated design variables for the next front as output. Initial simulation experiments have produced encouraging results in comparison to NSGA-II. Our motivation was to increase the speed of the hosting optimizer. We have compared the performance of the algorithm with respect to the total number of function evaluation and Hypervolume metric. This variation operator has worst case complexity of O(nkN3), where N is the population size, n and k is the number of design variables and objectives respectively.

This paper describes two performance measures for measuring an EMO (evolutionary multiobjective optimization) algorithm's ability to track a time-varying Pareto-front in a dynamic environment. These measures are evaluated using a dynamic multiobjective test function and a dynamic multiobjective PSO,maximinPSOD, which is capable of handling dynamic multiobjective optimization problems.maximinPSODis an extension from a previously proposed multiobjective PSO,maximinPSO. Our results suggest that these performance measures can be used to provide useful information about how well a dynamic EMO algorithm performs in tracking a time-varying Pareto-front. The results also show thatmaximinPSODcan be made self-adaptive, tracking effectively the dynamically changing Pareto-front.

Multiobjective evolutionary algorithms (MOEA) are an effective tool for solving search and optimization problems containing several incommensurable and possibly conflicting objectives. Unfortunately, many MOEAs face difficulties in solving problems when the number of objectives increases. In this paper, we investigate the efficacy of spatially structured MOEAs for scalable multiobjective problems. The algorithm is an extension of the standard cellular evolutionary algorithm, where the population is mapped to nodes of alternative complex networks. A selection regime based on a non-dominance rating and a crowding mechanism guides the evolutionary trajectory and an ε-dominance external archive is used to maintain a spread of solutions across the Pareto-optimal front. An important outcome of this work is the classification of the network models based on their impact on convergence speed and solution quality as the number of objectives increases for a given problem.

Introduction: Multiobjective optimization represents an important class of optimization techniques which have a direct implication for solving many real-world problems. In recent years, using evolutionary algorithms to solve multiobjective optimization problems, commonly known as EMO (Evolutionary Multi-objective Optimization), has gained rapid popularity. Since Evolutionary Algorithms (EAs) make use of a population of candidate solutions, a diverse set of optimal solutions so called Pareto-optimal solutions can be found within a single run. EAs offer a distinct advantage over many traditional optimization methods where multiple solutions must be found in multiple separate runs.

A robot swarm is a distributed entity that can sense andperform many actions simultaneously at different spatial locations. But how, with all this sensory information and capacity for action, can the individuals unite for a common purpose, coordinating their actions in space and time? Inthis preliminary simulation study, we suggest that a swarmcan be designed as an engineering control system characterised by a problem specific input/output (I/O) relationship that can be implemented through the simple (socialinsect inspired) indirect transfer of information between individuals. For such a system, the inputs represent sensory information acquired by one or more agents and the outputs are used to trigger actions that agents perform.

This paper describes a multi-objective parameter-less genetic algorithm (moPGA), which combines several recent developments including efficient non-dominated sorting, linkage learning, isin-Dominance, building-block mutation and convergence detection. Additionally, a novel method of clustering in the objective space using an isin-Pareto Set is introduced. Comparisons with well-known multi-objective GAs on scalable benchmark problems indicate that the algorithm scales well with problem size in terms of number of function evaluations and quality of solutions found. moPGA was built for easy usage and hence, in addition to the problem function and encoding, there are only two required user defined parameters; (1) the maximum running time or generations and (2) the precision of the desired solutions (isin).

This paper presents a hidden Markov model (HMM) based fuzzy rule extraction technique for predicting a time series generated by a chaotic dynamical system. The model uses three sequential phases. Firstly, the HMM is used to partition the input dataset based on the ordering of the calculated log-likelihood values (similarity measures). Then, a recursive top-down algorithm is used to generate the minimum number of rules required to accurately predict the next value in the time series using the training dataset. Finally, a gradient descent method is applied to the extracted fuzzy rules in order to fine-tune the model parameters. The performance of the proposed model is evaluated using a benchmark dataset -the Mackey-Glass time series. The results obtained clearly demonstrate significant improvement in prediction capabilities of the proposed HMM-fuzzy model when compared to the other techniques.

In this study, we investigate self-organizing social hierarchies in multi-agent systems. Agents occupy the nodes of a small-world network and interact exclusively with other agents in their local neighbourhood. Here, the interactions represent competition for a limited resource. Monte-Carlo simulations show that the changes in a network's structure can alter the steady-state attributes for fixed reward/penalty mechanisms. The results suggest that the expected phase transition from a homogeneous to a hierarchical society depends on: (a) the relative strengths of the feedback mechanisms employed, (b) the underlying communication topology, and (c) whether previously dominated agents are replaced in the population by agents with higher social status. A key contribution of this paper is the coherent picture painted of the relationship between social differentiation and spatial structure in a multi-agent system.

This paper introduces a new method for controlling selection pressure in fine-grained parallel GAs. Our model, inspired by percolation theory, employs a "seeding" mechanism, which provides a means of systematically increasing the population size until the carrying capacity of the lattice is reached. Initially, a relatively small number of individuals (solutions) occupy small isolated patches (demes). As time goes by, additional randomly generated individuals are added to the lattice. As the density increases, the small isolated demes gradually merge to form larger connected demes. This "percolation process" helps to balance the interplay between genetic and population forces. The implications of alternative migration schemes between demes are also investigated in terms of the population diversity, selection pressure and consequently algorithm performance. Experimental results using benchmark optimisation problems confirm that the "step-wise" increase in the population density does affect the quality of the solutions found in a given trial.

This paper introduces a metapopulation evolutionary algorithm (MEA) for multi-objective optimisation problems. Insights from landscape ecology and population dynamics are used to develop a robust algorithm that combines the "diffusion" properties of cellular parallel genetic algorithms and "island" properties of distributed models. Two alternate selection mechanisms-a Pareto based technique and a novel environmental gradient aggregation technique-are analysed. Preliminary results suggest that the hypothesis of improved performance for spatially heterogenous populations is correct. The dynamic selection pressure, which emerges as a result of the changing environmental structure, helps to maintain population diversity and subsequently solution quality.

Scheduling problems in general consist of a set of concurrent conflicting goals that are to be satisfied using a limited number of resources. They arise in diverse areas such as transportation and communication systems, logistics and manufacturing environments. The job shop scheduling problem (JSSP) is considered to be one of the hardest combinatorial optimisation problems. The coevolutionary genetic algorithm (CEGA) is proposed for solving the job shop scheduling problem. The JSSP is divided into a number of subproblems, and the CEGA encourages the parallel evolution of partial solutions. This approach combines and extends previous evolutionary computation techniques used to solve similar optimisation problems. Initial computational results indicate that the CEGA performs favourably when compared to other approaches and that a number of high quality solutions to the problem are produced on each run.