Rule representations significantly influence the search capabilities and decision boundaries within the search space of Learning Classifier Systems (LCSs). However, it is very difficult to choose an appropriate rule representation for each problem. Additionally, some problems benefit from using different representations for different subspaces within the input space. Thus, an adaptive mechanism is needed to choose an appropriate rule representation for each rule in LCSs. This article introduces a flexible rule representation using a four-parameter beta distribution and integrates it into a fuzzy-style LCS. The four-parameter beta distribution can form various function shapes, and this flexibility enables our LCS to automatically select appropriate representations for different subspaces. Our rule representation can represent crisp/fuzzy decision boundaries in various boundary shapes, such as rectangles and bells, by controlling four parameters, compared to the standard representations such as trapezoidal ones. Leveraging this flexibility, our LCS is designed to adapt the appropriate rule representation for each subspace. Moreover, our LCS has a generalization bias to produce as many crisp rules as possible. Experimental results on real-world classification tasks show that our LCS significantly outperformed LCSs with popular rule representations in test classification accuracy on up to 17 of the 25 datasets tested.

This study focuses on the dynamic optimization problems where a solution landscape "continuously" changes, unlike the conventional problems where a solution landscape "discretely" changes, which includes certain static (unchanged) periods before the landscape changes. Since such a problem becomes very difficult when the speed of changing the solution landscape is faster than the speed of evaluating all solutions, this paper proposes the swarm optimization method to tackle this problem. Concretely, our method excludes the landscape change detection mechanism unlike conventional approaches, but adapts to its change by exploring solutions according to the only current evaluation values. Through the experiment based on the high-frequency landscape change which is modeled by changing the multiple functions in the Moving Peaks Benchmark, the following implications have been revealed: (1) the proposed method outperforms the conventional methods even in the case of the high-frequency landscape change; and (2) not only the landscape change detection mechanism but also the past searched solution archive mechanism deteriorate the performance of the proposed method in the dynamic optimization problems based on the high-frequency landscape change.

In the "unbounded" search space, an exploration in the search space is more significant issue than that in the "bounded" search space which assumes the pre-defined bounded search space. This is because new areas which have not been searched yet are infinitely found during an exploration in the search space. This means that it is quite important carefully to control such exploration in the unbounded search space to search the targets (e.g., optimal solutions) effectively. However, it is difficult to control exploration in unbounded search space. For this purpose, this paper proposed Novelty-based Multi-objectivization with Local and Role-based Rough area Search (NM-LR2S) which control exploitation, not exploration by adding the mechanisms selecting or generating a good fitness individuals to the conventional method Novelty-based Multi-objectivization with Local and Rough area Search (NM-LRS) and indirectly control exploration. To investigate the effectiveness of the proposed method, the experiment is conducted with NM-LRS which is without exploration controlling mechanisms, and has revealed the following implications: (i) the peak ratio which is the ratio of finding optimal solution of NM-LR2S is better than other unbounded search space optimization methods include NM-LRS; and (ii) NM-LR2S can control the exploration to prevent over-exploration compared with NM-LRS.

This paper focuses on the flight schedule optimization that is required to minimize both the delay time and the altitude change from the desired altitudes of all aircrafts as the two objectives while maximizing the "constraint tolerance" which means the acceptable range of changing constraints as the third objective, and proposes Constrained Multi-objective Optimization Evolutionary Algorithm based on Dual Sets with Local Search and Archive (CMOEA/DS-LSA) for its optimization. CMOEA/DS-LSA is designed to find the feasible solutions (i.e., the flight schedules) from the infeasible ones while improving them by the local search and evolving them from the diverse solutions stored in an archive. In particular, the effectiveness of CMOEA/DS-LSA is investigated in not only the unimodal flight scheduling problems (which have the only one optimal solution) but also the multimodal problems (which have more than one optimal solution). The intensive simulations have revealed the following implications: (1) CMOEA/DS-LSA outperforms the conventional methods (i.e., Constrained NSGA-II (CNSGA-II) and Two-stage Non-dominated Sorting and Directed Mating (TNSDM)) in both the unimodal and multimodal problems from the viewpoint of AITDR, which evaluates both the two objectives (i.e., the delay time and altitude change) and the constraint tolerance simultaneously; and (2) CMOEA/DS-LSA can find the multiple solutions while the conventional methods can find only one solution in the multimodal problems.

This paper proposes a multitask knapsack problem framework as a discrete test suite that allows for the independent adjustment of both objective and constraint similarities among tasks. The proposed multitask knapsack problem framework introduces objective and constraint covariance matrices for multiple tasks. These covariance matrices influence the setting of profit and weight values in each knapsack problem. By adjusting the elements of the covariance matrices, both objective and constraint similarities among tasks can be precisely controlled. Experiments were conducted to observe the perfromance of multi-factorial evolutionary algorithms, MFEA and MFEA/TS, as well as a single-task evolutionary algorithm, SOEA, on multitask knapsack problems. Results revealed that estimating task similarities based on the distribution of solution sets and integrating this information into parent selection led to improved objective values for feasible solutions, thereby enhancing overall multitask optimization performance.

To tackle the dynamic optimization problem where the location and number of optimal solutions frequently change, this paper proposes NDSOT (Niching Swarm Dynamic Optimization with TCMA-ES) which can continuously track the multiple moving optimal solutions each of which is generated or eliminated as time goes on. For this purpose, the proposed algorithm integrates Tracking CMA-ES (TCMA-ES) with NMMSO (Niching Migratory Multi-Swarm Optimization), where the former aims to locally track the multiple moving optimal solutions with globally estimating their movement direction, while the latter aims to estimate the number of the multiple optimal solutions by adjusting the number of swarms composed of individuals. The intensive experiments of the three dynamic multimodal functions in 2D and 5D from the Moving Peaks Benchmark (MPB) have revealed that NDSOT succeeded to track the multiple moving and generated/eliminated optimal solutions. In detail, (1) the Offline-Error and Relative Error Distance of NDSOT is lowest and (2) the Peak Found Ratio of NDSOT is highest in comparison with the conventional methods of multiswarm-Quantum Particle Swarm Optimization (QPSO) and TSOPC.

Unlike the conventional multi-modal optimization where a “bounded search area” is pre-determined, this paper addresses the multi-modal optimization for an “unbounded search space”. For this purpose, this paper proposes Novelty-based Multi-objectivization with Local and Rough Search based on dynamic area exploration (NM-LRS), which adds the novelty criterion in the given optimization criteria to roughly search the unbounded search space for obtaining the “potential area” where the optimal solution is most likely located and then searches the “potential area” to find the optimal solution by a local search. To investigate the effectiveness of the proposed method, NM-LRS is compared with the other optimization methods for the unbounded search space, and the following implications have been revealed: the proposed method has a higher solution-finding rate than all existing methods for functions with complex landscapes, and it also finds the optimal solution far from the initial search area, which confirms the effectiveness of a rough search.

This paper proposes a constrained multi-factorial optimization algorithm, MFEA/TS (Multi-Factorial Evolutionary Algorithm based on Task Similarity), which estimates the constraint similarity and objective similarity through solution distributions in the variable space. It integrates these similarities into parent selection to enhance the simultaneous optimization of multiple problems. Additionally, this paper introduces continuous test problems that enable adjusting constraint and objective similarities visually by setting feasible regions of constraints and optimal solutions in the variable space, respectively. These test problems allow configuring conflicts between constraint and objective similarities. Experimental results on these test problems demonstrate that the proposed MFEA/TS can effectively detect the constraint and objective similarities designed in the test problems, thereby enhancing multi-factorial optimization. The proposed MFEA/TS achieves higher search performance compared to conventional algorithms such as MFEA, MFEA-II, MFDE, and SOEA.

Multiobjectivization via Helper Objectives (MHO) is the method for reformulating the original problem into a single optimization problem with more objectives by adding helper objectives. This paper proposes a method for solving multi-objective optimization problems inspired by MHO by transforming the problem by adding objective functions. The helper objective employed in the proposed is of three types: a function that adds up all the objectives of the original problem, a periodic function with global optima at equal space, and a function that partially simplifies the objectives of the original problem. The function that adds up all the objectives of the original problem aims to create new search pressure in the objective function space. The function with equally spaced global optima aims to keep the solution set diverse in the objective function space. The function that partially simplifies the original problem aim to escape from the local optima contained in the original problem. These helper objectives are added to the objective variables of the original problem. Adding helper objectives is expected to improve convergence to the global optima and diversity of the set of solutions. Through comparative experiments on the proposed method using the WFG problems as benchmark problems, the experimental results show the improvement of (1) the diversity of the solution set in the objective function space and (2) the convergence speed to the Pareto front. Multiobjectivization via Helper Objectives (MHO) is the method for reformulating the original problem into a single optimization problem with more objectives by adding helper objectives.

This paper aims to enhance the accuracy of the Pareto front estimation model as an aggregative representation of the non-dominated solutions and proposes an algorithm named the Pareto front Model Optimization Algorithm (PFMOA). The typical output of multi-objective optimization is a set of non-dominated solutions approximating the Pareto front, which is the optimal trade-off between objective function values. The more non-dominated solutions there are, the more accurately the Pareto front can be approximated. However, especially in real-world problems, there is often a limitation on increasing the number of solutions due to the time required to execute objective functions. For the issue, a Pareto front estimation method interpolates between a limited number of non-dominated solutions to represent changes in objective function values even in regions where non-dominated solutions are not actually obtained. The proposed PFMOA enhances the accuracy of the Pareto front estimation model while evaluating new solutions. PFMOA generates the estimated Pareto front based on a known non-dominated solution set using Kriging. PFMOA focuses on the point with the lowest confidence levels on the estimated Pareto front and evaluates the corresponding point on the estimated Pareto set. PFMOA also generates new solutions using evolutionary variation. PFMOA stochastically switches these two model-based and evolutionary-based solution generation methods. If the new solution is non-dominated, it is included in the known non-dominated solution set, and the process is repeated to enhance the accuracy of the Pareto front estimation model. The effectiveness of the proposed PFMOA is verified using DTLZ1-3, and WFG4 problems. The results show that, in all cases, the accuracy of the Pareto front approximation by the Pareto front estimation model is higher than that by the obtained solution set itself. Additionally, the combination of model-based and evolutionary-based solution generation is beneficial to enhancing the accuracy of the Pareto front estimation model.

The generational model maintaining both parent and offspring populations is frequently employed for designing multi-objective evolutionary algorithms. The archive population of non-dominated solutions acquired during the search is also often incorporated, especially for real-world problems that cannot lose any valuable information obtained. Although both the parent and archive populations should maintain good solutions, repeated generations may cause solutions in the parent population to be dominated by ones in the archive. This means that the parent population at the final generation cannot be the best solution set throughout the search. This is not problematic if the parent population, with lower optimality than the archive, is beneficial for offspring generation. However, if solutions with the highest optimality are useful for offspring generation, the archive should be used for it. This paper aims to investigate whether the parent population should always be the best non-dominated solution set. As a research methodology, this paper picks NSGA-II, NSGA-III, IBEA, NSGA-II-SDR, and$\boldsymbol{\theta}$-DEA, employing the generational model and re-selecting the parent population from the archive in every certain generation to make the parent population the best. The generational interval of the re-selection is a parameter that adjusts the optimality of the parent population. The shorter the interval, the higher the optimality in the parent population. Experimental results using the knapsack problems with 2–6 objectives show that the highest parent optimality with the shortest re-selection interval maximizes the search performance for many algorithms and problems, while the highest parent optimality does not necessarily maximize the search performance for some algorithms and problems.

Push and pull search (PPS) is an approach of evolutionary constrained multi-objective optimization that involves de-composing the objective space. PPS comprises two search phases: the ‘push’ and ‘pull’ phases. In the push phase, solutions evolve towards the optimal objective trade-off ignoring constraints. Subsequently, in the pull phase, the solutions evolve towards the optimal objective trade-off satisfying constraints. Depending on the characteristics of the problem, the pull phase starts with only infeasible solutions because constraints are ignored in the previous push phase. Although the feasible solutions discarded in the push phase may have worse objective function values than the infeasible ones in the population at the end of that phase, they can still contribute to the search for optimal feasible solutions in the pull phase. This paper aims to enhance the performance of constrained multi-objective optimization based on the PPS approach. We propose PPS-DM (PPS with directed mating), which archives feasible solutions obtained in the push phase and utilizes them for the search in the pull phase. To generate a new solution, the directed mating focuses on an infeasible solution, extracts feasible solutions dominated by the focused infeasible one from the archive, and applies the differential evolution operator between them. Experimental results using LIR-CMOP test problems show that the proposed PPS-DM improves the search of the pull phase and archives totally better performance than the conventional PPS, NSGA-II, NSGA-III, and MOEA/D.

Multi-objectivization transforms a single-objective optimization problem into a multi-objective one in order to facilitate the search for high-quality solutions with respect to the original target objective. This paper focuses on the multi-objectivization strategy of adding a helper objective. Depending on its definition, the helper objective might have a positive or negative impact on optimization. For multi-objectivization to work well, it is essential to select the helper objective with care, according to the nature of the target objective. However, the design of this helper objective remains unclear: should it be completely independent of the target objective or, by contrast, correlated in some respects? We propose and analyze different methods for generating helper objectives with varying degrees of correlation to the target objective, with the aim of guiding the setting of multi-objectivization. Inspired by existing works on multi-objective NK landscapes, we are particularly interested in the joint setting of the correlation between objective-values and the similarity of variable interactions on both objectives. We approximately decompose the target function into several sub-functions based on the Walsh transform. The proposed method combines these sub-functions to create helper objectives with different levels of correlation and heterogeneity. By analyzing bi-objective instances made of a target and of a helper objective under different definitions, we gain insights into the selection of helper objectives depending on the target objective. Our experimental findings suggest that a helper objective with a positive correlation and a smoother landscape is beneficial for multi-objectivization.

This paper focuses on “prototypes” as representative samples that can serve as a summary of the original dataset and proposes a novel Learning Classifier System (LCS) to generate a small number of prototypes that can achieve high classification accuracy in class classification. Concretely kNNUCS-PG is proposed to improve the sUpervised Classifier System (UCS) as one of LCSs by changing from the interval (rule) representation to the point representation to represent a prototype by employing k-nearest neighbors (kNN) to match the neighborhood prototypes. For a high classification accuracy with data reduction, selecting and generating prototypes that can maintain decision boundaries is necessary. Since UCS has generalization mechanisms, including rule merging, unnecessary rule deletion, and new rule discovery using niche Genetic Algorithm (GA), such techniques are highly useful for evolving indispensable prototypes as generalized prototypes. This paper compared conventional prototype-based methods with kNNUCS-PG in experiments using three benchmark problems and eight table datasets. kNNU CS-PG can maintain high classification accuracy even for complex problems with much overlap in the datasets. The results show that kNNUCS-PG is a robust PG that can maintain high classification accuracy while reducing data for various complex problems.

The design of automated landscape-aware techniques requires low-cost features that characterize the structure of the target optimization problem. This paper approximates network-based landscape models of multi-objective optimization problems, which were constructed by full search space enumeration in previous studies. Specifically, we propose a sampling method using dominance-based local search for constructing an approximation of the Pareto local optimal solution network (PLOS-net) and its variant, the compressed PLOS-net. Both models are valuable to visualize and compute features on the distribution of Pareto local optima. We conduct experiments with multi-objective nk-landscapes and compare the features of full-enumerated PLOS-nets with that of approximate PLOS-nets. We analyze the correlation between landscape features and the performance of well-established multi-objective evolutionary and local search algorithms. Our results show that approximated networks can predict algorithm performance and provide recommendation for algorithm selection with the same level of accuracy, even though they are much more computationally affordable compared to full-enumerated networks. We finally illustrate how the approximate PLOS-net scale to large-size instances.

This paper introduces the Decay Burst-based Multi-layered Cortical Learning Algorithm (Decay-BM-CLA), designed for forecasting time-series data with smoothly changing variation patterns. CLA is a neocortex-inspired forecasting algorithm that predicts time-series data by dynamically adjusting the states of memory and linking elements within the predictor. An extended version, BM-CLA, has a dual CLA predictor comprising the upper and lower layers to handle multiple variation patterns. The lower layer receives time-series data, while the upper layer detects changes in variation patterns based on the success or failure of predictions in the lower layer and adjusts the states in the lower layer to fit the current variation pattern. However, conventional BM-CLA faces difficulty in accurately forecasting time-series data with smoothly changing variation patterns. This limitation arises from its mechanism, which alters the states in the upper layer only when detecting a change in variation patterns. The states representing the pattern are then maintained until the next detection. In response, the proposed Decay-BM-CLA determines the states in the upper layer using active strengths that decay at every time step. Consequently, the states in the upper layer gradually change as time progresses, facilitating the adjustment of states in the lower layer to smoothly match the changing variation patterns in the data. This paper conducts experiments using artificial time-series data with smoothly changing variation patterns and real-world time-series data, including seasonal variations such as electricity consumption and temperature variations. Experimental results demonstrate that the proposed Decay-BM-CLA outperforms a neural network-based Online-LSTM, the latest FSNet, and conventional CLA variants in terms of prediction accuracy on these time-series data.

Since we cannot guarantee that the global optimal solution is included within a “pre-determined” search space in unknown problems such as real world problems, this paper addresses the “unbounded” search space exploration in swarm optimization. For this issue, this paper proposes the following three methods that dynamically extend the search area: Dynamic Search Area Exploration based on Gradient (DSAEG), which preferentially searches the area of a high gradient of solution space, Dynamic Search Area Exploration based on Novelty (DSAE-N), which preferentially searches the area where is far from the current search area, and Dynamic Search Area Exploration based on Gradient and Novelty (DSAE-GN), which integrates DSAE-G with DSAE-N. To investigate the effectiveness of the proposed three methods, this paper evaluates them in the six multi-modal optimization problems by applying them into Niching Migratory Multi-Swarm Optimiser (NMMSO) based on Particle Swarm Optimization (PSO). The intensive comparison of the proposed methods with NMMSO have been revealed the following implications: (1) DSAE-GN quickly finds almost of the global optimal solutions regardless of the shape of the evaluation function while DSAE-G and DSAE-N cannot always find them; and (2) DSAE-GN can find almost of the global optimal solutions even if the search area is not given, while NMMSO cannot find them even if the search area which contains all global optimal solutions is given.

To mine high-dimensional rules in Learning Classifier Systems (LCSs) through a reduction of the dimensionality of input data, this paper proposes a novel approach that indirectly learns the rules in the "latent space" based on the rewards of the reconstructed rules in the "observation space". We call this approach Learning Strategy by exploring rules in Observation space via Latent space (LS-OvL), which is based on two rule representations in the observation and latent space. Concretely, LS-OvL explores the rules by searching the latent space as the reduced dimensional input space by an autoencoder and evaluates them in the observation space by reconstructing them from the latent space. Such a design is significant because it prevents the generation of inaccurate rules during the reconstitution process from the latent space to the observation space. Through a comparison LS-OvL with the conventional learning strategy, which explores and evaluates the rules in the only latent space and reconstructs them in the observation space, the experimental results show that (1) LS-OvL outperforms the conventional learning strategy in terms of the acquired reward and the population size, and (2) LS-OvL can generate explainable and classifiable high-dimensional rules.

This paper proposes the Beta Distribution based XCS Classifier System (called j3-XCS) as the novel XCS having the new representation (1) that can handle curved surface hyperpolyhedral conditions, including hyperellipsoids, (2) that can “quickly” and “stably” evolve classifiers that appropri-ately classify the area, and (3) that is robust to the initial hyperparameters of the representation. Concretely, j3-XCS is composed of classifiers that condition part in each dimension is represented by the beta distribution that can change a flexible distribution shape according to its parameters. Through the intensive experiments of the different types of continuous space problems, the following implications have been revealed: (1) j3-X CS can show higher classification performance and function approximation performance with fewer classifiers than other XCSs with the conventional representations such as XCS with the hyperrectangular representation (i.e., XCSR) and XCS with the hyperellipsoidal representations (i.e., hyperellipsoid-based XCS); (2) fJ-XCS can quickly and stably evolve the classifiers that can appropriately match the line and curved shapes in comparison with XCSR and the ellipsoidal-based XCS; and (3) while the performance of the conventional XCSs is highly sensitive to the hyperparameter that defines the generality of the covering classifier, the performance of fJ-XCS is the most robust to its values.

This work proposes a supervised multi-objective optimization algorithm that assumes the existence of non-dominated solutions that serve as supervised data. In an expensive multi-objective optimization problem, it is required to obtain a solution set that approximates the Pareto front with an extremely small number of function evaluations. We often know some good solutions in advance when dealing with optimization problems. In this case, instead of generating solutions from scratch, generating solutions from known good solutions can be a shortcut for optimization. The proposed method estimates the Pareto front and Pareto set using the response surface methodology with existing non-dominated solutions as the supervised data. The proposed method selects a subset of objective vectors on the estimated Pareto front and obtains the subset as the solution set. Experimental results using DTLZ and WFG test suites show that the proposed method works well even with only ten non-dominated solutions and 150 function evaluations.

This work revealed a relationship between a multi-objective optimization problem and single-objective optimization problems that exist in the multi-objective problem. This work focused on combinatorial problems and investigated the relations between the local optima networks of the single-objective problems and the Pareto optima network of the multi-objective problem. Each of their networks has a graph structure. We divided the entire network into subgraphs. Each subgraph was called a component and characterized by overlapping relations between the single-objective local optima networks and the multi-objective Pareto optima network. Results on multi-objective landscape problems showed that most Pareto optimal solutions were reachable from the single-objective local optimal solutions. This tendency was emphasized by increasing the number of objectives and the objective correlation. The number of co-variables impacted the number of cross-link relations between the single-objective local optima networks and the multi-objective Pareto optima network. The results suggested that searching for single-objective problems is a clue to multi-objective optimization.

This paper focuses on the matching mechanism of Learning Classifier System (LCS) in a continuous space and proposes a novel matching mechanism based on Gaussian distribution. This mechanism can match the “area” instead of the “point (one value)” in the continuous space unlike the conventional LCS such as XCSR (XCS with Continuous-Valued Inputs). Such an area matching contributes to generating the rules (called classifiers) with less-overlapped with other rules. Concretely, the proposed area matching mechanism employed in XCSR using VAE can generate appropriate classifiers for latent variables with high-dimensional inputs by VAE and create a human-interpretable observation space of human-interpretable classifiers. Since the latent variable in VAE is followed by Gaus-sian distribution, the following three matching mechanisms are compared: (i) the (single) point matching that selects the classifier which condition covers the mean of Gaussian distribution M; (ii) the multiple points matching that selects the classifier which condition covers the data sampled from Gaussian distribution (M, u); and (iii) the area matching that selects the classifier which condition roughly covers a certain area of Gaussian distribution (M, o). Through the intensive experiments on the high dimension maze problem, the following implications have been revealed: (1) the point matching in XCSR with VAE generates the ambiguous classifiers which conditions are overlapped with the other classifiers with the different action; (2) the sampling multiple points matching in XCSR with VAE has a potential of generating the less-overlapped classifiers by improving the data set through sampling. (3) the proposed area matching can generate the less-overlapped classifiers with the same learning steps, which corresponds to the time of the point matching.

This paper focuses on the concept of "absumption" which restrains over-general rules by decomposing them into several concrete rules, proposes the novel "absumption" for continuous spaces by improving the conventional absumption to achieve high performance (e.g., the acquired rewards) in a noisy environment, and integrates it into the XCS for real-valued inputs (XCSR) to evaluate it through a comparison with the conventional absumption. Concretely, the proposed absumption mechanism based on Overgenerality and Condition-clustering based specialization (called Absumption-OC) manipulates the balance between the Overgenerality of the rules and the specialization of Condition of the rules. Through the intensive experiments of three different types of continuous space problems, the following implications have been revealed: (1) XCSR with Absumption-OC shows the statistically significant performance in the acquired reward, the system error, and the population size against XCSR with the conventional absumption; and (2) this effectiveness of Absumption-OC becomes to be clear in noisy reward environments in comparison within noiseless reward environments.

This paper focuses on the rule representation in Learning Classifier System (LCS) and proposes a flexible representation mechanism that can generate a variety of shapes of its matching area with one rule condition of a classifier. Concretely, the proposed representation mechanism changes the shape of the matching area according to the logical product or multiplication of the values of the probability distribution in the multiple dimension. As one of its implementation, this paper introduces the beta distribution in XCS for continuous space. Through intensive experiments of different types of continuous space problems, the following implications have been revealed: XCS based on the beta distribution (1) can match line and curved shapes using the same classifier; (2) can obtain higher reward values with the same or fewer classifiers than the conventional representations (i.e., the hyperrectangular and hyperellipsoidal representations); and (3) is robust to variations in the shape of the class boundary, contributing to stable classification performance.

This paper proposes ELPSDeCS (Encoding, Learning, "Plausible" Sampling, and Decoding Classifier System) by extending ELSDeCS (Encoding, Learning, Sampling, and Decoding Classifier System) to increase both the accuracy and interpretability of the generated classifiers which matches the high-dimensional input such as images. The experimental results on the complex multi-class classification problem of the handwritten numerals show that both the accuracy and interpretability of ELPSDeCS are higher than that of ELSDeCS.

In this paper, we propose MVN-ELSDeCS, which is a combination of VAE, a dimensionality reduction network, and MVN-XCSR, an XCSR extended to a distributional representation. In addition, additional learning of high-dimensional data with XCS is performed to reduce the information loss in learning caused by dimensionality reduction. We applied the proposed method to the benchmark problem of 10-class classification of handwritten digit images, and the experimental results have the following implications: 1) MVN-XCSR, which is a component of MVN-ELSDeCS, not only shows higher classification performance from the early stage of training in the dimensionally compressed latent space, but also 2) the reconstructed rules generated by MVN-ELSDeCS shows higher classification performance for the original high-dimensional data. Furthermore, 3) by applying additional learning with XCS to the reconstructed rules, the classification accuracy of rules for the 10-class classification task was significantly improved.

This work proposes an arrangement method of weight vectors using virtual objective vectors supplementing the Pareto front estimation. In decomposition-based evolutionary multi-objective optimization, weight vectors decompose the Pareto front. Appropriate weight vector distribution depends on the Pareto front shape, which is generally unknown before the search. Objective vectors of obtained non-dominated solutions become a clue to estimate the Pareto front shape and arrange an appropriate weight vector set. However, a sizeable objective vector set is required for a high-quality Pareto front estimation and weight vector arrangement. The proposed method generates and utilizes a virtual objective vector set based on the objective vectors of obtained non-dominated solutions and an extended weight vector set for the Pareto front estimation. Experimental results using benchmark problems with different Pareto front shapes show that the virtual objective vectors generated from a limited number of actual objective vectors contribute to improving the search performance of decomposition-based evolutionary multi-objective optimization.

This paper focuses on the covering mechanism in Learning Classifier System (LCS) which generates a new classifier (i.e., an if-then rule) when no classifier matches the input. We propose Local Covering, a niche-based rule generation method for XCS, to reduce the sensitivity of a hyperparameter that determines the generalization probability of initial rules. In Local Covering, the system looks up classifiers in the population and finds the closest match from the input. After that, the selected classifier is copied as the covering classifier and its condition is generalized to cover the input. To integrate the Local Covering method with XCS, XCS-LCPCI (XCS with Local Covering for Previously Covered Inputs) is proposed, which executes Local Covering only if the input has been previously covered by the covering processes. The experimental results with three different problems show that XCS-LCPCI successfully acquires the general classifiers with any of six different parameter settings, while the performance of the conventional XCS varies depending on the parameter settings.

This work focuses on the environmental selection methods incorporated in several evolutionary multi-objective optimization (EMO) algorithms for sampling representative nondominated solutions from a large non-dominated solution set. Evolutionary multi- and many-objective optimization generally provides a large set of non-dominated solutions. They are useful for precisely approximating the Pareto front but harm decision making when selecting one solution among them. Sampling and presenting a representative set of solutions is a promising method for addressing this issue. The selection of a subset of solutions from a large set of solutions is a type of combinatorial optimization problem. Its difficulty is increased by increasing the size of the non-dominated solution set, because the number of selection combinations of the solutions increases exponentially. This work focuses on environmental selection as a reasonable method to sample a solution subset from a large set. We compare 17 environmental selection methods incorporated in EMO algorithms and show that the one-by-one selection or deletion approach is suitable for sampling a representative nondominated set.

Evolutionary algorithms (EAs) are often used for multimodal optimization which is modeled as real-world problem. However, most EAs still not enough to find multiple local optima because of the concept of the solution movement between nearest neighbor solutions. This paper proposes the niche radius-based bat algorithm (NRBA), which is designed to find multiple local optima in multimodal optimization. We focus on bat algorithm (BA) which deals with the trade-off between exploration and exploitation in the evolutionary process and extend it with niche radius which can control and modify the search space of solutions to avoid overlapping the found optima. In detail, the proposed BA consists of three search phases: (i) the movement from neighbors for avoiding overlapping the same found optima; (ii) the exploitation for searching nearby the best solution of its domain with Niche Radius; (iii) the exploration for searching randomly in all domain of the radius. In order to evaluate the performance of NRBA, this paper employs some test-bed multimodal functions and compare NRBA with BA and NSBA. The experimental results suggest that NRBA is able to provide the better search performance than BA and NSBA to find multiple global optima in most of benchmark functions.

This paper proposes a novel learning classifier system (LCS) framework named ELSDeCS (Encoding, Learning, Sampling, and Decoding Classifier System) which can employ any dimensionality reduction method as pre-processing of learning and has its own components for extracting interpretable rule representations. We also propose two LCSs as examples of ELSDeCS. The first is DCAXCSR2, which is a revised version of the conventional system, and the second is VAEXCSR, which employs a deep generative model for dimensionality reduction. The experimental results on a classification task of handwritten digits show that only VAEXCSR can extract useful rule representations thanks to its robustness of decoding newly generated samples.

This paper proposes Complex-Valued-based Learning Classifier System (CVLCS) that can learn an appropriate policy for the POMDP environments by extending Complex-Valued Reinforcement Learning (CVRL). Concretely, CVLCS explores the optimal policy by not only evolving classifiers but also updating Q-values (i.e., strength) of evolved ones, while CVRL explores the optimal policy by only updating Q-values of the state-action pairs prepared beforehand. To investigate the effectiveness of CVLCS, this paper applies it to various types of the POMDP environments. The experimental results have revealed that (1) CVLCS can derive the good performance which is close to the optimal one and shows such a performance faster than the conventional methods (i.e., Q-Learning as one of CVRL and ZCSM as one of LCS) and (2) CVLCS can stably derive the good performance even in the difficult environments where the conventional methods fail to derive good performance.

Accuracy based Learning Classifier System (XCS) acquires generalized classifiers that can guess the appropriate output for all inputs with a small number of the classifiers in ideal environments where there is no uncertainty in inputs, outputs, and rewards. However, if uncertainty is included in any of inputs, outputs, and rewards, XCS cannot be properly learned and cannot stably acquire generalized classifiers. We proposed Learning Classifier Systems that can properly learn in environments to which specific noise is added. These methods are divided into two types: (i) statistical table based XCS that record the mean of rewards acquired in all input-output pairs, and (ii) non-statistical table based XCS that do not record their values. This paper applies these methods to multiple noise environments and clarifies the features of each method.

This paper proposes a parallel asynchronous evolutionary algorithm (EA) with different asynchrony and verifies its effectiveness on multi-objective optimization problems. We represent such EA with different asynchrony as semi-asynchronous EA. The semi-asynchronous EA continuously evolves solutions whenever a part of solutions in the population completes their evaluations in the master-slave parallel computation environment, unlike a conventional synchronous EA, which waits for evaluations of all solutions to generate next population. To establish the semi-asynchronous EA, this paper proposes the asynchrony parameter to decide how many solutions are waited, and clarifies the effectual asynchrony related to the number of slave nodes. In the experiment, we apply the semi-asynchronous EA to NSGA-II, which is a well-known multi-objective evolutionary algorithm, and the semi-asynchronous NSGA-IIs with different asynchrony are compared with synchronous one on the multi-objective optimization benchmark problems with several variances of evaluation time. The experimental result reveals that the semi-asynchronous NSGA-II with low asynchrony has possibility to perform the best search ability than the complete asynchronous and the synchronous NSGA-II in the optimization problems with large variance of evaluation time.

This paper focuses on a generalization of classifiers in noisy problems and aims at exploring learning classifier systems (LCSs) that can evolve accurately generalized classifiers as an optimal solution in several environments which include different type of noise. For this purpose, this paper employs XCS-CRE (XCS without Convergence of Reward Estimation) which can correctly identify classifiers as either accurate or inaccurate ones even in a noisy problem, and investigates its effectiveness in several noisy problems. Through intensive experiments of three LCSs (i.e., XCS as the conventional LCS, XCS-SAC (XCS with Self-adaptive Accuracy Criterion) as our previous LCS, and XCS-CRE) on the noisy 11-multiplexer problem where reward value changes according to (a) Gaussian distribution, (b) Cauchy distribution, or (c) Lognormal distribution, the following implications have been revealed: (1) the correct rate of the classifier of XCS-CRE and XCS-SAC converge to 100% in all three types of the reward distribution while that of XCS cannot reach 100%; (2) the population size of XCS-CRE is smallest followed by that of XCS-SAC and XCS; and (3) the percentage of the acquired optimal classifiers of XCS-CRE is highest followed by that of XCS-SAC and XCS.

XCS is the most popular type of Learning Classifier System, but setting optimum parameter values is more of an art than a science. Early theoretical work required the impractical assumption that classifier parameters had fully converged with infinite update times. The aim of this work is to derive a theoretical condition to mathematically guarantee that XCS identifies maximally accurate classifiers, such that subsequent deletion methods can be used optimally, in as few updates as possible. Consequently, our theory provides a universally usable setup guide for three important parameter settings; the learning rate, the accuracy update and the threshold for subsumption deletion. XCS with our best parameter settings solves the 70-bit multiplexer problem with only 21% of instances that the standard XCS setup needs. On a highly class-imbalanced multiplexer problem with inaccurate classifiers having more than 99.99% classification accuracy, our theory enables XCS to identify only 100% accurate classifiers as accurate and thus obtain the optimal performance.

XCS (Accuracy-based learning classifier system) can acquire accurate classifiers on the basis of consistent reward, but it does not always receive the consistent reward in real world problems even if it provides the same output for the same input. Such a situation prevents XCS from reducing the number of overspecific accurate classifiers by the subsumption mechanism. This means that XCS finds it hard to acquire the optimal classifiers. For this issue, our previous research proposed XCS-MR (XCS based on Mean of Reward) which can reduce the number of classifiers even in the environments where the size of the rewards is uncertain. However, XCS-MR requires a large amount of learning data to correctly determine the accuracy of classifiers because XCS-MR needs to record the average and variance of the rewards in all input-output space. To overcome this problem, this paper proposes a new XCS that can reduce the number of the classifiers even in the uncertain reward environments without recording the average and variance of the rewards in all input-output space. This paper shows the effectiveness of the proposed XCS through the experiments.

A default hierarchy is set of rules containing one or more exceptions to one or more default rules e.g. all dogs are friendly, except my neighbour's. Default hierarchies were the subject of considerable interest in early Learning Classifier Systems research, but they were abandoned due to the considerable difficulty of solving the credit assignment problems they involve. The most popular Learning Classifier System, XCS, and its derivatives do not support default hierarchies because in XCS each rule must be accurate, whereas in a default hierarchy an overgeneral rule may be overridden by a correct rule. In this work we enable XCS to evolve minimal default hierarchies by allowing two conditions in one rule, but evaluating only the accuracy and fitness of the whole as a whole. This simple step avoids the credit assignment issues faced by earlier systems. We call this XCS-DH. Preliminary evaluation of XCS-DH on a number of Boolean functions indicates a strong tendency to exploit the increased expressiveness of its rules. On some functions we observe slower learning and a larger population size, which we attribute to the increased rule expressiveness, which increases the search space. However, we also observe that in a problem that is particularly suitable for XCS-DH representation, and that is sufficient difficult for XCS, XCS-DH's learning rate is faster than XCS's. We take this as confirmation of the potential of learning default hierarchies with XCS-DH.

This paper proposes a novel Learning Classifier System (LCS) which integrates Deep AutoEncoder named DAE to solve high-dimensional problems. In the proposed LCS, DAE starts to compress (encode) an environmental input as a high-dimensional information to an input of LCS as a low-dimensional information and decompresses (decodes) an output of LCS as a low-dimensional information to a system output as a high-dimensional information. Since the compressed inputs are encoded by real value, this paper employs XCSR (i.e., an LCS with real value coding) and combines XCSR with DAE. In order to investigate the effectiveness of the proposed LCS, XCSR with DAE, this paper conducts the preliminary experiment on the benchmark classification problem, i.e., 6-Multiplexer problem. The intensive experiments on the compression from 6 to 5 bits have revealed the following implications: (1) XCSR with DAE performs as well as XCSR even learning from the compressed input data; and (2) XCSR with DAE successfully decodes the compressed rules to extract the rules which are the same as those learned with not compressed input data.

In evolutionary multi-objective optimization, each solution in the population generally has two roles. The first one is to approximate a part of the Pareto front, and the second one is to be a variable information resource to generate offspring. In many-objective optimization involving four or more conflicting objectives, solutions in the population have to be sparsely distributed in the objective space and the variable space to approximate a high-dimensional Pareto front, and each solution faces the difficulty to play the second role since variables are drastically individualized in the population. To overcome this problem, we focus on MOEA/D algorithm framework and propose a method to introduce supplemental weight vectors and solutions which maintain variable information resource to enhance the solution search for each part of the Pareto front. Experimental results using many-objective knapsack problems show that the supplemental weight vectors and solutions improves the search performance of MOEA/D by improving the diversity of the obtained solutions.

This paper proposes a simple modification of the Cuckoo Search called CS for a dynamic environment. In this paper, we consider a dynamic optimization problem where the global optimum can be cyclically changed depending on time. Our modified CS algorithm holds good candidates in order to effectively explore the search space near those candidates with an intensive local search. Our first experiment tests the prosed method on a set of static optimization problems, which aims at evaluating the potential performance of the proposed method. Then, we apply it to a dynamic optimization problem. Experimental results on the static problems show that the proposed method derives a better performance than the conventional method, which suggest the proposed method potentially has a good capability of finding a good solution. On the dynamic problem, the proposed method also performs well while the conventional method fails to find a better solution.

In evolutionary constrained multi-objective optimization, the directed mating utilizing useful infeasible solutions having better objective function values than feasible solutions significantly contributes to improving the search performance. This work tries to further improve the effectiveness of the directed mating by focusing on the search directions in the objective space. Since the conventional directed mating picks useful infeasible solutions based on Pareto dominance, all solutions are given the same search direction regardless of their locations in the objective space. To improve the diversity of the obtained solutions in evolutionary constrained multi-objective optimization, we propose a variant of the directed mating using the inverted PBI (IPBI) scalarizing function. The proposed IPBI-based directed mating gives unique search directions to all solutions depending on their locations in the objective space. Also, the proposed IPBI-based directed mating can control the strength of directionality for each solution's search direction by the parameter θ. We use discrete m-objective k-knapsack problems and continuous mCDTLZ problems with 2-4 objectives and compare the search performances of TNSDM algorithm using the conventional directed mating and the proposed TNSDM-IPBI using IPBI-based directed mating. The experimental results shows that the proposed TNSDM-IPBI using the appropriate θ* achieves higher search performance than the conventional TNSDM in all test problems used in this work by improving the diversity of solutions in the objective space.

A learning strategy in Learning Classifier Systems (LCSs) defines how classifiers cover a state-action space in a problem. Previous analyses in classification problems have empirically claimed an adequate learning strategy can be decided depending on the types of noise in the problem. This issue is still arguable from two aspects. First, there lacks comparison of learning strategies in reinforcement learning problems with different types of noise. Second, when we can claim so, a further issue is how should classifiers cover the state-action space in order to improve the stability of LCS performance on as many types of noise as possible? This paper first attempts to empirically conclude these issues on a version of LCSs (i.e., the XCS classifier system). That is, we present a new concept of learning strategy for LCSs, and complement that claim by comparing it with the existing learning strategies on a reinforcement learning problem. Our learning strategy covers all state-action pairs but assigns more classifiers to the highest-return action at each state than other actions. Our results support that claim that existing learning strategies have dependencies on the types of noise in reinforcement learning problems. However, our learning strategy improves the stability of XCS performance compared with the existing strategies on all types of noise employed in this paper.

This paper explores a novel Learning Classifier System (LCS) that can detect shoplifting behavior from the class-imbalanced sequence data of customer-behaviors. The shoplifting behavior detection is related to the sequence labeling as a time-series classification. More importantly, the target problem has a difficulty of the class-imbalanced problem in addition to the time-series classification because the number of data of shoplifters might be much fewer than that of customers who do not shoplift. To tackle this difficult issue, this paper proposes a feature extraction method for the sequence labeling in the class-imbalanced problem and applies it into XCS-SL (LCS for sequence labeling). The proposed LCS (called as XCS-SLFEM (XCS-SL for Feature Extraction of Minority class data)) extracts the features of the minority class from those of the majority one by representing them as the classifiers. The intensive simulation using the customer-behavior dataset that includes the shoplifting behaviors has revealed the following implications: (1) XCS-SLFEM shows the superior performance as compared with XCS-SL in the customer-behavior dataset including the class-imbalanced sequence data; (2) the classification accuracy of XCS-SLFEM increases as the size of memory for the sequence histories increases; and (3) XCS-SLFEM has the potential of predicting shoplifting before the shoplifters do shoplift.

This paper proposes XCS using Attribute Tracking and Feedback (XCS-ATF) that simultaneously extracts both of the generalized and specialized knowledge, and evaluates its effectiveness by investigating how the extracted knowledge contribute to deriving deep/light sleep of aged persons. The data mining of the daily activities of aged person by XCS-ATF has revealed the following implications: (1) XCS-ATF succeeds to extract the knowledge from the dataset including many contradict data; (2) XCS-ATF can extract not only the generalized knowledge as the daily activities that are usually performed with deriving deep/light sleep but also the specialized knowledge as the daily activities (e.g., birthday party) that are not often performed with deriving deep/light sleep, even though the specialized knowledge which does not often occur tends to be deleted as a noise by the general data mining methods; and (3) XCS-ATF can extract the daily activities that provides nine years younger sleep in the healthy aged persons and seven years younger sleep even in dementia persons who are hard to have a deep sleep in comparison with non-dementia persons.

This paper proposes a ship route evolutionary optimization method for competitive ship companies in the industrial logistic network, where many alliances composed of several ship companies compete with others to acquire their resources (i.e., container) for maximizing their profits. One of the significant issues in the industrial logistic network is to find the best distribution of the resources in all alliances even in a competitive market. For this purpose, this paper explores the ship route optimization method for all competitive alliances, which can find their ship routes having higher profit than their actual routes through a good distributed coordination of resources. The intensive analysis of the results on the Pacific Ocean liner route with the actual data have revealed that the following implications: (1) even in competitive situation, the proposed evolutionary optimization method succeeds to find the ship routes of all alliances which can improve their own profits in comparison with those optimized by the conventional approach and those of actual routes, and (2) the ship routes generated by the proposed method have more anchor ports than the actual ship routes while keeping the ship constraints (e.g., the type of ships that each alliance has), which contributes to obtaining the appropriate resources as a good distributed coordination.

This paper focuses on Artificial Bee Colony (ABC) algorithm in multimodal problems with dynamic environmental change, and proposes the additional improvement of ABC algorithm based on local information sharing (ABC-lis) toward robustness against environmental change speed. The additional improvement is that scout bee's phase is modified to calculate by sigmoid function. To investigate the global search ability of ABC-lis and the additional improvement, we compare these algorithms to 3 case of environmental change speeds. The experimental result revealed that the following implications: (1) ABC-lis cannot always maintains the search capability in any change speed. (2) ABC-lis with the additional improvement is able to exert a high performance at every change speed. (3) The number of bees in each local area is able to be controlled by the novel parameter Nlin ABC-lis with the additional improvement.

XCS is an accuracy-based learning classifier system (LCS) which is powered by a reinforcement algorithm. We expect it will have when the reward for a state / action pair is unstable, because it is not possible to correctly estimate the evaluation. This paper focuses on learning in a different level of an unstable reward environment and proposes XCS-URE (XCS for Unstable Reward Environment) by improving XCS for such an environment. For this purpose, XCS-URE estimates the reward distribution of the classifier (i.e., if-then rule) by using the standard deviation of the acquired reward, and adjusts the accuracy of the classifier depending on the reward distribution. In order to investigate the effectiveness of XCS-URE, this paper applies XCS and XCS-URE into the multiple unstable reward environments which have a different level of the unstable rewards added by Gaussian noise. The experiments on the modified multiplexer problems have the following implications: (1) in the environment same Gaussian noise is added, XCS cannot performs properly due to the low accuracy of the classifier in the noisy environments, while XCS-URE can perform properly by acquiring the appropriate classifiers even in such an environment; (2) in the same environment, XCS-URE can reduce the population size without decreasing the correct rate as compared to XCS; and (3) even in the environment different Gaussian noises depending on the situation are added, XCS-URE can reduce the population size without decreasing the correct rate by adjusting the accuracy of the classifier depending on the reward distribution.

This paper reports our latest experimental results on analyzing human's continuous learning ability with the reflection cost. To fill in the missing piece of reinforcement learning framework for the learning robot, we focus on two human mental learning processes, awareness as pre-learning process and reflection as post-learning process. To observe mental learning processes of a human, we propose a new method for visualizing them by the reflection subtask with invisible mazes. In our previous work, there is a strong negative correlation between the number of continuous learning stages and the reflection cost. It suggests that the continuous learner performs a very good job of the reflection subtask. To examine the reason why the non-continuous learner stops learning the task, we analyze the learner's performance of both the main learning task by achievement cost and the reflection subtask by reflection cost in each learning stage. As the experimental results, the reflection cost of the continuous learner is stable during the learning stages as compared to non-continuous learners. It suggests that the continuous learner can perform the reflection subtask in a certain amount of time, even though it becomes more difficult as the learning stage progressed.

The asynchronous evolution has an advantage when evolving solutions with excessively different evaluation time since the asynchronous evolution evolves each solution independently without waiting for other evaluations, unlike the synchronous evolution requires evaluations of all solutions at the same time. As a novel asynchronous evolution approach, this paper proposes Asynchronous Reference-based Evaluation (ARE) that asynchronously selects good parents by the tournament selection using reference solution in order to evolve solutions through a crossover of the good parents. To investigate the effectiveness of ARE in the case of evolving solutions with excessively different evaluation time, this paper applies ARE to Genetic Programming (GP), and compares GP using ARE (ARE-GP) with GP using (μ+λ) selection ((μ+λ)-GP) as the synchronous approach in particular situation where the evaluation time of individuals differs from each other. The intensive experiments have revealed the following implications: (1) ARE-GP greatly outperforms (μ+λ)-GP from the viewpoint of the elapsed unit time in the parallel computation environment, (2) ARE-GP can evolve individuals without decreasing the searching ability in the situation where the computing speed of each individual differs from each other and some individuals fail in their execution.

As an evolutionary approach to solve constrained multi-objective optimization problems (CMOPs), recently a MOEA using the two-stage non-dominated sorting and the directed mating (TNSDM) has been proposed. In TNSDM, the directed mating utilizes infeasible solutions dominating feasible solutions to generate offspring. Although the directed mating contributes to improve the search performance of TNSDM in CMOPs, there are two problems. First, since the number of infeasible solutions dominating feasible solutions in the population depends on each CMOP, the effectiveness of the directed mating also depends on each CMOP. Second, infeasible solutions utilized in the directed mating are discarded in the selection process of parents (elites) population and cannot be utilized in the next generation. To overcome these problems and further improve the effectiveness of the directed mating in TNSDM, in this work we propose an improved TNSDM introducing a method to control selection area of infeasible solutions and an archiving strategy of useful infeasible solutions for the directed mating. The experimental results on m objectives k knapsacks problems shows that the improved TNSDM improves the search performance by controlling the directionality of the directed mating and increasing the number of directed mating executions in the solution search.

This paper introduces XCS-SL, an extension of XCS for sequence labeling, a form of time-series classification where every input has a class label. Specifically, we consider sequence labeling tasks where on each time step we receive an input/class pair. In sequence labeling the correct class of an input may depend on data received on previous time stamps, so a learner may need to refer to data at previous time stamps. That is, some classification rules (called classifiers' here) must include conditions on previous inputs (a kind of memory). We assume the agent does not know how many conditions on previous inputs are needed to classify the current input, and the number of conditions/memories needed may be different for each input. Hence, using a fixed number of conditions is not a good solution. A novel idea we introduce is classifiers that have a variable-length condition to refer back to data at previous times. The condition can grow and shrink to find a suitable memory size. On a benchmark problem XCS-SL can learn optimal classifiers, and on a real-world sequence labeling task, it derived high classification accuracy and discovered interesting knowledge that shows dependencies between inputs at different times.

We study two existing Learning Classifier Systems (LCSs): XCS, which has a complete map (which covers all actions in each state), and XCSAMm, which has a best action map (which covers only the highest-return action in each state). This allows XCSAM to learn with a smaller population size limit (but larger population size) and to learn faster than XCS on well-behaved tasks. However, many tasks have dif- ficulties like noise and class imbalances. XCS and XCSAM have not been compared on such problems before. This pa- per aims to discover which kind of map is more robust to these difficulties. We apply them to a classification problem (the multiplexer problem) with class imbalance, Gaussian noise or alternating noise (where we return the reward for a different action). We also compare them on real-world data from the UCI repository without adding noise. We analyze how XCSAM focuses on the best action map and introduce a novel deletion mechanism that helps to evolve classifiers towards a best action map. Results show the best action map is more robust (has higher accuracy and sometimes learns faster) in all cases except small amounts of alternat- ing noise.

This paper focuses on cooperation among autonomous rescue agents in dynamic disaster environments, proposes Multiagent-based Artificial Bee Colony (M-ABC) algorithm by improving ABC algorithm without using global information (i.e., local information only), and investigates its effectiveness from the viewpoint of finding victim quickly and efficiently. The intensive simulations on the victim rescue in RoboCup Rescue Simulation System (RCRSS) have revealed the following implications: (1) M-ABC algorithm can rescue victims faster than the full search method as the conventional method. In particular, M-ABC distance (as one of the proposed M-ABC algorithms) can derive the highest performance; (2) M-ABC distance can keep high performance even in dynamical environments where victims move elsewhere; and (3) M-ABC distance can completely rescue victims in dynamical environments, while Ri-one method as the 2012 champion of RoboCup Rescue Simulation League (RCRSL) cannot in such a case.

This paper proposes a novel rule discovery mechanism for the XCS classifier system, which is an extension of the compact genetic algorithm (cGA) to XCS. Our rule discovery mechanism, like cGA, extracts appropriate attributes of classifier conditions through a probability vector and evolves classifiers using the extracted attributes. Unlike cGA, it newly builds the probability vector at every generations (i.e., it keeps no any probability vectors) not so that it requires XCS to have a lot of probability vectors that represent all available attributes, and mutates classifier conditions based on the extracted attributes as attribute feedback. Experimental results show that XCS with our rule discovery mechanism (or XCScGA) can reach optimal performance with fewer rule evaluations and requires smaller population sizes than XCS. Our conclusion is that the proposed rule discovery mechanism promotes a recombination of building blocks, and that our mutation operator works to repair the classifier conditions towards a compact solutions, hence, XCScGA can generate good offspring which represent maximally general, maximally accurate, and compact solutions.

An agent-based simulation developed as a tool to analyze economic system and social systems since the 1990s. Previous paper reported that the simulation results indicated that the number of agents affects the trading prices and their distributions. To analyze the effect of the number of agents, this paper analyzes the relationship between the number of agents and simulation results using XCS agents for artificial trading. We report the market price fluctuation and population size of internal model by the number of agents. The revealed the following remarkable implications: (1) increasing number of XCS agents does not affect the convergence of population size of all agents; and (2) all agents converge towards approximately form 15 % to 20 %of population size by learning classifier system of XCS agents; and (3) increasing number of XCS agents reduce the variance of the market price.

We propose a novel constrained MOEA introducing a parents selection based on a two-stage non-dominated sorting of solutions and directed mating in the objective space. In the parents selection, first, we classify the entire population into several fronts by non-dominated sorting based on constraint violation values. Then, we re-classify each obtained front by non-dominated sorting based on objective function values, and select the parents population from upper fronts. The two-stage non-dominated sorting leads to find feasible solutions having better objective function values in the evolutionary process of infeasible solutions. Also, in the directed mating, we select a primary parent from the parents population and pick solutions dominating the primary parent from the entire population including infeasible solutions. Then we select a secondary parent from the picked solutions and apply genetic operators. The directed mating utilizes valuable genetic information of infeasible solutions to enhance convergence of each primary parent toward its search direction in the objective space. We compare the search performance of the two proposed algorithms using greedy selection (GS) and tournament selection (TS) in the directed mating with the conventional CNSGA-II and RTS algorithms on SRN, TNK, OSY and m objectives k knapsacks problems. We show that the proposed algorithms achieve higher search performance than CNSGA-II and RTS on all benchmark problems used in this work.

XCS with Adaptive Action Mapping (XCSAM) evolves so- lutions focused on classifiers that advocate the best action in every state. Accordingly, XCSAM usually evolves more compact solutions than XCS which, in contrast, works to- ward solutions representing complete state-action mappings. Experimental results have however shown that, in some prob- lems, XCSAM may produce bigger populations than XCS. In this paper, we extend XCSAM with a novel selection strat- egy to reduce, even further, the size of the solutions XCSAM produces. The proposed strategy selects the parent classi- fiers based both on their fitness values (like XCS) and on the effect they have on the adaptive map. We present experi- mental results showing that XCSAM with the new selection strategy can evolve more compact solutions than XCS which, at the same time, are also maximally general and maximally accurate.

This paper proposes the extended version of Exemplar-based Learning Classifier System (ECS) called DMR-ECS which introduces the basis function for the dynamic matching selection in ECS. In comparison with our previous match selection in ECS, the proposed dynamic match selection in DMR-ECS can control an appropriate range of the match selection automatically to extract the exemplars that cover given problem space. Intensive simulation on the cargo layout problem has revealed that DMR-ECS contributes to not only improving the performance but also reducing the number of the exemplars with an appropriate range of the match selection.

This paper proposes a novel method, Hierarchical Importance Sampling (HIS), which can be used instead of converging the population for Evolutionary Algorithms based on Probabilistic Models (EAPM). In HIS, multiple populations are simulated simultaneously so that they have different diversities. This mechanism allows HIS to obtain promising solutions with various diversities. Experimental comparisons between HIS and the annealing (i.e., general EAPM) have revealed that HIS outperforms the annealing when applying to a problem of a 2D Ising model, which have many local optima. Advantages of HIS can be summarized as follows: (1) Since populations do not need to converge and do not change rapidly, HIS can build probability models with stability; (2) Since samples with better cost function values can be used for building probability models in HIS, HIS can obtain better probability models; (3)HIS can reuse historical results, which are normally discarded in the annealing.

This paper explores how to achieve goals at the macro level without controlling self-interested economic agents at the micro level and investigates the effectiveness of our claim suggesting that we make use of properties arising from interaction among economic agents to address the above issue. Intensive experiments on a complex domain problem have found the following implications: (1) as an institution design, it is important not to control economic agents at the micro level, but to promote them to self-activate in order to achieve goals at the macro level and (2) as a role of an administrative party like a government, it is important to have a clear view to determine which results are good because the timing for finding such results depends on the environmental situation and there is no guarantee that these results will converge. Other implications are summarized as follows: (1) it is important to remove evaluation level intervention to find good results, while it is important to introduce this intervention to reduce costs and (2) behavior intervention does not contribute to finding good results nor reducing costs.

This paper investigates the ability of reorganization in our organizational learning model to maintain the collective performance of multiple robots in terms of fault tolerance. In real applications using these robots, when the membership of robots is changed according to situation or some robots become defective or inoperative, it is necessary for those robots that remain to reform their organization in order to continue to complete given tasks. Through intensive simulations on the same truss construction task, the following experimental results were obtained: (1) Our model enables robots to continue to complete given tasks by reforming their organization, when a membership of robots is changed or some faulty robots are removed, and (2) The number of steps before operation does not increase very much as compared with the steps after operation.