This paper proposes a new design support approach, which efficiently utilizes the information of many non-dominated solutions obtained from evolutionary multi-criterion optimization (EMO). The proposed approach consists of four mechanisms: grouping (clustering), reducing the number of candidates (selecting the representative solutions), dimensionality reduction, and estimation.
Non-dominated solutions can be regarded as a beneficial subspace in whole search space, which have the feature of being non-inferior to other solutions. Therefore, we think the proposed approach can be used to estimate the characteristics of a problem through the interaction with the designer.
In this paper, we examine the characteristics and effectiveness of the proposed approach through computational experiments on a design problem of a counter rotating axial fan turbojet engine. A counter rotating axial fan turbojet engine with two spools is chosen for the design target of the present study. We handle this task as a seven-objective design problem.
A new approach for multi-objective robust design optimization was proposed and applied to a real-world design problem with a large number of objective functions. The present approach is assisted by response surface approximation and visual data-mining, and resulted in two major gains regarding computational time and data interpretation. The Kriging model for response surface approximation can markedly reduce the computational time for predictions of robustness. In addition, the use of self-organizing maps as a data-mining technique allows visualization of complicated design information between optimality and robustness in a comprehensible two-dimensional form. Therefore, the extraction and interpretation of trade-off relations between optimality and robustness of design, and also the location of sweet spots in the design space, can be performed in a comprehensive manner.
Firstly, we propose a spatial planning algorithm inspired by cellar automaton and spatial growth rules for spatial planning support, i.e. generating multiple subspaces and making their layouts. Their features are that there is less restrictions in the shapes, sizes, and positions of the generated subspaces and gap sizes among the subspaces are controllable. We also show the framework of our final spatial planning support system that consists of (1) a spatial layout generator including the mentioned algorithm and rules as main parts and a visualization part generating layout diagrams and (2) an optimization part which main components, i.e. evolutionary multi-objective optimization (EMO) and interactive evolutionary computation, optimize the generated spatial plans. Secondly, we make a concrete architectural room planning support system based on some parts of the said framework and confirm that the EMO makes the generated architectural room plans converge, experimentally. We confirm the performance of the system using two EMO's with four and six objectives, respectively. We also evaluate the effect of introducing a niche technique into the EMO to obtain the variety of architectural room plans. The experiments showed that the convergence of each objective over generations and variety of architectural room plans among individuals of higher scores. This experimental evaluation implies that the combination of our proposed spatial planning algorithms and spatial growth rules is applicable to spatial planning support systems.
Researches on constrained optimization using evolutionary algorithms have been actively studied. However, evolutionary algorithms often need a large number of function evaluations before a well acceptable solution can be found. Thus, in order to solve expensive or costly problems, it needs to reduce the number of function evaluations. There are many studies on reducing function evaluations by constructing an approximation model and optimizing problems using approximate values. In general, it is difficult to learn proper approximation model which has enough generalization ability, and it needs much time to learn the model. We have proposed Estimated Comparison Method, where function evaluations are efficiently reduced even when an approximation model with low accuracy is used. In the method, a comparison which compares approximate or estimated values is introduced. The potential model, which is an approximation model with low accuracy and does not need to learn model parameters, is used for approximation. Also, we have proposed the ε constrained method that can convert algorithms for unconstrained problems to algorithms for constrained problems using the ε-level comparison, which compares the search points based on the constraint violation of them. In this study, we propose an effective method to combine the ε constrained method and the estimated comparison method. We define the εDEpm by applying the method to Differential Evolution. The εDEpm realizes stable and very efficient search to solve constrained optimization problems. The advantage of the εDEpm is shown by applying it to various type of well-known 13 constrained problems and comparing the results with the results by other methods.
In this paper, we propose several types of parallel ant colony optimization algorithms with symmetric multi processing for solving the quadratic assignment problem (QAP). These models include the master-slave models and the island models. As a base ant colony optimization algorithm, we used the cunning Ant System (cAS) which showed promising performance our in previous studies. We evaluated each parallel algorithm with a condition that the run time for each parallel algorithm and the base sequential algorithm are the same. The results suggest that using the master-slave model with increased iteration of ant colony optimization algorithms is promising in solving quadratic assignment problems for real or real-like instances.
This paper aims the design of efficient and effective optimization algorithms for function optimization. For that purpose we present a new framework of the derandomized evolution strategy with covariance matrix adaptation, which combines the hybrid step size adaptation that is proposed in this paper as a robust alternate to the cumulative step size adaptation and normalization mechanism of covariance matrix. Experiment is conducted on 8 classical unimodal and multimodal test functions and the performance of the proposed strategy is compared with that of the standard strategy. Results show that the proposed strategy beats the standard strategy when the population size becomes larger than the default one, while the performance of proposed strategy is as well or better than that of the standard strategy under the default population size.
Local dominance has been shown to improve significantly the overall performance of multiobjective evolutionary algorithms (MOEAs) on combinatorial optimization problems. This work proposes the control of dominance area of solutions in local dominance MOEAs to enhance Pareto selection aiming to find solutions with high convergence and diversity properties. We control the expansion or contraction of the dominance area of solutions and analyze its effects on the search performance of a local dominance MOEA using 0/1 multiobjective knapsack problems. We show that convergence can be significantly improved while keeping a good distribution of solutions along the whole true Pareto front by using the local dominance MOEA with expansion of dominance area of solutions. We also show that dominance can be applied within very small neighborhoods by controlling the dominance area of solutions, which reduces significantly the computational cost of the local dominance MOEA.
Estimation of distribution algorithms (EDAs) are evolutionary algorithms which substitute traditional genetic operators with distribution estimation and sampling. Recently, the application of probabilistic techniques to program and function evolution has received increasing attention, and promises to provide a strong alternative to the traditional genetic programming (GP) techniques. Although PAGE (Programming with Annotated Grammar Estimation) is a state-of-art GP-EDA based on PCFG-LA (PCFG with Latent Annotations), PAGE can not effectively estimate the distribution with multiple solutions. In this paper, we proposed extended PCFG-LA named PCFG-LAMM (PCFG-LA Mixture Model) and proposed UPAGE (Unsupervised PAGE) based on PCFG-LAMM. By applying the proposed algorithm to three computational problems, it is demonstrated that our approach requires fewer fitness evaluations. We also show that UPAGE is capable of obtaining multiple solutions in a multimodal problem.
Niching GAs have been widely investigated to apply genetic algorithms (GAs) to multimodal function optimization problems. In this paper, we suggest a new niching GA that attempts to form niches, each consisting of an equal number of individuals. The proposed GA can be applied also to combinatorial optimization problems by defining a distance metric in the search space. We apply the proposed GA to the job-shop scheduling problem (JSP) and demonstrate that the proposed niching method enhances the ability to maintain niches and improve the performance of GAs.
The stabilization control of nonholonomic systems have been extensively studied because it is essential for nonholonomic robot control problems. The difficulty in this problem is that the theoretical derivation of control policy is not necessarily guaranteed achievable. In this paper, we present a reinforcement learning (RL) method with instance-based policy (IBP) representation, in which control policies for this class are optimized with respect to user-defined cost functions. Direct policy search (DPS) is an approach for RL; the policy is represented by parametric models and the model parameters are directly searched by optimization techniques including genetic algorithms (GAs). In IBP representation an instance consists of a state and an action pair; a policy consists of a set of instances. Several DPSs with IBP have been previously proposed. In these methods, sometimes fail to obtain optimal control policies when state-action variables are continuous. In this paper, we present a real-coded GA for DPSs with IBP. Our method is specifically designed for continuous domains.
Optimization of IBP has three difficulties; high-dimensionality, epistasis, and multi-modality. Our solution is designed for overcoming these difficulties. The policy search with IBP representation appears to be high-dimensional optimization; however, instances which can improve the fitness are often limited to active instances (instances used for the evaluation). In fact, the number of active instances is small. Therefore, we treat the search problem as a low dimensional problem by restricting search variables only to active instances. It has been commonly known that functions with epistasis can be efficiently optimized with crossovers which satisfy the inheritance of statistics. For efficient search of IBP, we propose extended crossover-like mutation (extended XLM) which generates a new instance around an instance with satisfying the inheritance of statistics. For overcoming multi-modality, we propose extended CCM for selection. Extended CCM always chooses the child for next generation among children and a parent which generates the children. By doing so, the diversity of the population is expected to be well maintained. Our proposals, FLIP (Functionally sophisticated Learner for IBP), consist of extended XLM and extended CCM. The effectiveness of FLIP is shown by experiments with nonholonomic control problems, a space robot, a car-like robot, and a parallel-type double inverted pendulum.
This paper presents a Genetic Algorithm (GA) for multi-objective function optimization. To find a precise and widely-distributed set of solutions in difficult multi-objective function optimization problems which have multimodality and curved Pareto-optimal set, a GA would be required conflicting behaviors in the early stage and the last stage of search. That is, in the early stage of search, GA should perform local-Pareto-optima-overcoming search which aims to overcome local Pareto-optima and converge the population to promising areas in the decision variable space. On the other hand, in the last stage of search, GA should perform Pareto-frontier-covering search which aims to spread the population along the Pareto-optimal set. NSGA-II and SPEA2, the most widely used conventional methods, have problems in local-Pareto-optima-overcoming and Pareto-frontier-covering search. In local-Pareto-optima-overcoming search, their selection pressure is too high to maintain the diversity for overcoming local Pareto-optima. In Pareto-frontier-covering search, their abilities of extrapolation-directed sampling are not enough to spread the population and they cannot sample along the Pareto-optimal set properly. To resolve above problems, the proposed method adaptively switches two search strategies, each of which is specialized for local-Pareto-optima-overcoming and Pareto-frontier-covering search, respectively. We examine the effectiveness of the proposed method using two benchmark problems. The experimental results show that our approach outperforms the conventional methods in terms of both local-Pareto-optima-overcoming and Pareto-frontier-covering search.
In interactive genetic algorithms (iGAs), computer simulations prepare design candidates that are then evaluated by the user. Therefore, iGA can predict a user's preferences. Conventional iGA problems involve a search for a single optimum solution, and iGA were developed to find this single optimum. On the other hand, our target problems have several peaks in a function and there are small differences among these peaks. For such problems, it is better to show all the peaks to the user. Product recommendation in shopping sites on the web is one example of such problems. Several types of preference trend should be prepared for users in shopping sites. Exploitation and exploration are important mechanisms in GA search. To perform effective exploitation, the offspring generation method (crossover) is very important. Here, we introduced a new offspring generation method for iGA in multimodal problems. In the proposed method, individuals are clustered into subgroups and offspring are generated in each group. The proposed method was applied to an experimental iGA system to examine its effectiveness. In the experimental iGA system, users can decide on preferable t-shirts to buy. The results of the subjective experiment confirmed that the proposed method enables offspring generation with consideration of multimodal preferences, and the proposed mechanism was also shown not to adversely affect the performance of preference prediction.
In combinatorial problems Genetic Algorithms (GAs) actualize effectual searches using genetic operators for inheritance and acquisition of characteristics. These two classes of search, focusing on inheritance or acquisition, are called, respectively, the interpolation search and the extrapolation search by introducing a distance measure. dMSXF and dMSMF is a promising interpolation/extrapolation-directed method based on neighborhood search. The previous experiments qualitatively demonstrated the effectiveness of dMSXF+dMSMF, under using sophisticated neighborhood structures and distance metrics that adequately perceive the characteristics of each problem. In this paper, we analyse overall local search performance and behavior of dMSXF and dMSMF with NK model which explains various intrinsic structures observed in combinatorial problems. In addition, parameter presumption of dMSXF and dMSMF are discussed focusing on the correlation length which is one of indicators for the epistasis intensity.
Real-coded genetic algorithms (RCGA) are expected to solve efficiently real parameter optimization problems of multimodality, parameter dependency, and ill-scale. Multi-parental crossovers such as the simplex crossover (SPX) and the UNDX-m as extensions of the unimodal normal distribution crossove (UNDX) show relatively good performance for RCGA. The minimal generation gap (MGG) is used widely as a generation alternation model for RCGA. However, the MGG is not suited for multi-parental crossovers. Both the SPX and the UNDX-m have their own drawbacks respectively. Therefore, RCGA composed of them cannot be applied to highly dimensional problems, because their hidden faults appear. This paper presents a new and robust faramework for RCGA. First, we propose a generation alternation model called JGG (just generation gap) suited for multi-parental crossovers. The JGG replaces parents with children completely every generation. To solve the asymmetry and bias of children distribution generated by the SPX and the UNDX-m, an enhanced SPX (e-SPX) and an enhanced UNDX (e-UNDX) are proposed. Moreover, we propose a crossover called REX(φ,n+k) as a generlization of the e-UNDX, where φ and n+k denote some probability distribution and the number of parents respectively. A concept of the globally descent direction (GDD) is introduced to handle the situations where the population does not cover any optimum. The GDD can be used under the big valley structure. Then, we propose REXstar as an extention of the REX(φ,n+k) that can generate children to the GDD efficiently. Several experiments show excellent performance and robustness of the REXstar. Finally, the future work is discussed.
Estimation of a caregiver's view is one of the most important capabilities for a child to understand the behavior demonstrated by the caregiver, that is, to infer the intention of behavior and/or to learn the observed behavior efficiently. We hypothesize that the child develops this ability in the same way as behavior learning motivated by an intrinsic reward, that is, he/she updates the model of the estimated view of his/her own during the behavior imitated from the observation of the behavior demonstrated by the caregiver based on minimizing the estimation error of the reward during the behavior. From this view, this paper shows a method for acquiring such a capability based on a value system from which values can be obtained by reinforcement learning. The parameters of the view estimation are updated based on the temporal difference error (hereafter TD error: estimation error of the state value), analogous to the way such that the parameters of the state value of the behavior are updated based on the TD error. Experiments with simple humanoid robots show the validity of the method, and the developmental process parallel to young children's estimation of its own view during the imitation of the observed behavior of the caregiver is discussed.
For decision by majority, each voter often exercises his right by delegating to trustable other voters. Multi-step delegates rule allows indirect delegating through more than one voter, and this helps each voter finding his delegate voters. In this paper, we propose powerful voter selection method depending on the multi-step delegate rule. This method sequentially selects voters who is most delegated indirectly. Multi-agent simulation demonstrate that we can achieve highly fair poll results from small number of vote by using proposed method. Here, fairness is prediction accuracy to sum of all voters preferences for choices. In simulation, each voter selects choices arranged on one dimensional preference axis for voting. Acquaintance relationships among voters were generated as a random network, and each voter delegates some of his acquaintances who has similar preferences. We obtained simulation results from various acquaintance networks, and then averaged these results. Firstly, if each voter has enough acquaintances in average, proposed method can help predicting sum of all voters' preferences of choices from small number of vote. Secondly, if the number of each voter's acquaintances increases corresponding to an increase in the number of voters, prediction accuracy (fairness) from small number of vote can be kept in appropriate level.
Tierra and Avida are well-known models of digital organisms. They describe a life process as a sequence of computation codes. A linear sequence model may not be the only way to describe a digital organism, though it is very simple for a computer-based model. Thus we propose a new digital organism model based on a tree structure, which is rather similar to the generic programming. With our model, a life process is a combination of various functions, as if life in the real world is. This implies that our model can easily describe the hierarchical structure of life, and it can simulate evolutionary computation through mutual interaction of functions. We verified our model by simulations that our model can be regarded as a digital organism model according to its definitions. Our model even succeeded in creating species such as viruses and parasites.
In skill discovery of a robot, the number of trials (i.e., evaluations of a score function) is highly limited since each trial takes much time and cost. In this case, memory-based learning, which retains and utilizes the history of trials, is efficient. There are mainly two approaches in studies of memory-based learning. One is an approach to estimate scores by using an approximation model of an original score function despite evaluating the score function. The other is an approach to estimate proper scores in a noisy score function. In this paper, we take another approach to find unpromising search points and skip over the evaluations by characterizing a function class which a score function belongs to. We call this approach thinning-out of search points in contrast to pruning of search trees. The main advantage of thinning-out is to make correct judgments definitely, which means that thinning-out skips over only unpromising search points, as long as the defined function class is proper. We show the properties of thinning-out by addressing the maximization problems of several test functions. In addition, we apply thinning-out to the problem of discovering of physical motions of virtual legged robots and show that the virtual robots can discover sophisticated motions that are much different from the initial motion in a reasonable amount of trials.