Creating Human Activity Recognition Systems Using Pareto-based Multiobjective Optimization

The hypervolume indicator has frequently been used for comparing evolutionary multi-objective optimization (EMO) algorithms. A reference point is needed for hypervolume calculation. However, its specification has not been discussed in detail from a viewpoint of fair performance comparison. A slightly worse point than the nadir point is usually used for hypervolume calculation in the EMO community. In this paper, we propose a reference point specification method for fair performance comparison of EMO algorithms. First, we discuss the relation between the reference point specification and the optimal distribution of solutions for hypervolume maximization. It is demonstrated that the optimal distribution of solutions strongly depends on the location of the reference point when a multi-objective problem has an inverted triangular Pareto front. Next, we propose a reference point specification method based on theoretical discussions on the optimal distribution of solutions. The basic idea is to specify the reference point so that a set of well-distributed solutions over the entire linear Pareto front has a large hypervolume and all solutions in such a solution set have similar hypervolume contributions. Then, we examine whether the proposed method can appropriately specify the reference point through computational experiments on various test problems. Finally, we examine the usefulness of the proposed method in a hypervolume-based EMO algorithm. Our discussions and experimental results clearly show that a slightly worse point than the nadir point is not always appropriate for performance comparison of EMO algorithms.

An efficient combination of multi-objective evolutionary optimization and reliability analysis for reliability-based design optimization of truss structures

Various evolutionary multiobjective optimization (EMO) algorithms have been used in the field of evolutionary fuzzy systems (EFS), because EMO algorithms can easily handle multiple objective functions such as the accuracy maximization and complexity minimization for fuzzy system design. Most EMO algorithms used in EFS are Pareto dominance-based algorithms such as NSGA-II, SPEA2, and PAES. There are a few studies where other types of EMO algorithms are used in EFS. In this paper, we apply a multiobjective evolutionary algorithm based on decomposition called MOEA/D to EFS for fuzzy classifier design. MOEA/D is one of the most well-known decomposition-based EMO algorithms. The key idea is to divide a multiobjective optimization problem into a number of single-objective problems using a set of uniformly distributed weight vectors in a scalarizing function. We propose a new scalarizing function called an accuracy-oriented function (AOF) which is specialized for classifier design. We examine the effects of using AOF in MOEA/D on the search ability of our multiobjective fuzzy genetics-based machine learning (GBML). We also examine the synergy effect of MOEA/D with AOF and parallel distributed implementation of fuzzy GBML on the generalization ability.

There is an increasing trend in the use of multi-objective evolutionary algorithms (MOEAs) to solve multi-objective optimization problems of the allocation of water resources. However, typically the outcome is a set of Pareto optimal solutions which make up a trade-off surface between the objective functions. For decision makers to choose a satisfactory alternative from a set of Pareto-optimal solutions, this paper suggests a new method based on least squares support vector machine (LSSVM) and k-means clustering for ranking the optimal solutions for the multi-objective allocation of water resources. First, the k-means clustering method was adopted to reduce the large set of solutions to a few representative solutions. Then, to capture and represent the decision maker's preferences as well as to select the most desirable alternative, the LSSVM method was applied to obtain the utility value for each representative solution. According to the magnitude of the utility values, the final priority orders of the representative solutions were determined. Finally, this methodology was applied to rank the Pareto optimal solution set obtained from the multi-objective optimization problems of water resources allocation for the water-receiving areas of the South-to-North Water Transfer Project in Hebei Province, China. Moreover, the comparisons of the proposed method with the information entropy method and the artificial neural network (ANN) model were given. The results of the comparison indicate that the proposed method has the ability to rank the non-dominated solutions of the multi-objective operation optimization model and that it can be employed for decision-making on water allocation and management in a river basin.

A large number of multi-objective optimization evolutionary algorithms(MOEAs) have been developed in the past two decades. To compare these methods rigorously, or to measure the performance of a particular MOEA quantitatively, a variety of performance measures have been proposed. In this paper, some existing widely-used performance measures are briefly reviewed and compared according different properties. Two new performance measures computing the convergence towards the Pareto front and the solution diversity on the Pareto front are proposed. And an outlook on how to further deepen insight in performance measures of MOEAs is given.

As a platform for Near space-based Earth-observation network, stratospheric airship has attracted a lot of attention in recent years, because of its advantages in endurance, coverage, cost, and durability. However, the airship has low conversion speed and large vehicle inertia, so it is significant to deploy Multi-airship Earth-observation Coverage Network (MAEON) collaboratively. To this end, this paper proposes an Earth-observation model with considerations of loading devices side-swing characteristics and field of view (FOV), and establishes a collaborative deployment model of MAEON to realize objectives of observation coverage, target point statistics, observation resolution, multi-airship community profit. To obtain the solution set of cooperative deployment problem efficiently and widely, a multi-objective evolutionary optimization algorithm (MOEA) with associated bi-criterion is proposed. Then, weight vector distribution control with dynamic adjustment is introduced to ensure that the solution set spreads more uniform and extensive. By embedding improved evolution factors, Non-Pareto criterion (NPC) and Pareto criterion (PC) based parts co-evolve and exchange information, which is effective in diversity and convergence. The normalized weight sum method is modified by adding the moderators, which are controlled by the population outcome in the iterative process. The experiment is repeated in 8 groups of data, and compared with 4 popular MOEAs. Through simulation experiments, it can be seen that the proposed algorithm has advantages in performance, universality, and stability.

Hybrid multi-objective Harris Hawk optimization algorithm based on elite non-dominated sorting and grid index mechanism

Multi-objective algorithms are aimed to obtain a set of solutions, called Pareto set, covering the whole Pareto front, i.e. the representation of the optimal set of solutions. To this end, the algorithms should yield a wide amount of near-optimal solutions with a good diversity or spread along this front. This work presents a study on different coarse-grained distribution schemes dealing with Multi-Objective Ant Colony Optimization Algorithms (MOACOs). Two of them are a variation of independent multi-colony structures, respectively having a fixed number of ants in every subset or distributing the whole amount of ants into small sub-colonies. We introduce in this paper a third method: an island-based model where the colonies communicate by migrating ants, following a neighbourhood topology which fits to the search space. All the methods are aimed to cover the whole PF, thus each sub-colony or island tries to search for solutions in a limited area, complemented by the rest of colonies, in order to obtain a more diverse high-quality set of solutions. The models have been tested by implementing them considering three different MOACOs: two well-known and CHAC, an algorithm previously proposed by the authors. Three different instances of the bi-Criteria travelling salesman problem have been considered. The experiments have been performed in a parallel environment (inside a cluster platform), in order to get a time improvement. Moreover, the system scaling factor with respect to the number of processors will be also analysed. The results show that the proposed Pareto-island model and its novel neighbourhood topology performs better than the other models, yielding a more diverse and more optimized set of solutions. Moreover, from the algorithmic point of view, the proposed algorithm, named CHAC, yields the best results on average.

Evolutionary algorithm has gained a worldwide popularity among multi-objective optimization. The paper proposes a self-adaptive evolutionary algorithm (called SEA) for multi-objective optimization. In the SEA, the probability of crossover and mutation, P cand P m, are varied depending on the fitness values of the solutions. Fitness assignment of SEA realizes the twin goals of maintaining diversity in the population and guiding the population to the true Pareto Front; fitness value of individual not only depends on improved density estimation but also depends on non-dominated rank. The density estimation can keep diversity in all instances including when scalars of all objectives are much different from each other. SEA is compared against the Non-dominated Sorting Genetic Algorithm (NSGA-II) on a set of test problems introduced by the MOEA community. Simulated results show that SEA is as effective as NSGA-II in most of test functions, but when scalar of objectives are much different from each other, SEA has better distribution of non-dominated solutions.

Fireworks Algorithm(FWA) is a recently developed swarm intelligence algorithm for single objective optimization problems which gains very promising performances in many areas. In this paper, we extend the original FWA to solve multi-objective optimization problems with the help of S-metric. The S-metric is a frequently used quality measure for solution sets comparison in evolutionary multi-objective optimization algorithms (EMOAs). Besides, S-metric can also be used to evaluate the contribution of a single solution among the solution set. Traditional multi-objective optimization algorithms usually perform a (μ + 1) strategy and update the external archive one by one, while the proposed S-metric based multi-objective fireworks algorithm(S-MOFWA) performs a (μ + μ) strategy, thus converging faster to a set of pareto solutions by three steps: 1)Exploring the solution space by mimicking the explosion of fireworks; 2)Performing a simple selection strategy for choosing the next generation of fireworks according to their S-metric; 3)Utilizing an external archive to maintain the best solution set ever found, with a new archive definition and a novel updating strategy, which can update the archive with μ solutions in a single process. The experimental results on benchmark functions suggest that the proposed S-MOFWA outperforms three other well-known algorithms, i.e. NSGA-II, SPEA2 and PESA2 in terms of the convergence measure and covered space measure.

Human activity recognition is concerned with identifying the specific movement of a person based on sensor data. In recent years, many different techniques have been proposed for modelling and recognising human activities, with a specific focus on the development of approaches to classifying human activities using deep learning techniques. The research presented in this paper proposes a fuzzy feature representation approach to represent occupancy sensor data, along with a Convolutional Neural Network Classifier (CNNC) for human activity modelling and recognition. Sensory data gathered from a home environment are converted into occupancy data representing human activities and then fuzzified before being fed as inputs into the CNNC. The learning capability of CNNC allows the model to learn the relationship between the fuzzified inputs and their corresponding output activities during training mode. The relations learned in the trained CNNC model are then used to identify human activity patterns and classify these when the testing dataset is applied. The proposed method is evaluated using a dataset representing activities of daily living for a single user gathered from a real-home environment.

In multi-objective Bayesian optimization, an infill criterion is an important part, as it is the indicator to evaluate how much good a new set of solutions is, compared to a Pareto-front approximation set. This paper presents a deterministic algorithm for computing the Expected R2 Indicator for bi-objective problems and studies its use as an infill criterion in Bayesian Global Optimization. The R2-Indicator was introduced in 1998 by M. Hansen and A. Jaszkiewicz for performance assessment in multi-objective optimization and is more recently also used in indicator-based multi-criterion evolutionary algorithms (IBEAs). In Bayesian Global Optimization, we propose the Expected R2-indicator Improvement (ER2I) as an infill criterion. It is defined as the expected decrease of the R2 indicator by a point that is sampled from a predictive Gaussian distribution. The ER2I can also be used as a pre-selection criterion in surrogate-assisted IBEAs. It provides an alternative to the Expected Hypervolume-Indicator Improvement (EHVI) that requires a reference point, bounding the Pareto front from above. In contrast, the ER2I works with a utopian reference point that bounds the Pareto front from below. In addition, the ER2I supports preference modelling with utility functions and its computation time grows only linearly with the number of considered weight combinations. It is straightforward to approximate the ER2I by Monte Carlo Integration, but so far a deterministic algorithm to solve the non-linear integral remained unknown. We outline a deterministic algorithm for the computation of the bi-objective ER2I with Chebychev utility functions. Moreover, we study monotonicity properties of the ER2I w.r.t. parameters of the predictive distribution and numerical simulations demonstrate fast convergence to Pareto fronts of different shapes and the ability of the ER2I Bayesian optimization to fill gaps in the Pareto front approximation.

In the past few years, multi-objective optimization algorithms have been extensively applied in several fields including engineering design problems. A major reason is the advancement of evolutionary multi-objective optimization (EMO) algorithms that are able to find a set of non-dominated points spread on the respective Pareto-optimal front in a single simulation. Besides just finding a set of Pareto-optimal solutions, one is often interested in capturing knowledge about the variation of variable values over the Pareto-optimal front. Recent innovization approaches for knowledge discovery from Pareto-optimal solutions remain as a major activity in this direction. In this article, a different data-fitting approach for continuous parameterization of the Pareto-optimal front is presented. Cubic B-spline basis functions are used for fitting the data returned by an EMO procedure in a continuous variable space. No prior knowledge about the order in the data is assumed. An automatic procedure for detecting gaps in the Pareto-optimal front is also implemented. The algorithm takes points returned by the EMO as input and returns the control points of the B-spline manifold representing the Pareto-optimal set. Results for several standard and engineering, bi-objective and tri-objective optimization problems demonstrate the usefulness of the proposed procedure.

Big Data enforces the usage of data mining techniques to provide the user valuable insights. There is a broad range of data mining and machine learning techniques tackling different tasks. Generic approaches are classification algorithms, which label given data points by a pretrained model. Decision tree-based classification algorithms are often used, as they provide a human-explainable model, which can be represented by simple induced rules. In order to present the classification results and the concrete model to the user, there exist for both problems a set of different solutions. Current visualizations either project labeled data into the plane or three-dimensional space, or the visualizations illustrate the decision tree rules as e.g. graph structures. But they lack to provide a possibility to show both, data and the model, within a single plot. Therefore, we propose a projection strategy to present both decision tree model and data in a single plot. Furthermore, we developed an interactive visualization to showcase the proposed approach and evaluated the visualization on open-source datasets. The results show that the plots can be computed in short time and projection adjustments are reasonably low.

Multi-objective as well as dynamic characteristics appear in many real-world problems. In order to use multi-objective evolutionary optimization algorithms (MOEA) efficiently, a systematic analysis of the algorithms’ behavior in dynamic environments by means of dynamic test functions is necessary. These functions can be classified into problems with changing Pareto sets and/or Pareto fronts with different dynamic criteria. Thus, a test suite with existing benchmark functions having dynamic behavior and new designed dynamic test functions for yet uncovered cases is proposed. Convergence and solution distribution features of modern MOEA, namely NSGA-II, SPEA2, and MSOPS using different variation operators (Simulated Binary Crossover with Polynomial Mutation and Differential Evolution) will be analyzed. For this reason, a new path integral metric is introduced. Especially the transfer of singleobjective results and the ability of the algorithms to use historically evolved population properties will be discussed.