Patients who are undergoing physical rehabilitation, benefit from feedback that follows from reliable assessment of their cumulative performance attained at a given time. In this paper, we provide a method for the learning of the recovery trajectory of an individual patient, as they undertake exercises as part of their physical therapy towards recovery of their loss of movement ability, following a critical illness. The difference between the Movement Recovery Scores (MRSs) attained by a patient, when undertaking a given exercise routine on successive instances, is given by a statistical distance/divergence between the (posterior) probabilities of random graphs that are Bayesianly learnt using time series data on locations of 20 of the patient's joints, recorded on an e-platform as the patient exercises. This allows for the computation of the MRS on every occasion the patient undertakes this exercise, using which, the recovery trajectory is drawn. We learn each graph as a Random Geometric Graph drawn in a probabilistic metric space, and identify the closed-form marginal posterior of any edge of the graph, given the correlation structure of the multivariate time series data on joint locations. On the basis of our recovery learning, we offer recommendations on the optimal exercise routines for patients with given level of mobility impairment.

Abstract In this study, we propose a new genetic algorithm that uses a statistical-based chromosome replacement strategy determined by the empirical distribution of the objective function values. The proposed genetic algorithm is further used in the training process of a multiplicative neuron model artificial neural network. The objective function value for the genetic algorithm is the root mean square error of the multiplicative neuron model artificial neural network prediction. This combination of methods is proposed for a particular type of problems, that is, time-series prediction. We use different subsets of three stock exchange time series to test the performance of the proposed method and compare it against similar approaches, and the results prove that the proposed genetic algorithm for the multiplicative neuron model of the artificial neural network works better than many other artificial intelligence optimization methods. The ranks of the proposed method are 1.78 for the Nikkei data sets, 1.55 for the S&P500 data sets and 1.22 for the DOW JONES data sets for data corresponding to different years, according to the root mean square error, respectively. Moreover, the overall mean rank is 1.50 for the proposed method. Also, the proposed method obtains the best performance overall as well as the best performance for all the individual tests. The results certify that our method is robust and efficient for the task investigated.

We investigate the learning of quantitative structure activity relationships (QSARs) as a case-study of meta-learning. This application area is of the highest societal importance, as it is a key step in the development of new medicines. The standard QSAR learning problem is: given a target (usually a protein) and a set of chemical compounds (small molecules) with associated bioactivities (e.g. inhibition of the target), learn a predictive mapping from molecular representation to activity. Although almost every type of machine learning method has been applied to QSAR learning there is no agreed single best way of learning QSARs, and therefore the problem area is well-suited to meta-learning. We first carried out the most comprehensive ever comparison of machine learning methods for QSAR learning: 18 regression methods, 3 molecular representations, applied to more than 2700 QSAR problems. (These results have been made publicly available on OpenML and represent a valuable resource for testing novel meta-learning methods.) We then investigated the utility of algorithm selection for QSAR problems. We found that this meta-learning approach outperformed the best individual QSAR learning method (random forests using a molecular fingerprint representation) by up to 13%, on average. We conclude that meta-learning outperforms base-learning methods for QSAR learning, and as this investigation is one of the most extensive ever comparisons of base and meta-learning methods ever made, it provides evidence for the general effectiveness of meta-learning over base-learning.

Studying the search behavior of evolutionary many-objective optimization is an important, but challenging issue. Existing studies rely mainly on the use of performance indicators which, however, not only encounter increasing difficulties with the number of objectives, but also fail to provide the visual information of the evolutionary search. In this paper, we propose a class of scalable test problems, called multiline distance minimization problem (ML-DMP), which are used to visually examine the behavior of many-objective search. Two key characteristics of the ML-DMP problem are: 1) its Pareto optimal solutions lie in a regular polygon in the 2-D decision space and 2) these solutions are similar (in the sense of Euclidean geometry) to their images in the high-dimensional objective space. This allows a straightforward understanding of the distribution of the objective vector set (e.g., its uniformity and coverage over the Pareto front) via observing the solution set in the 2-D decision space. Fifteen well-established algorithms have been investigated on three types of ten ML-DMP problem instances. Weakness has been revealed across classic multiobjective algorithms (such as Pareto-based, decomposition-based, and indicator-based algorithms) and even state-of-the-art algorithms designed especially for many-objective optimization. This, together with some interesting observations from the experimental studies, suggests that the proposed ML-DMP may also be used as a benchmark function to challenge the search ability of optimization algorithms.

In this paper, a variant of gray wolf optimization (GWO) that uses reinforcement learning principles combined with neural networks to enhance the performance is proposed. The aim is to overcome, by reinforced learning, the common challenge of setting the right parameters for the algorithm. In GWO, a single parameter is used to control the exploration/exploitation rate, which influences the performance of the algorithm. Rather than using a global way to change this parameter for all the agents, we use reinforcement learning to set it on an individual basis. The adaptation of the exploration rate for each agent depends on the agent's own experience and the current terrain of the search space. In order to achieve this, experience repository is built based on the neural network to map a set of agents' states to a set of corresponding actions that specifically influence the exploration rate. The experience repository is updated by all the search agents to reflect experience and to enhance the future actions continuously. The resulted algorithm is called experienced GWO (EGWO) and its performance is assessed on solving feature selection problems and on finding optimal weights for neural networks algorithm. We use a set of performance indicators to evaluate the efficiency of the method. Results over various data sets demonstrate an advance of the EGWO over the original GWO and over other metaheuristics, such as genetic algorithms and particle swarm optimization.

Function optimization and finding simultaneous solutions of a system of nonlinear equations (SNE) are two closely related and important optimization problems. However, unlike in the case of function optimization in which one is required to find the global minimum and sometimes local minima, a database of challenging SNEs where one is required to find stationary points (extrama and saddle points) is not readily available. In this article, we initiate building such a database of important SNE (which also includes related function optimization problems), arising from Science, Engineering and Economics. After providing a short review of the most commonly used mathematical and computational approaches to find solutions of such systems, we provide a preliminary list of challenging problems by writing the Mathematical formulation down, briefly explaning the origin and importance of the problem and giving a short account on the currently known results, for each of the problems. We anticipate that this database will not only help benchmarking novel numerical methods for solving SNEs and function optimization problems but also will help advancing the corresponding research areas.

The interaction of biological compounds in cells has been enforced to a proper understanding by the numerous bioinformatics projects which contributed with a vast amount of biological information. The construction of biochemical systems (systems of chemical reactions) which include both topology and kinetic rates of the chemical reactions is an NP-hard problem. In this paper we propose a hybrid architecture which combines genetic programming and simulated annealing in order to generate and optimize both the topology (the network) and the reaction rates of a biochemical systems. Simulations and analysis of two real models show promising results for the proposed method.

Component selection is a crucial problem in Component Based Software Engineering (CBSE). CBSE is concerned with the assembly of pre-existing software components that leads to a software system that responds to client-specific requirements. This work deals with the component selection problem which we formulate as multiobjective optimization, involving four objectives: the number of used components, the number of new requirements, the number of provided interfaces and the number of the initial requirements that are not in solution. We use the Pareto dominance principle to deal with the multiobjective optimization problem. Needles to say the last two objectives should be zero. Afterwards, we investigate the problem in an dynamic or changing environment for which two practical scenarios are envisaged: the repository containing the components varies over time and the system requirements change over time. The algorithm employed uses a combination of evolutionary algorithms and repair mechanism. The idea behind this was to avoid restarting the algorithm from randomly generated solutions and to make use of the ones found at the previous step.

Risk assessment is often done by human experts, because there is no exact and mathematical solution to the problem. Usually the human reasoning and perception process cannot be expressed precisely. This paper propose a light weight risk assessment system based on an Hierarchical Takagi-Sugeno model designed using evolutionary algorithms. Performance comparison is done with neuro-fuzzy and genetic programming methods. Empirical results indicate that the techniques are robust and suitable for developing light weight risk assessment models, which could be integrated with intrusion detection and prevention systems.

Differential evolution (DE) is a novel evolutionary approach capable of handling non-differentiable, non-linear and multi-modal objective functions. DE has been consistently ranked as one of the best search algorithm for solving global optimization problems in several case studies. Mutation operation plays the most significant role in the performance of a DE algorithm. This paper proposes a simple modified version of classical DE called MDE. MDE makes use of a new mutant vector in which the scaling factor F is a random variable following Laplace distribution. The proposed algorithm is examined on a set of ten standard, nonlinear, benchmark, global optimization problems having different dimensions, taken from literature. The preliminary numerical results show that the incorporation of the proposed mutant vector helps in improving the performance of DE in terms of final convergence rate without compromising with the fitness function value.

Several types of line search methods are documented in the literature and are well known for unconstraint optimization problems. This paper proposes a modified line search method, which makes use of partial derivatives and restarts the search process after a given number of iterations by modifying the boundaries based on the best solution obtained at the previous iteration (or set of iterations). Using several high-dimensional benchmark functions, we illustrate that the proposed line search restart (LSRS) approach is very suitable for high-dimensional global optimization problems. Performance of the proposed algorithm is compared with two popular global optimization approaches, namely, genetic algorithm and particle swarm optimization method. Empirical results for up to 2000 dimensions clearly illustrate that the proposed approach performs very well for the tested high-dimensional functions. © 2009 Wiley Periodicals, Inc.

Quasirandom or low discrepancy sequences, such as the Van der Corput, Sobol, Faure, Halton (named after their inventors) etc. are less random than a pseudorandom number sequences, but are more useful for computational methods which depend on the generation of random numbers. Some of these tasks involve approximation of integrals in higher dimensions, simulation and global optimization. Sobol, Faure and Halton sequences have already been used [7, 8, 9, 10] for initializing the swarm in a PSO. This paper investigates the effect of initiating the swarm with another classical low discrepancy sequence called Vander Corput sequence for solving global optimization problems in large dimension search spaces. The proposed algorithm called VC-PSO and another PSO using Sobol sequence (SO-PSO) are tested on standard benchmark problems and the results are compared with the Basic Particle Swarm Optimization (BPSO) which follows the uniform distribution for initializing the swarm. The simulation results show that a significant improvement can be made in the performance of BPSO, by simply changing the distribution of random numbers to quasi random sequence as the proposed VC-PSO and SO-PSO algorithms outperform the BPSO algorithm by noticeable percentage, particularly for problems with large search space dimensions.

Hardware/software partitioning is a crucial problem in embedded system design. In this paper, we provide an alternative approach to solve this problem using particle swarm optimization (PSO) algorithm. Performance analysis of the proposed scheme with integer linear programming, genetic algorithm and ant colony optimization technique has been compared using standard benchmark datasets, and the computer simulations reveal that the proposed approach outperforms all the meta-heuristic based existing techniques with respect to cumulative runtimes for several runs of the same program. The integer linear programming has been found to yield the optimal solutions, and the proposed swarm scheme yields sub-optimal solution, sufficiently close to the reported results obtained for integer programming.

This paper proposes a new perspective for solving systems of complex nonlinear equations by simply viewing them as a multiobjective optimization problem. Every equation in the system represents an objective function whose goal is to minimize the difference between the right and left terms of the corresponding equation. An evolutionary computation technique is applied to solve the problem obtained by transforming the system into a multiobjective optimization problem. The results obtained are compared with a very new technique that is considered as efficient and is also compared with some of the standard techniques that are used for solving nonlinear equations systems. Several well-known and difficult applications (such as interval arithmetic benchmark, kinematic application, neuropsychology application, combustion application, and chemical equilibrium application) are considered for testing the performance of the new approach. Empirical results reveal that the proposed approach is able to deal with high-dimensional equations systems.

This paper proposes a new approach for multicriteria optimization which aggregates the objective functions and uses a line search method in order to locate an approximate efficient point. Once the first Pareto solution is obtained, a simplified version of the former one is used in the context of Pareto dominance to obtain a set of efficient points, which will assure a thorough distribution of solutions on the Pareto frontier. In the current form, the proposed technique is well suitable for problems having multiple objectives (it is not limited to bi-objective problems) and require the functions to be continuous twice differentiable. In order to assess the effectiveness of this approach, some experiments were performed and compared with two well known population-based meta-heuristics. When compared to the population-based meta-heuristic, the proposed approach not only assures a better convergence to the Pareto frontier but also illustrates a good distribution of solutions. We propose a fuzzy logic controller to adapt the parameter required to control the distribution of solutions in the spreading phase. Our goal is to find a good distribution of solutions as quick as possible. From a computational point of view, both stages of the line search converge within a short time (average about 150 milliseconds for the first stage and about 20 milliseconds for the second stage). Apart from this, the proposed technique is very simple, easy to implement to solve multiobjective problems.

Traceless genetic programming (TGP) is a genetic programming (GP) variant that is used in cases where the focus is on the output of the program rather than the program itself. The main difference between TGP and other GP techniques is that TGP does not explicitly store the evolved computer programs. Two genetic operators are used in conjunction with TGP: crossover and insertion. In this paper, we will focus on applying TGP to solving multi-objective optimization problems, which are quite unusual in GP. Each TGP individual stores the output of a computer program (tree), representing a point in the search space. Numerical experiments show that TGP is able to solve the considered test problems both rapidly and accurately.

This paper presents two variants of genetic programming (GP) approaches for intelligent online performance monitoring of electronic circuits and systems. Reliability modeling of electronic circuits can be best performed by the stressor - susceptibility interaction model. A circuit or a system is deemed to be failed once the stressor has exceeded the susceptibility limits. For on-line prediction, validated stressor vectors may be obtained by direct measurements or sensors, which after preprocessing and standardization are fed into the GP models. Empirical results are compared with artificial neural networks trained using backpropagation algorithm. The performance of the proposed method is evaluated by comparing the experiment results with the actual failure model values. The developed model reveals that GP could play an important role for future fault monitoring systems.

In this paper, we present an ensemble combination of two genetic programming models namely linear genetic programming (LGP) and multi expression programming (MEP). The proposed model is designed to assist the conventional power control systems with added intelligence. For on-line control, voltage and current are fed into the network after preprocessing and standardization. The model was trained with a 24-hour load demand pattern and performance of the proposed method is evaluated by comparing the test results with the actual expected values. For performance comparison purposes, we also used an artificial neural network trained by a backpropagation algorithm. Test results reveal that the proposed ensemble method performed better than the individual GP approaches and artificial neural network in terms of accuracy and computational requirements.

Due to the wide deployment of sensor networks recently security in sensor networks has become a hot research topic. Popular ways to secure a sensor network are by including cryptographic techniques or by safeguarding sensitive information from unauthorized access/manipulation and by implementing efficient intrusion detection mechanisms. This paper proposes a novel ant colony based intrusion detection mechanism which could also keep track of the intruder trials. The IDEAS technique could work in conjunction with the conventional machine learning based intrusion detection techniques to secure the sensor networks. The algorithm is presented and illustrated by simulating a sensor network.

This paper proposes a novel adaptive representation for evolutionary multiobjective optimization for solving a stock modeling problem. The standard Pareto achieved evolution strategy (PAES) uses real or binary representation for encoding solutions. Adaptive Pareto archived evolution strategy (APAES) uses dynamic alphabets for encoding solutions. APAES is applied for modeling two popular stock indices involving 4 objective functions. Further, two bench mark test functions for multiobjective optimization are also used to illustrate the performance of the algorithm. Empirical results demonstrate APAES performs well when compared to the standard PAES,.

The 0/1 knapsack problem is a well known problem occurring in many real world applications. The problem is NP-complete. The multiobjective 0/1 knapsack problem is a generalization of the 0/1 knapsack problem in which multiple knapsacks are considered. A new evolutionary algorithm for solving multiobjective 0/1 knapsack problem is proposed in this paper. This algorithm used a /spl epsiv/-dominance relation for direct comparison of two solutions. Several numerical experiments are performed using the best recent algorithms proposed for this problem. Experimental results clearly show that the proposed algorithm outperforms the existing evolutionary approaches for this problem.