Population-based Incremental Learning Research Articles

Surrogate-Assisted Evolutionary Optimizers for Multiobjective Design of a Torque Arm Structure

This paper presents two surrogate-assisted optimization strategies for structural constrained multiobjective optimization. The optimization strategies are based on hybridization of multiobjective population-based incremental learning (MOPBIL) and radial-basis function (RBF) interpolation. The first strategy uses MOPBIL for generating training points while the second strategy uses a Latin hypercube sampling (LHS) technique. The design case study is the shape and sizing design of a torque arm structure. A design problem is set to minimize structural mass and displacement while constraints include stresses due to three different load cases. Structural analysis is carried out by means of a finite element approach. The design problem is then tackled by the proposed surrogate-assisted design strategies. Numerical results show that the use of MOPBIL for generating training points is superior to the use of LHS based on a hypervolume indicator and root mean square error (RMSE).

Optimal Design of a Pin-Fin Heat Sink Using a Surrogate-Assisted Multiobjective Evolutionary Algorithm

In this work, performance enhancement of a multiobjective evolutionary algorithm (MOEA) by integrating a surrogate model to the design process is presented. The MOEA used in this work is multiobjective population-based incremental learning (PBIL). The bi-objective design problem of a pin-fin heat sink (PFHS) is posed to minimize junction temperature and fan pumping power while meeting design constraints. A Kriging (KRG) model is used for improving the performance of PBIL. The training points for constructing a surrogate KRG model are sampled by means of a Latin hypercube sampling (LHS) technique. It is shown that hybridization of PBIL and KRG can enhance the search performance of PBIL.

Topology and Sizing Optimization of Trusses with Adaptive Ground Finite Elements Using Multiobjective PBIL

This paper presents an integrated design technique to carry out simultaneous topology and sizing optimization of a two-dimensional truss structure. An optimization problem is set to find a structural layout and elements’ cross-sectional areas of a 2D truss such that objective functions including mass, compliance, and buckling factor are optimized. Design constraints consist of stress, buckling, and compliance. The concept of an adaptive ground elements approach and the encoding/decoding process are detailed. The multiobjective version of population-based incremental learning (PBIL) is employed to solve the design problem. The results reveal that the proposed design strategy is efficient and can be an effective engineering design tool.

A hybrid PBIL-based harmony search method

The harmony search (HS) method is a popular meta-heuristic optimization algorithm, which has been extensively employed to handle various engineering problems. However, it sometimes fails to offer a satisfactory convergence performance under certain circumstances. In this paper, we propose and study a hybrid HS approach, HS–PBIL, by merging the HS together with the population-based incremental learning (PBIL). Numerical simulations demonstrate that our HS–PBIL is well capable of outperforming the regular HS method in dealing with nonlinear function optimization and a practical wind generator optimization problem.

Performance evaluation of power system stabilizers based on Population-Based Incremental Learning (PBIL) algorithm

This paper proposes a method of optimally tuning the parameters of power system stabilizers (PSSs) for a multi-machine power system using Population-Based Incremental Learning (PBIL). PBIL is a technique that combines aspects of GAs and competitive learning-based on Artificial Neural Network. The main features of PBIL are that it is simple, transparent, and robust with respect to problem representation. PBIL has no crossover operator, but works with a probability vector (PV). The probability vector is used to create better individuals through learning. Simulation results based on small and large disturbances show that overall, PBIL-PSS gives better performances than GA-PSS over the range of operating conditions considered.

Breaking Knapsack Cipher Using Population Based Incremental Learning

The demand for effective internet security is increasing exponentially day by day. Businesses have an obligation to protect sensitive data from loss or theft. Such sensitive data can be potentially damaging if it is altered, destroyed or if it falls into the wrong hands. So they need to develop a scheme that guarantees to protect the information from attacker. Cryptology which is the science and study of systems for secret communication is at the heart of providing such guarantee. Breaking knapsack cipher using Population Based Incremental Learning (PBIL) is sug gested in this paper. Results of this implementation are compared with results of Poonam Grag, Aditya Shastri, and D.C. Agarwal (2006) which had made an enhancement on the efficiency of genetic algorithm attack on knapsack cipher suggested by Spillman in 1 993. The result of comparison shows that Population Based Incremental Learning has less complexity and enjoys high speed (i.e. correct results will be generated with less number of generation compared to that generated using genetic algorithm) also the overhead for genetic algorithm operations is significantly higher than for Population Based Incremental Learning.

Evolutionary algorithms for solving multi-objective travelling salesman problem

This paper studies the application of evolutionary algorithms for bi-objective travelling salesman problem. Two evolutionary algorithms, including estimation of distribution algorithm (EDA) and genetic algorithm (GA), are considered. The solution to this problem is a set of trade-off alternatives. The problem is solved by optimizing the order of the cities so as to simultaneously minimize the two objectives of travelling distance and travelling cost incurred by the travelling salesman. In this paper, binary-representation-based evolutionary algorithms are replaced with an integer-representation. Three existing EDAs are altered to use this integer-representation, namely restricted Boltzmann machine (RBM), univariate marginal distribution algorithm (UMDA), and population-based incremental learning (PBIL). Each city is associated with a representative integer, and the probability of any of this representative integer to be located in any position of the chromosome is constructed through the modeling approach of the EDAs. New sequences of cities are obtained by sampling from the probabilistic model. A refinement operator and a local search operator are proposed in this piece of work. The EDAs are subsequently hybridized with GA in order to complement the limitations of both algorithms. The effect that each of these operators has on the quality of the solutions are investigated. Empirical results show that the hybrid algorithms are capable of finding a set of good trade-off solutions.

Adaptive spectral clustering ensemble selection via resampling and population-based incremental learning algorithm

In this paper, we explore a novel ensemble method for spectral clustering. In contrast to the traditional clustering ensemble methods that combine all the obtained clustering results, we propose the adaptive spectral clustering ensemble method to achieve a better clustering solution. This method can adaptively assess the number of the component members, which is not owned by many other algorithms. The component clusterings of the ensemble system are generated by spectral clustering (SC) which bears some good characteristics to engender the diverse committees. The selection process works by evaluating the generated component spectral clustering through resampling technique and population-based incremental learning algorithm (PBIL). Experimental results on UCI datasets demonstrate that the proposed algorithm can achieve better results compared with traditional clustering ensemble methods, especially when the number of component clusterings is large.

Multi-objective topology optimization using evolutionary algorithms

This article deals with the comparative performance of some established multi-objective evolutionary algorithms (MOEAs) for structural topology optimization. Four multi-objective problems, having design objectives like structural compliance, natural frequency and mass, and subjected to constraints on stress, etc., are posed for performance testing. The MOEAs include Pareto archive evolution strategy (PAES), population-based incremental learning (PBIL), non-dominated sorting genetic algorithm (NSGA), strength Pareto evolutionary algorithm (SPEA), and multi-objective particle swarm optimization (MPSO). The various MOEAs are implemented to solve the problems. The ground element filtering (GEF) technique is used to suppress checkerboard patterns on topologies. The results obtained from the various optimizers are illustrated and compared. It is shown that PBIL is far superior to the others. The optimal topologies from using PBIL can be compared with those obtained by employing the classical gradient-based approach. It can be considered as a powerful tool for structural topological design.

A Population-Based Incremental Learning Vector Algorithm for Multiobjective Optimal Designs

To alleviate the deficiency of crossover and mutation operations in standard genetic algorithms, the population-based incremental learning (PBIL) method is extended for multiobjective designs of inverse problems. To quantitatively measure the number of improvements in the whole objective functions and to quantify the amount of improvements in a specific objective function, a novel metric is proposed to “penalize” the fitness of a solution. Moreover, a selecting strategy for the best solutions of the latest iterations of an individual is introduced. Furthermore, multiple probability vectors are employed to enhance the diversity of the found solutions. Numerical experiments on low- and high-frequency inverse problems are carried out to demonstrate the feasibility of the proposed vector PBIL algorithm for hard multiobjective engineering inverse problems.

A hybrid ant colony optimization for continuous domains

Research on optimization in continuous domains gains much of focus in swarm computation recently. A hybrid ant colony optimization approach which combines with the continuous population-based incremental learning and the differential evolution for continuous domains is proposed in this paper. It utilizes the ant population distribution and combines the continuous population-based incremental learning to dynamically generate the Gaussian probability density functions during evolution. To alleviate the less diversity problem in traditional population-based ant colony algorithms, differential evolution is employed to calculate Gaussian mean values for the next generation in the proposed method. Experimental results on a large set of test functions show that the new approach is promising and performs better than most of the state-of-the-art ACO algorithms do in continuous domains.

The convergence analysis and specification of the Population-Based Incremental Learning algorithm

In this paper, we investigate the global convergence properties in probability of the Population-Based Incremental Learning (PBIL) algorithm when the initial configuration p ( 0 ) is fixed and the learning rate α is close to zero. The convergence in probability of PBIL is confirmed by the experimental results. This paper presents a meaningful discussion on how to establish a unified convergence theory of PBIL that is not affected by the population and the selected individuals.

Conformational searching using a population-based incremental learning algorithm

A new population-based incremental learning algorithm for conformational searching of molecules is presented. This algorithm is particularly effective at determining, by relatively small number of energy minimizations, global energy minima of large flexible molecules. The algorithm is also able to find a large set of low energy conformations of more rigid small molecules. The performance of the algorithm is relation to other algorithm is examined via the test molecules: C(18) H(38) , C(39)H(80) , cycloheptadecane and a set of five drug-like molecules.

Multiobjective Evolutionary Optimization of Splayed Pin-Fin Heat Sink

This paper presents the use of a multiobjective evolutionary algorithm, namely population-based incremental learning (PBIL), for the design/optimization of a splayed pin-fin heat sink. An innovative design strategy based on evolutionary optimization is presented for the enhancement of the heat sink’s performance. The design problem is to simultaneously minimize the junction temperature and the fan pumping power of the heat sink. Design variables determine the sizes and geometry of the heat sink. The new encoding/decoding process of the design variables, using surface spline interpolation, is detailed. There are 24 design parameters including fin number, fin height, fin width, heat sink base thickness and size, fin bevel, and inlet air velocity. Manufacturing tolerances, such as the heat sink aspect ratio and the device free space, are taken as design constraints. Computational fluid dynamics is used for the objective function evaluation. Numerical results show that PBIL is a powerful tool for the optimal design of a splayed pin-fin heat sink. This new design approach results in heat sinks with variation in fin heights, and it is said to be superior to available commercial splayed pin-fin heat sinks.

Cant sawing log positioning in a sawmill: searching for an optimal solution

Automated three-dimensional log scanning and positioning systems in a sawmill have a limited time available to reach an optimal positioning solution before primary breakdown sawing starts. In this study a search algorithm (tentacle algorithm) was developed for this task and was empirically evaluated in terms of its ability to find an optimal or close-to-optimal positioning solution in a limited number of iterations. This algorithm was compared to the population-based incremental learning algorithm, the simulated annealing algorithm, and the particle swarm optimisation algorithm. The tentacle algorithm performed the best of all the algorithms evaluated in terms of the mean volume recovery obtained. However, exhaustive searches around the centred and ‘horns-up’ and ‘horns-down’ positions using smaller ranges resulted in better mean volume recovery results than any of the algorithms, although the mean results using this strategy did not differ significantly from that of the tentacle algorithm.

An evolutionary multi-objective optimization of trading rules in call markets

SUMMARY We evaluate an agent-based model featuring near-zero-intelligence traders operating in a call market with a wide range of trading rules governing the determination of prices and which orders are executed, as well as a range of parameters regarding market intervention by market makers and the presence of informed traders. We optimize these trading rules using a multi-objective population-based incremental learning algorithm seeking to maximize the trading volume and minimize the bid–ask spread. Our results suggest that markets should choose a small tick size if concerns about the bid–ask spread are dominating and a large tick size if maximizing trading volume is the main aim. We also find that unless concerns about trading volume dominate, time priority is the optimal priority rule. Copyright © 2011 John Wiley & Sons, Ltd.

Optimization of nuclear reactor core fuel reload using the new Quantum PBIL

An issue of great interest in nuclear engineering is to optimize the reload of fuel assemblies in the reactor core, which means to find the best configuration of shuffling between the fresh fuel and the remnants ones from previous cycles. Quantum inspired evolutionary algorithms were developed as an alternative to make the conventional evolutionary algorithms more efficient regarding future hardware implementations. This paper presents a new quantum inspired evolutionary algorithm, named Quantum PBIL (QPBIL). It combines the basic concepts of Population-Based Incremental Learning (PBIL) with the concepts of quantum computing as quantum bit and the linear superposition of states used in evolutionary algorithms with quantum inspirations. To prove its effectiveness as an optimization tool, QPBIL was applied to the optimization of cycle 7 of Angra 1, and the results obtained were comparable to those of efficient optimization techniques based on artificial intelligence currently available.

On the Optimal Convergence Probability of Univariate Estimation of Distribution Algorithms

In this paper we obtain bounds on the probability of convergence to the optimal solution for the compact genetic algorithm (cGA) and the population based incremental learning (PBIL). Moreover, we give a sufficient condition for convergence of these algorithms to the optimal solution and compute a range of possible values for algorithm parameters at which there is convergence to the optimal solution with a predefined confidence level.

A Population-Based Incremental Learning Method for Robust Optimal Solutions

A population-based incremental learning (PBIL) method is proposed to search for both robust and global optimal solutions of an inverse problem in which there are inevitable tolerances on the decision variables. To reduce the computational costs of the proposed algorithm, a methodology for evaluating the expectancy measures and a philosophy for worst-case solutions are proposed. Moreover, a novel mechanism for selecting the performance metrics is introduced to enable the algorithm to find both global and robust optimal solutions in a single run. Two numerical examples are reported to validate the proposed algorithm.

Determining the optimal market structure using near-zero intelligence traders

We evaluate an agent-based model featuring near-zero-intelligence traders operating in a call market with a wide range of trading rules governing the determination of prices, which orders are executed as well as a range of parameters regarding market intervention by specialists and the presence of informed traders. We optimize these trading rules using a population-based incremental learning algorithm seeking to maximize the trading volume. Our results suggest markets should choose a large tick size and ensure only a small fraction of traders are informed about the order book. The effect of trading rules regarding the determination of prices, priority rules, and specialist intervention, we find to have an ambiguous effect on the outcome.