Population-based Evolutionary Algorithm Research Articles

Solving the Associated Weakness of Biogeography-Based Optimization Algorithm

Biogeography-based optimization (BBO) is a new population-based evolutionary algorithm and is based on an old theory of island biogeography that explains the geographical distribution of biological organisms. BBO was introduced in 2008 and then a lot of modifications and hybridizations were employed to enhance its performance. The researchers found that the original version of BBO has some weakness on its exploration. This paper tries to solve the root problems itself instead of solving its effect by using different techniques. It proposes two modifications; firstly, modifying the probabilistic selection process of the migration and mutation stages to give a fairly randomized selection for all the features of the islands. Secondly, the clear duplication process, which is located after the mutation stage, is sized to avoid any corruption on the suitability index variables of the non-mutated islands. The proposed modifications are extensively tested on 120 test functions with different dimensions and complexities. The results proved that the BBO performance can be enhanced effectively without embedding any additional sub-algorithm, and without using any complicated form of the immigration and emigration rates. In addition, the new BBO algorithm requires less CPU time and becomes even faster than the original simplified partial migration-based BBO. These essential modifications have to be considered as an initial step for any other modifications.

A cell evolution method for reliability-based design optimization

The reliability-based design optimization (RBDO) presents to be a systematic and powerful approach for process designs under uncertainties. The traditional double-loop methods for solving RBDO problems can be computationally inefficient because the inner reliability analysis loop has to be iteratively performed for each probabilistic constraint. To solve RBDOs in an alternative and more effective way, Deb et al. [1] proposed recently the use of evolutionary algorithms with an incorporated fastPMA. Since the imbedded fastPMA needs the gradient calculations and the initial guesses of the most probable points (MPPs), their proposed algorithm would encounter difficulties in dealing with non-differentiable constraints and the effectiveness could be degraded significantly as the initial guesses are far from the true MPPs. In this paper, a novel population-based evolutionary algorithm, named cell evolution method, is proposed to improve the computational efficiency and effectiveness of solving the RBDO problems. By using the proposed cell evolution method, a family of test cells is generated based on the target reliability index and with these reliability test cells the determination of the MPPs for probabilistic constraints becomes a simple parallel calculation task, without the needs of gradient calculations and any initial guesses. Having determined the MPPs, a modified real-coded genetic algorithm is applied to evolve these cells into a final one that satisfies all the constraints and has the best objective function value for the RBDO. Especially, the nucleus of the final cell contains the reliable solution to the RBDO problem. Illustrative examples are provided to demonstrate the effectiveness and applicability of the proposed cell evolution method in solving RBDOs. Simulation results reveal that the proposed cell evolution method outperforms comparative methods in both the computational efficiency and solution accuracy, especially for multi-modal RBDO problems.

A population-based evolutionary search approach to the multiple minima problem in de novo protein structure prediction

BackgroundElucidating the native structure of a protein molecule from its sequence of amino acids, a problem known as de novo structure prediction, is a long standing challenge in computational structural biology. Difficulties in silico arise due to the high dimensionality of the protein conformational space and the ruggedness of the associated energy surface. The issue of multiple minima is a particularly troublesome hallmark of energy surfaces probed with current energy functions. In contrast to the true energy surface, these surfaces are weakly-funneled and rich in comparably deep minima populated by non-native structures. For this reason, many algorithms seek to be inclusive and obtain a broad view of the low-energy regions through an ensemble of low-energy (decoy) conformations. Conformational diversity in this ensemble is key to increasing the likelihood that the native structure has been captured.MethodsWe propose an evolutionary search approach to address the multiple-minima problem in decoy sampling for de novo structure prediction. Two population-based evolutionary search algorithms are presented that follow the basic approach of treating conformations as individuals in an evolving population. Coarse graining and molecular fragment replacement are used to efficiently obtain protein-like child conformations from parents. Potential energy is used both to bias parent selection and determine which subset of parents and children will be retained in the evolving population. The effect on the decoy ensemble of sampling minima directly is measured by additionally mapping a conformation to its nearest local minimum before considering it for retainment. The resulting memetic algorithm thus evolves not just a population of conformations but a population of local minima.Results and conclusionsResults show that both algorithms are effective in terms of sampling conformations in proximity of the known native structure. The additional minimization is shown to be key to enhancing sampling capability and obtaining a diverse ensemble of decoy conformations, circumventing premature convergence to sub-optimal regions in the conformational space, and approaching the native structure with proximity that is comparable to state-of-the-art decoy sampling methods. The results are shown to be robust and valid when using two representative state-of-the-art coarse-grained energy functions.

Differential Evolution for Prediction of Longitudinal Dispersion Coefficients in Natural Streams

Differential evolution (DE) is a population-based evolutionary algorithm widely used for solving multidimensional global optimization problems over continuous spaces, and has been successfully used to solve several kinds of problems. In this paper, a novel expression for the prediction of longitudinal dispersion coefficient in natural streams is proposed to minimize the sum-square error using differential evolution algorithm. The new expression considers the hydraulic and geometric characteristics of rivers. Datasets consisting 65 sets of observations from 29 rivers in the unite states are used to test the proposed algorithm, and results demonstrate the performance and applicability of the proposed differential evolution. Compared with the previous methods, the new expression using differential evolution is superior to other expressions. Moreover, 56.92 % of the prediction using the new expression lie with the 0.5 < Kpre/Kmeas < 1.5 that is better than other expressions.

A memory efficient stochastic evolution based algorithm for the multi-objective shortest path problem

Multi-objective shortest path (MOSP) problem aims to find the shortest path between a pair of source and a destination nodes in a network. This paper presents a stochastic evolution (StocE) algorithm for solving the MOSP problem. The proposed algorithm is a single-solution-based evolutionary algorithm (EA) with an archive for storing several non-dominant solutions. The solution quality of the proposed algorithm is comparable to the established population-based EAs. In StocE, the solution replaces its bad characteristics as the generations evolve. In the proposed algorithm, different sub-paths are the characteristics of the solution. Using the proposed perturb operation, it eliminates the bad sub-paths from generation to generation. The experiments were conducted on huge real road networks. The proposed algorithm is comparable to well-known single-solution and population-based EAs. The single-solution-based EAs are memory efficient, whereas, the population-based EAs are known for their good solution quality. The performance measures were the solution quality, speed and memory consumption, assessed by the hypervolume (HV) metric, total number of evaluations and memory requirements in megabytes. The HV metric of the proposed algorithm is superior to that of the existing single-solution and population-based EAs. The memory requirements of the proposed algorithm is at least half than the EAs delivering similar solution quality. The proposed algorithms also executes more rapidly than the existing single-solution-based algorithms. The experimental results show that the proposed algorithm is suitable for solving MOSP problems in embedded systems.

An implementation of differential evolution algorithm for inversion of geoelectrical data

Abstract Differential evolution (DE), a population-based evolutionary algorithm (EA) has been implemented to invert self-potential (SP) and vertical electrical sounding (VES) data sets. The algorithm uses three operators including mutation, crossover and selection similar to genetic algorithm (GA). Mutation is the most important operator for the success of DE. Three commonly used mutation strategies including DE/best/1 (strategy 1), DE/rand/1 (strategy 2) and DE/rand-to-best/1 (strategy 3) were applied together with a binomial type crossover. Evolution cycle of DE was realized without boundary constraints. For the test studies performed with SP data, in addition to both noise-free and noisy synthetic data sets two field data sets observed over the sulfide ore body in the Malachite mine (Colorado) and over the ore bodies in the Neem-Ka Thana cooper belt (India) were considered. VES test studies were carried out using synthetically produced resistivity data representing a three-layered earth model and a field data set example from Gokceada (Turkey), which displays a seawater infiltration problem. Mutation strategies mentioned above were also extensively tested on both synthetic and field data sets in consideration. Of these, strategy 1 was found to be the most effective strategy for the parameter estimation by providing less computational cost together with a good accuracy. The solutions obtained by DE for the synthetic cases of SP were quite consistent with particle swarm optimization (PSO) which is a more widely used population-based optimization algorithm than DE in geophysics. Estimated parameters of SP and VES data were also compared with those obtained from Metropolis–Hastings (M–H) sampling algorithm based on simulated annealing (SA) without cooling to clarify uncertainties in the solutions. Comparison to the M–H algorithm shows that DE performs a fast approximate posterior sampling for the case of low-dimensional inverse geophysical problems.

An analysis of the migration rates for biogeography-based optimization

Biogeography-Based Optimization (BBO), inspired by the science of biogeography, is a novel population-based Evolutionary Algorithm (EA). For optimization problems, BBO builds the matching mathematical model of the organism distribution. In this evolutionary mechanism, species migrating among islands can be considered as the information transition among different solutions represented by habitats. Solutions are reassembled according to migration rates. However, so far, the migration models are generally designed by empirical studies. This leads to immature conclusions that are unreliable. To complete the previous works, this paper investigates transition probability matrices of BBO to clarify that the transition probability of median number of species is not the only determinant factor to influence performance. The impact of migration rates on BBO is mathematically discussed, which is helpful to design migration models. Using numerical simulations, the BBO and several other classical evolutionary algorithms are compared. The simulations also comprehensively explain the effect of the BBO’s properties on its performance including dimension, population size, and migration models. The results validate the theoretical analysis in this paper.

Imperialist Competitive Algorithms with Perturbed Moves for Global Optimization

Imperialist Competitive Algorithm (ICA) is a new population-based evolutionary algorithm. Previous works have shown that ICA converges quickly but often to a local optimum. To overcome this problem, this work proposed two modifications to ICA: perturbed assimilation move and boundary bouncing. The proposed modifications were applied to ICA and tested using six well-known benchmark functions with 30 dimensions. The experimental results indicate that these two modifications significantly improve the performance of ICA on all six benchmark functions.

An imperialist competitive algorithm for multi-objective U-type assembly line design

Many assembly lines are now being designed as U-type assembly lines rather than straight lines because of the pressure of the just-in-time (JIT) manufacturing concept. Since any type of an assembly line balancing problem is known to be NP-hard, there has been a growing tendency toward using evolutionary algorithms to solve such a hard problem. This paper proposes a new population-based evolutionary algorithm, namely imperialist competitive algorithm (ICA) inspired by the process of socio-political evolution, to address the multi-objective U-type assembly line balancing problem (UALBP). Two considered objectives are to minimize the line efficiency and minimize the variation of workload. Furthermore, the Taguchi design is applied to tune the effective parameters of the proposed ICA. To demonstrate the efficiency of the proposed algorithm, the associated results are compared against an efficient genetic algorithm (GA) in the literature over a large group of benchmarks taken from the literature. The computational results show that the proposed ICA outperforms GA.

Interaction Enhanced Imperialist Competitive Algorithms

Imperialist Competitive Algorithm (ICA) is a new population-based evolutionary algorithm. It divides its population of solutions into several sub-populations, and then searches for the optimal solution through two operations: assimilation and competition. The assimilation operation moves each non-best solution (called colony) in a sub-population toward the best solution (called imperialist) in the same sub-population. The competition operation removes a colony from the weakest sub-population and adds it to another sub-population. Previous work on ICA focuses mostly on improving the assimilation operation or replacing the assimilation operation with more powerful meta-heuristics, but none focuses on the improvement of the competition operation. Since the competition operation simply moves a colony (i.e., an inferior solution) from one sub-population to another sub-population, it incurs weak interaction among these sub-populations. This work proposes Interaction Enhanced ICA that strengthens the interaction among the imperialists of all sub-populations. The performance of Interaction Enhanced ICA is validated on a set of benchmark functions for global optimization. The results indicate that the performance of Interaction Enhanced ICA is superior to that of ICA and its existing variants.

On the Impact of Mutation-Selection Balance on the Runtime of Evolutionary Algorithms

The interplay between mutation and selection plays a fundamental role in the behavior of evolutionary algorithms (EAs). However, this interplay is still not completely understood. This paper presents a rigorous runtime analysis of a non-elitist population-based EA that uses the linear ranking selection mechanism. The analysis focuses on how the balance between parameter η, controlling the selection pressure in linear ranking, and parameter χ controlling the bit-wise mutation rate, impacts the runtime of the algorithm. The results point out situations where a correct balance between selection pressure and mutation rate is essential for finding the optimal solution in polynomial time. In particular, it is shown that there exist fitness functions which can only be solved in polynomial time if the ratio between parameters η and χ is within a narrow critical interval, and where a small change in this ratio can increase the runtime exponentially. Furthermore, it is shown quantitatively how the appropriate parameter choice depends on the characteristics of the fitness function. In addition to the original results on the runtime of EAs, this paper also introduces a very useful analytical tool, i.e., multi-type branching processes, to the runtime analysis of non-elitist population-based EAs.

Evolution of heterogeneous ensembles through dynamic particle swarm optimization for video-based face recognition

In many real-world applications, pattern recognition systems are designed a priori using limited and imbalanced data acquired from complex changing environments. Since new reference data often becomes available during operations, performance could be maintained or improved by adapting these systems through supervised incremental learning. To avoid knowledge corruption and sustain a high level of accuracy over time, an adaptive multiclassifier system (AMCS) may integrate information from diverse classifiers that are guided by a population-based evolutionary optimization algorithm. In this paper, an incremental learning strategy based on dynamic particle swarm optimization (DPSO) is proposed to evolve heterogeneous ensembles of classifiers (where each classifier corresponds to a particle) in response to new reference samples. This new strategy is applied to video-based face recognition, using an AMCS that consists of a pool of fuzzy ARTMAP (FAM) neural networks for classification of facial regions, and a niching version of DPSO that optimizes all FAM parameters such that the classification rate is maximized. Given that diversity within a dynamic particle swarm is correlated with diversity within a corresponding pool of base classifiers, DPSO properties are exploited to generate and evolve diversified pools of FAM classifiers, and to efficiently select ensembles among the pools based on accuracy and particle swarm diversity. Performance of the proposed strategy is assessed in terms of classification rate and resource requirements under different incremental learning scenarios, where new reference data is extracted from real-world video streams. Simulation results indicate the DPSO strategy provides an efficient way to evolve ensembles of FAM networks in an AMCS. Maintaining particle diversity in the optimization space yields a level of accuracy that is comparable to AMCS using reference ensemble-based and batch learning techniques, but requires significantly lower computational complexity than assessing diversity among classifiers in the feature or decision spaces.

A memetic grammar inference algorithm for language learning

An unsupervised incremental algorithm for grammar inference and its application to domain-specific language development are described. Grammatical inference is the process of learning a grammar from the set of positive and optionally negative sentences. Learning general context-free grammars is still considered a hard problem in machine learning and is not completely solved yet. The main contribution of the paper is a newly developed memetic algorithm, which is a population-based evolutionary algorithm enhanced with local search and a generalization process. The learning process is incremental since a new grammar is obtained from the current grammar and false negative samples, which are not parsed by the current grammar. Despite being incremental, the learning process is not sensitive to the order of samples. All important parts of this algorithm are explained and discussed. Finally, a case study of a domain specific language for rendering graphical objects is used to show the applicability of this approach.

Particle Swarm Optimization Algorithm Based on Escape Boundary

The particle swarm optimization (PSO) is a population-based stochastic evolutionary algorithm, noted for its capability of searching for the global optimum of complex problems. Particles flying out of the solution space will lead to invalid solutions. So often in engineering applications, boundary condition is used to confine the particles within the solution space. In this paper, a new boundary is proposed, which is called as escape boundary. The solution space is divided into three sections, that is, the inside，escape boundary and the outside of the boundary. The location of the global solution in the solution space, accordingly has two types, that is, the global optimum around the center of the solution space, and the global optimum close to the escape boundary. The proposed boundary is introduced into the PSO algorithm, and is compared to the damping boundary. The experimental results show that the PSO based on escape boundary has better search ability and faster convergence rate.

Convergence Properties of (μ + λ) Evolutionary Algorithms

We present a number of convergence properties of population-based Evolutionary Algorithms (EAs) on a set of test functions. Focus is on EA using k-Bit-Swap (kBS) operator. We compare our findings to past research.

Thermoeconomic optimization of a combined-cycle solar tower power plant

A dynamic model of a pure-solar combined-cycle power plant has been developed in order to allow determination of the thermodynamic and economic performance of the plant for a variety of operating conditions and superstructure layouts. The model was then used for multi-objective thermoeconomic optimization of both the power plant performance and cost, using a population-based evolutionary algorithm. In order to examine the trade-offs that must be made, two conflicting objectives will be considered, namely minimal investment costs and minimal levelized electricity costs. It was shown that efficiencies in the region of 18–24% can be achieved, and this for levelized electricity costs in the region of 12–24 UScts/kWhe, depending on the magnitude of the initial investment, making the system competitive with current solar thermal technology.

An Adaptive Clonal Selection Algorithm with Stage Mutation Operation for Unrelated Parallel Machine Scheduling Problem with Sequence-Dependent Setup Times

This paper proposes an adaptive clonal selection algorithm (CSA) to solve the unrelated parallel machine scheduling problem (UPMSP) with sequence-dependent setup time constraints. The objective is to find the sequence which minimizes the makesepan. CSA is a newly discovered population-based evolutionary algorithm based on the clonal selection principle and the immune system. In order to improve the performance of CSA, a local search operation is adopted to strengthen the search ability. In addition, an adaptive clonal factor and a stage mutation operation are introduced to enhance the exploration and exploitation of the algorithm. The performance of the proposed adaptive clonal selection algorithm is compared with genetic algorithm (GA), Simulated Annealing (SA) and basic CSA on 320 randomly generated instances. The results demonstrate the superiority of the proposed method and confirm its potential to solve the UPMSP with sequence-dependent setup time constraints especially when the scale of the instances is very large.

Simulation optimization based on Taylor Kriging and evolutionary algorithm

This paper develops a simulation optimization algorithm based on Taylor Kriging and evolutionary algorithm (SOAKEA) for simulation models with high computational expenses. In SOAKEA, an evolutionary algorithm is used to search for optimal solutions of a simulation model, and Taylor Kriging temporarily serves as a surrogate fitness function of this evolutionary algorithm to evaluate solutions. Taylor Kriging is an enhanced version of Kriging where Taylor expansion is used to approximate the drift function of Kriging, and it improves the interpolation accuracy of Kriging. The structures and properties of SOAKEA are analyzed. A combination correction strategy is created, and it effectively reduces the computational expense of SOAKEA. The empirical comparison of SOAKEA with some other well-known metaheuristics is conducted, and the proposed SOAKEA uses particle swam optimization, a population-based evolutionary algorithm, to solve four simulation problems based on multimodal benchmark functions. The results indicate that SOAKEA has significant advantages in optimizing simulation models with high computational expenses.

Constrained mean-risk portfolio optimisation: an application of multiobjective simulated annealing

We solve different constrained mean-risk portfolio optimisation models using a recently developed simulated annealing-based multiobjective optimisation algorithm. We consider practical and widely used constraints in portfolio modelling, i.e., the cardinality constraint which imposes a limit on the number of assets in the portfolio and the quantity constraints which restrict the proportion of each asset in the portfolio to lie between lower and upper bounds. Various risk measures are employed – the classical variance and three risk measures that form the so called downside-risk family, i.e., expected shortfall, value-at-risk and semivariance. The experimental results demonstrate that the algorithm generates a number of efficient portfolios capturing a great range of the trade-offs between mean and risk independently of the risk function used. Comparison with benchmark (when possible) efficient frontiers provides strong evidence that the algorithm effectively solves the discrete constrained mean-risk problems. Furthermore, a computational comparison with a population-based evolutionary algorithm, namely SPEA2, shows that the simulated annealing-based multiobjective optimisation technique achieves almost as good performance in a timely manner.

A Probabilistic Analysis of a Simplified Biogeography-Based Optimization Algorithm

Biogeography-based optimization (BBO) is a population-based evolutionary algorithm (EA) that is based on the mathematics of biogeography. Biogeography is the study of the geographical distribution of biological organisms. We present a simplified version of BBO and perform an approximate analysis of the BBO population using probability theory. Our analysis provides approximate values for the expected number of generations before the population's best solution improves, and the expected amount of improvement. These expected values are functions of the population size. We quantify three behaviors as the population size increases: first, we see that the best solution in the initial randomly generated population improves; second, we see that the expected number of generations before improvement increases; and third, we see that the expected amount of improvement decreases.