Expensive Fitness Evaluations Research Articles

Parallel PSO for Efficient Neural Network Training Using GPGPU and Apache Spark in Edge Computing Sets

The training phase of a deep learning neural network (DLNN) is a computationally demanding process, particularly for models comprising multiple layers of intermediate neurons.This paper presents a novel approach to accelerating DLNN training using the particle swarm optimisation (PSO) algorithm, which exploits the GPGPU architecture and the Apache Spark analytics engine for large-scale data processing tasks. PSO is a bio-inspired stochastic optimisation method whose objective is to iteratively enhance the solution to a (usually complex) problem by approximating a given objective. The expensive fitness evaluation and updating of particle positions can be supported more effectively by parallel processing. Nevertheless, the parallelisation of an efficient PSO is not a simple process due to the complexity of the computations performed on the swarm of particles and the iterative execution of the algorithm until a solution close to the objective with minimal error is achieved. In this study, two forms of parallelisation have been developed for the PSO algorithm, both of which are designed for execution in a distributed execution environment. The synchronous parallel PSO implementation guarantees consistency but may result in idle time due to global synchronisation. In contrast, the asynchronous parallel PSO approach reduces the necessity for global synchronization, thereby enhancing execution time and making it more appropriate for large datasets and distributed environments such as Apache Spark. The two variants of PSO have been implemented with the objective of distributing the computational load supported by the algorithm across the different executor nodes of the Spark cluster to effectively achieve coarse-grained parallelism. The result is a significant performance improvement over current sequential variants of PSO.

Surrogate-Assisted Differential Evolution with multiple sampling mechanisms for high-dimensional expensive problems

Recently, Surrogate-Assisted Evolutionary Algorithms (SAEAs) have been widely employed in solving Expensive Optimization Problems (EOPs) due to their efficiency in obtaining satisfactory solutions with limited resources. By leveraging historical data to construct surrogate models for approximation, SAEAs can significantly reduce the number of expensive fitness evaluations for EOPs. A hierarchical SAEA optimization framework based on evolutionary sampling methods has achieved remarkable success in High-dimensional EOPs (HEOPs), which can effectively balance the exploration and exploitation capabilities. However, the majority of existing hierarchical SAEAs focus on either switching between different sampling strategies or enhancing a single sampling strategy, potentially overlooking the potential to improve multiple sampling strategies simultaneously. In this paper, we propose a Surrogate-Assisted Differential Evolution with Multiple Sampling Mechanisms (SADE-MSM) to tackle HEOPs, incorporating three sampling strategies with different mechanisms. The contributions of SADE-MSM are summarized as follows: 1) A centroid sampling method is applied before iterative optimization to enhance the early exploration ability; 2) An improved global prescreening sampling strategy is introduced to balance the exploration and exploitation capabilities; 3) A local search sampling with the adaptive optimal region strategy is proposed, significantly improving the exploitation ability. To validate the performance of SADE-MSM, we compared it with the state-of-the-art SAEAs on benchmark problems with dimensions ranging from 30 to 500. Experimental results demonstrate that SADE-MSM has a significant performance superiority.

A Global and Local Surrogate-Assisted Genetic Programming Approach to Image Classification

Genetic programming (GP) has achieved promising performance in image classification. However, GP-based methods usually require a long computation time for fitness evaluations, posing a challenge to real-world applications. Surrogate models can be efficiently computable approximations of expensive fitness evaluations. However, most existing surrogate methods are designed for evolutionary computation techniques with a vector-based representation consisting of numerical values, thus cannot be directly used for GP with a tree-based representation consisting of functions/operators. The variable sizes of GP trees further increase the difficulty of building the surrogate model for fitness approximations. To address these limitations, we propose a new surrogate-assisted GP approach including global and local surrogate models, which can accelerate the evolutionary learning process and achieve competitive classification performance simultaneously. The global surrogate model can assist GP in exploring the entire search space, while the local surrogate model can speed up convergence and further improve performance. Furthermore, a new surrogate training set is constructed to assist in establishing the relationship between the GP tree and its fitness, and effective surrogate models can be built accordingly. Experimental results on ten datasets of varying difficulty show that the new approach significantly reduces the computational cost of the GP-based method without sacrificing the classification accuracy. The comparisons with other state-of-the-art methods also demonstrate the effectiveness of the new approach. Further analysis reveals the significance of the global and local surrogates and the new surrogate training set on improving or maintaining the performance of the proposed approach while reducing the computational cost.

Radial projection-based adaptive sampling strategies for surrogate-assisted many-objective optimization

Intelligent manufacturing and industrial control systems frequently encounter expensive many-objective optimization problems (EMaOPs). Surrogate-assisted evolutionary algorithms (SAEAs) build predictive models to substitute the expensive fitness evaluation, enabling them to solve optimization more efficiently. In SAEAs, to enhance the exploration of optimization and the generalization of the surrogate model, the diversity of infill offspring and training database should be well-maintained, which is challenging in high-dimensional spaces or problems with disconnected Pareto front. This paper suggests a radial projection-based surrogate-assisted framework for solving EMaOPs. The radial projection can map the high-dimensional objective space into a 2-dimensional radial space. Based on this, a dynamic quadratic division method is proposed to enhance the diversity of solutions. Furthermore, an adaptive infill sampling criterion is introduced based on the distribution of selected convergent solutions, and a training database updating strategy is designed under the premise of maintaining its diversity and the model training efficiency. The presented framework exhibits a notable level of flexibility and adaptability as it can be effortlessly combined with other multi-objective optimization algorithms. Several experimental results on a set of expensive multi/many-objective test problems have demonstrated the superiority of the framework.

Classification model-based and assisted environment selection for evolutionary algorithms to solve high-dimensional expensive problems

Surrogate-assisted evolutionary algorithms (SAEAs) have been proven to be very effective in tackling low-dimensional expensive problems. However, it remains a challenge to solve high-dimensional expensive problems (HEPs) with the curse of dimensionality. Therefore, this paper proposes a surrogate-assisted improved multioperator differential evolution (SA-IMODE) algorithm to address HEPs up to 2000 dimensions. Specifically, this paper proposes a novel relationship classification model-based environment selection strategy (RCES), in which a classification model is used to distinguish between “good” and “bad” solutions to assist in environment selection. By doing this, the “unpromising” solutions are thrown away directly without evaluation to reduce the number of expensive fitness evaluations. Moreover, the solution-improvement data point and error samples are added to construct the training dataset to improve the model's prediction accuracy. Two coordinate systems are utilized to produce five types of DE operators to suit different fitness landscapes. An adaptive strategy is also used to select suitable DE operators to generate promising offspring. Furthermore, a local search mechanism is applied to refine the best solution in the current population to accelerate the algorithm's convergence. The systematic experiment results show SA-IMODE has a significant advantage over thirteen state-of-the-art algorithms on benchmark problems.

Instance Selection-Based Surrogate-Assisted Genetic Programming for Feature Learning in Image Classification.

Genetic programming (GP) has been applied to feature learning for image classification and achieved promising results. However, many GP-based feature learning algorithms are computationally expensive due to a large number of expensive fitness evaluations, especially when using a large number of training instances/images. Instance selection aims to select a small subset of training instances, which can reduce the computational cost. Surrogate-assisted evolutionary algorithms often replace expensive fitness evaluations by building surrogate models. This article proposes an instance selection-based surrogate-assisted GP for fast feature learning in image classification. The instance selection method selects multiple small subsets of images from the original training set to form surrogate training sets of different sizes. The proposed approach gradually uses these surrogate training sets to reduce the overall computational cost using a static or dynamic strategy. At each generation, the proposed approach evaluates the entire population on the small surrogate training sets and only evaluates ten current best individuals on the entire training set. The features learned by the proposed approach are fed into linear support vector machines for classification. Extensive experiments show that the proposed approach can not only significantly reduce the computational cost but also improve the generalisation performance over the baseline method, which uses the entire training set for fitness evaluations, on 11 different image datasets. The comparisons with other state-of-the-art GP and non-GP methods further demonstrate the effectiveness of the proposed approach. Further analysis shows that using multiple surrogate training sets in the proposed approach achieves better performance than using a single surrogate training set and using a random instance selection method.

A surrogate-assisted variable grouping algorithm for general large-scale global optimization problems

Problem decomposition plays an important role when applying cooperative coevolution (CC) to large-scale global optimization problems. However, most learning-based decomposition algorithms only apply to additively separable problems, while the others insensitive to problem type perform low decomposition accuracy and efficiency. Given this limitation, this study designs a general-separability-oriented detection criterion, and further proposes a novel decomposition algorithm called surrogate-assisted variable grouping (SVG). The new criterion detects the separability between a variable and some other variables by checking whether its optimum changes with the latter. Consistent with the definition of general separability, this criterion endows SVG with strong applicability and high accuracy. To reduce expensive fitness evaluations, SVG locates the optimum of a variable with the help of a surrogate model rather than the original high-dimensional model. Moreover, it converts the variable-grouping process into a search process in a binary tree by taking variable subsets as tree nodes. This facilitates the reutilization of historical separability information, thereby reducing separability detection times. Experimental results on a general benchmark suite indicate that compared with six state-of-the-art decomposition algorithms, SVG achieves higher accuracy and efficiency on both additively and nonadditively separable problems. Furthermore, it can significantly enhance the optimization performance of CC.

A surrogate-assisted controller for expensive evolutionary reinforcement learning

The integration of Reinforcement Learning (RL) and Evolutionary Algorithms (EAs) aims at simultaneously exploiting the sample efficiency as well as the diversity and robustness of the two paradigms. Recently, hybrid learning frameworks based on this principle have achieved great success in robot control tasks. However, in these methods, policies from the genetic population are evaluated via interactions with the real environments, severely restricting their applicability when such interactions are prohibitively costly. In this work, we propose Surrogate-assisted Controller (SC), a generic module that can be applied on top of existing hybrid frameworks to alleviate the computational burden of expensive fitness evaluation. The key to our approach is to leverage the critic network that is implemented in existing hybrid frameworks as a novel surrogate model, making it possible to estimate the fitness of individuals without environmental interactions. In addition, two model management strategies with the elite protection mechanism are introduced in SC to control the workflow, leading to a fast and stable optimization process. In the empirical studies, we combine SC with two state-of-the-art evolutionary reinforcement learning approaches to highlight its functionality and effectiveness. Experiments on six challenging continuous control benchmarks from the OpenAI Gym platform show that SC can not only significantly reduce the cost of interaction with the environment, but also bring better sample efficiency and dramatically boost the learning progress of the original hybrid framework.

Surrogate-assisted evolutionary optimization of expensive many-objective irregular problems

Surrogate-assisted evolutionary algorithms are one effective approach to handling expensive problems and have attracted increasing attention over the past decades. However, existing surrogate-assisted evolutionary algorithms pay little attention to expensive many-objective problems with irregular Pareto fronts, also called irregular problems. In this study, we propose a surrogate-assisted evolutionary algorithm for dealing with expensive irregular problems, where only a small number of expensive fitness evaluations is allowed. In the proposed algorithm, the reference vectors are adapted based on both the individuals in the current population and the non-dominated solutions that have been evaluated using the real objective functions. A surrogate management strategy is then designed to balance convergence and diversity according to the adaptive reference vectors as well as the non-dominated solutions that have been evaluated using the expensive objective functions so that the irregularity of the Pareto front can be taken into account. To reduce the computational cost for updating the Gaussian process based surrogates, a subset of training data near the adaptive reference vectors are prioritized. Experimental results on the DTLZ, WFG, DPF and MaF test suites demonstrate that the proposed algorithm is able to solve expensive many-objective optimization problems with both irregular and regular Pareto fronts. The proposed algorithm is also tested on a real-world application example to further confirm its effectiveness and competitiveness.

A multi-model assisted differential evolution algorithm for computationally expensive optimization problems

Surrogate models are commonly used to reduce the number of required expensive fitness evaluations in optimizing computationally expensive problems. Although many competitive surrogate-assisted evolutionary algorithms have been proposed, it remains a challenging issue to develop an effective model management strategy to address problems with different landscape features under a limited computational budget. This paper adopts a coarse-to-fine evaluation scheme basing on two surrogate models, i.e., a coarse Gaussian process and a fine radial basis function, for assisting a differential evolution algorithm to solve computationally expensive optimization problems. The coarse Gaussian process model is meant to capture the general contour of the fitness landscape to estimate the fitness and its degree of uncertainty. A surrogate-assisted environmental selection strategy is then developed according to the non-dominance relationship between approximated fitness and estimated uncertainty. Meanwhile, the fine radial basis function model aims to learn the details of the local fitness landscape to refine the approximation quality of the new parent population and find the local optima for real-evaluations. The performance and scalability of the proposed method are extensively evaluated on two sets of widely used benchmark problems. Experimental results show that the proposed method can outperform several state-of-the-art algorithms within a limited computational budget.

A random forest assisted evolutionary algorithm using competitive neighborhood search for expensive constrained combinatorial optimization

Many real-world combinatorial optimization problems have both expensive objective and constraint functions. Although surrogate models for the discrete decision variables can be trained to replace the expensive fitness evaluations in evolutionary algorithms, the approximation errors of the surrogate models for the constraint function easily misguide the search. The classic genetic algorithm, which is often applied straightforwardly to the combinatorial optimization problems, gradually exposes its inefficiency in the search process. Therefore, we proposed a random forest assisted evolutionary algorithm using a new competitive neighborhood search, where random forest is used as the surrogate models to approximate both the objective and constraint functions and the competitive neighborhood search is to improve the search efficiency. Moreover, competitive neighborhood search shows a natural adaptability to the surrogate model, which helps to reduce the impact of approximation errors. The proposed algorithm is tested on 01 knapsack problems and quadratic knapsack problems with various dimensions and constraints. The experimental results demonstrate that the proposed algorithm is able to solve the expensive constrained combinatorial optimization problems efficiently.

A Search History-Driven Offspring Generation Method for the Real-Coded Genetic Algorithm.

In evolutionary algorithms, genetic operators iteratively generate new offspring which constitute a potentially valuable set of search history. To boost the performance of offspring generation in the real-coded genetic algorithm (RCGA), in this paper, we propose to exploit the search history cached so far in an online style during the iteration. Specifically, survivor individuals over the past few generations are collected and stored in the archive to form the search history. We introduce a simple yet effective crossover model driven by the search history (abbreviated as SHX). In particular, the search history is clustered, and each cluster is assigned a score for SHX. In essence, the proposed SHX is a data-driven method which exploits the search history to perform offspring selection after the offspring generation. Since no additional fitness evaluations are needed, SHX is favorable for the tasks with limited budget or expensive fitness evaluations. We experimentally verify the effectiveness of SHX over 15 benchmark functions. Quantitative results show that our SHX can significantly enhance the performance of RCGA, in terms of both accuracy and convergence speed. Also, the induced additional runtime is negligible compared to the total processing time.

Optimizing the performance of optimization in the cloud environment–An intelligent auto-scaling approach

Abstract The cloud computing paradigm has gained wide acceptance in the scientific community, taking a significant share from fields previously reserved exclusively for High Performance Computing (HPC). On-demand access to a large amount of computing resources provided by Cloud makes it ideal for executing large-scale optimizations using evolutionary algorithms without the need for owning any computing infrastructure. In this regard, we extended WoBinGO, an existing parallel software framework for genetic algorithm based optimization, to be used in Cloud. With these extensions, the framework is capable of elastically and frugally utilizing the underlying cloud computing infrastructure for performing computationally expensive fitness evaluations. We studied two issues that are pertinent when dealing with large-scale optimization in the elastic cloud environment: the computing instance launching overhead and the price of engaging Cloud for solving optimization problems, in terms of the instances’ cumulative uptime. To explain the usability limits of WoBinGO framework running in the IaaS environment, a comprehensive analysis of the framework’s performance was given. Optimization of both total optimization time and total cumulative uptime, leads to minimizing the cost of cloud resources utilization. In this way, we are proposing an intelligent decision support engine based on artificial neural networks and metaheuristics to provide the user with an assessment of the framework’s behavior on the underlying infrastructure in terms of optimization duration and the cost of resource consumption. According to a given assessment, the user can decide upon faster delivery of results or lower infrastructure costs. The proposed software framework has been used to solve a complex real-world optimization problem of a subsurface rock mass model calibration. The results obtained from the private OpenStack deployment show that by using the proposed decision support engine, significant savings can be achieved in both optimization time and optimization cost.

A problem approximation surrogate model (PASM) for fitness approximation in optimizing the quantization table for the JPEG baseline algorithm

The quantization table in the baseline Joint Photographic Experts Group (JPEG) algorithm plays an important role in compression/quality trade-off. Hence the detection of the optimal quantization table is viewed as an optimization problem. The genetic algorithm (GA) is an attractive optimization tool by many researchers for this application due to its ability in dealing with complex problems. In spite of its advantages, the GA requires more computation time to achieve an optimal solution if it has an expensive fitness evaluation. This paper proposes a problem approximation surrogate model (PASM) for fitness approximation to assist the GA in optimizing the quantization table for a target bits per pixel. This proposal reduces the computational time of the GA without any loss in performance. The PASM uses an image block clustering process and an indirect evaluation method to approximate the fitness value. The number of clusters in the clustering process may influence the performance of the PASM. A performance analysis with different number of clusters has been done and a suitable cluster number is identified with the help of measuring criteria such as mean squared difference, correct selection, potentially correct selection, and rank correlation. In addition, the results acquired from these measuring criteria are confirmed using statistical hypothesis tests such as Friedman's ANOVA and Wilcoxon signed rank. The PASM with suitable cluster number has been tested in a classical genetic algorithm and knowledge based genetic algorithm. Several benchmark images with different complexity levels have been examined in three different target bits per pixel to validate the performance of the PASM. The results proved that the PASM guarantees better results in terms of peak signal-to-noise ratio with a reduction in computational time.

Reduction of function evaluation in differential evolution using nearest neighbor comparison

Approximation models have recently been introduced to differential evolution (DE) to reduce expensive fitness evaluation in function optimization. These models basically require additional control parameters and/or external storage for the learning process. Depending on the choice of the additional parameters, the strategies may have different levels of efficiency. The present paper introduces an alternative way for reducing function evaluations in differential evolution, which does not require additional control parameter and external archive. The algorithm uses a nearest neighbor in the search population to judge whether a new point is worth evaluating, so that unnecessary evaluations can be avoided. The performance of this new scheme of differential evolution, known as differential evolution with nearest neighbor comparison (DE-NNC), is demonstrated and compared with that of standard DE as well as approximation models including differential evolution using k-nearest neighbor predictor (DE-kNN), differential evolution using speeded-up k-nearest neighbor estimator (DE-EkNN) and DE with estimated comparison method through some test functions. The results show that DE-NNC can produce considerable reduction of actual function calls compared to DE and is competitive to DE-kNN, DE-EkNN and DE with estimated comparison.

On Using Surrogates with Genetic Programming.

One way to accelerate evolutionary algorithms with expensive fitness evaluations is to combine them with surrogate models. Surrogate models are efficiently computable approximations of the fitness function, derived by means of statistical or machine learning techniques from samples of fully evaluated solutions. But these models usually require a numerical representation, and therefore cannot be used with the tree representation of genetic programming (GP). In this paper, we present a new way to use surrogate models with GP. Rather than using the genotype directly as input to the surrogate model, we propose using a phenotypic characterization. This phenotypic characterization can be computed efficiently and allows us to define approximate measures of equivalence and similarity. Using a stochastic, dynamic job shop scenario as an example of simulation-based GP with an expensive fitness evaluation, we show how these ideas can be used to construct surrogate models and improve the convergence speed and solution quality of GP.

Parameter calibration framework for environmental emergency models

Simulation systems that predict the propagation of environmental emergencies have to satisfy hard real-time constraints to prevent tragedy. To obtain more reliable forecasts, input parameter calibration mechanisms should be integrated because it is often impossible to measure highly dynamic input parameters in a correct and timely manner. Evolutionary optimisation methods showed promising calibration potential but involve numerous expensive fitness evaluations. This makes their application to time-restricted real-world problems impractical, especially when only limited computing resources are available. We therefore propose a framework for efficient parameter calibration based on evolutionary intelligent systems. A genetic algorithm is joined with a case-based reasoner to form a hybrid calibration approach. The suggested framework allows the user to select the configuration of the calibration process according to emergency and prediction characteristics and available computing resources. The possibility to generate quick calibration estimates thus minimising the additional computational effort caused by the introduction of parameter calibration is highlighted. The framework was tested in the area of forest fire spread prediction. A case base was generated from real historical and synthetical forest fires. Experiments show that case-based reasoning generates results comparable to pure evolutionary optimisation approaches, clearly outperforming the latter in runtime.