The main feature of the Dynamic Multi-objective Optimization Problems (DMOPs) is that optimization objective functions will change with times or environments. One of the promising approaches for solving the DMOPs is reusing the obtained Pareto optimal set (POS) to train prediction models via machine learning approaches. In this paper, we train an Incremental Support Vector Machine (ISVM) classifier with the past POS, and then the solutions of the DMOP we want to solve at the next moment are filtered through the trained ISVM classifier. A high-quality initial population will be generated by the ISVM classifier, and a variety of different types of population-based dynamic multi-objective optimization algorithms can benefit from the population. To verify this idea, we incorporate the proposed approach into three evolutionary algorithms, the multi-objective particle swarm optimization(MOPSO), Nondominated Sorting Genetic Algorithm II (NSGA-II), and the Regularity Model-based multi-objective estimation of distribution algorithm(RE-MEDA). We employ experiments to test these algorithms, and experimental results show the effectiveness.
Real-world problems typically require the simultaneous optimization of several, often conflicting objectives. Many of these multi-objective optimization problems are characterized by wide ranges of uncertainties in their decision variables or objective functions, which further increases the complexity of optimization. To cope with such uncertainties, robust optimization is widely studied aiming to distinguish candidate solutions with uncertain objectives specified by confidence intervals, probability distributions or sampled data. However, existing techniques mostly either fail to consider the actual distributions or assume uncertainty as instances of uniform or Gaussian distributions. This paper introduces an empirical approach that enables an efficient comparison of candidate solutions with uncertain objectives that can follow arbitrary distributions. Given two candidate solutions under comparison, this operator calculates the probability that one solution dominates the other in terms of each uncertain objective. It can substitute for the standard comparison operator of existing optimization techniques such as evolutionary algorithms to enable discovering robust solutions to problems with multiple uncertain objectives. This paper also proposes to incorporate various uncertainties in well-known multi-objective problems to provide a benchmark for evaluating uncertainty-aware optimization techniques. The proposed comparison operator and benchmark suite are integrated into an existing optimization tool that features a selection of multi-objective optimization problems and algorithms. Experiments show that in comparison with existing techniques, the proposed approach achieves higher optimization quality at lower overheads.
Population-based evolutionary algorithms have great potential to handle multiobjective optimisation problems. However, these algorithms depends largely on problem characteristics, and there is a need to improve their performance for a wider range of problems. References, which are often specified by the decision maker's preference in different forms, are a very effective method to improve the performance of algorithms but have not been fully explored in literature. This paper proposes a novel framework for effective use of references to strengthen algorithms. This framework considers references as search targets which can be adjusted based on the information collected during the search. The proposed framework is combined with new strategies, such as reference adaptation and adaptive local mating, to solve different types of problems. The proposed algorithm is compared with state of the arts on a wide range of problems with diverse characteristics. The comparison and extensive sensitivity analysis demonstrate that the proposed algorithm is competitive and robust across different types of problems studied in this paper.
Population diversity plays a key role in evolutionary algorithms that enables global exploration and avoids premature convergence. This is especially more crucial in dynamic optimization in which diversity can ensure that the population keeps track of the global optimum by adapting to the changing environment. Dynamic constrained optimization problems (DCOPs) have been the target for many researchers in recent years as they comprehend many of the current real-world problems. Regardless of the importance of diversity in dynamic optimization, there is not an extensive study investigating the effects of diversity promotion techniques in DCOPs so far. To address this gap, this paper aims to investigate how the use of different diversity mechanisms may influence the behavior of algorithms in DCOPs. To achieve this goal, we apply and adapt the most common diversity promotion mechanisms for dynamic environments using differential evolution (DE) as our base algorithm. The results show that applying diversity techniques to solve DCOPs in most test cases lead to significant enhancement in the baseline algorithm in terms of modified offline error values.
As evolutionary algorithms (EAs) are general-purpose optimization algorithms, recent theoretical studies have tried to analyze their performance for solving general problem classes, with the goal of providing a general theoretical explanation of the behavior of EAs. Particularly, a simple multi-objective EA, i.e., GSEMO, has been shown to be able to achieve good polynomial-time approximation guarantees for submodular optimization, where the objective function is only required to satisfy some properties but without explicit formulation. Submodular optimization has wide applications in diverse areas, and previous studies have considered the cases where the objective functions are monotone submodular, monotone non-submodular, or non-monotone submodular. To complement this line of research, this paper studies the problem class of maximizing monotone approximately submodular minus modular functions (i.e., $f=g-c$) with a size constraint, where $g$ is a non-negative monotone approximately submodular function and $c$ is a non-negative modular function, resulting in the objective function $f$ being non-monotone non-submodular. We prove that the GSEMO can achieve the best-known polynomial-time approximation guarantee. Empirical studies on the applications of Bayesian experimental design and directed vertex cover show the excellent performance of the GSEMO.
Accurate early diagnosis and monitoring of neurodegenerative conditions is essential for effective disease management and delivery of medication and treatment. This research develops automatic methods for detecting brain imaging preclinical biomarkers for Parkinson's disease (PD) by considering the novel application of evolutionary algorithms. A fundamental novel element of this work is the use of evolutionary algorithms to both map and predict the functional connectivity in patients using resting state functional MRI data taken from the PPMI to identify PD progression biomarkers. Specifically, Cartesian Genetic Programming was used to classify DCM data as well as time-series data. The findings were validated using two other commonly used classification methods (Artificial Neural Networks and Support Vector Machines) and by employing k-fold cross-validation. Across DCM and time-series analyses, findings revealed maximum accuracies of 75.21% for early stage (prodromal) PD patients versus healthy controls, 85.87% for PD patients versus prodromal PD patients, and 92.09% for PD patients versus healthy controls. Prodromal PD patients were classified from healthy controls with high accuracy - this is notable and represents the key finding of this research since current methods of diagnosing prodromal PD have both low reliability and low accuracy. Furthermore, Cartesian Genetic Programming provided comparable performance accuracy relative to ANN and SVM. Evolutionary algorithms enable us to decode the classifier in terms of understanding the data inputs that are used, more easily than in ANN and SVM. Hence, these findings underscore the relevance of both DCM analyses for classification and CGP as a novel classification tool for brain imaging data with medical implications for disease diagnosis, particularly in early and asymptomatic stages.
Recently, more and more works have proposed to drive evolutionary algorithms using machine learning models. Usually, the performance of such model based evolutionary algorithms is highly dependent on the training qualities of the adopted models. Since it usually requires a certain amount of data (i.e. the candidate solutions generated by the algorithms) for model training, the performance deteriorates rapidly with the increase of the problem scales, due to the curse of dimensionality. To address this issue, we propose a multi-objective evolutionary algorithm driven by the generative adversarial networks (GANs). At each generation of the proposed algorithm, the parent solutions are first classified into real and fake samples to train the GANs; then the offspring solutions are sampled by the trained GANs. Thanks to the powerful generative ability of the GANs, our proposed algorithm is capable of generating promising offspring solutions in high-dimensional decision space with limited training data. The proposed algorithm is tested on 10 benchmark problems with up to 200 decision variables. Experimental results on these test problems demonstrate the effectiveness of the proposed algorithm.
Wave energy technologies have the potential to play a significant role in the supply of renewable energy on a world scale. One of the most promising designs for wave energy converters (WECs) are fully submerged buoys. In this work, we explore the optimisation of WEC arrays consisting of a three-tether buoy model called CETO. Such arrays can be optimised for total energy output by adjusting both the relative positions of buoys in farms and also the power-take-off (PTO) parameters for each buoy. The search space for these parameters is complex and multi-modal. Moreover, the evaluation of each parameter setting is computationally expensive -- limiting the number of full model evaluations that can be made. To handle this problem, we propose a new hybrid cooperative co-evolution algorithm (HCCA). HCCA consists of a symmetric local search plus Nelder-Mead and a cooperative co-evolution algorithm (CC) with a backtracking strategy for optimising the positions and PTO settings of WECs, respectively. Moreover, a new adaptive scenario is proposed for tuning grey wolf optimiser (AGWO) hyper-parameter. AGWO participates notably with other applied optimisers in HCCA. For assessing the effectiveness of the proposed approach five popular Evolutionary Algorithms (EAs), four alternating optimisation methods and two modern hybrid ideas (LS-NM and SLS-NM-B) are carefully compared in four real wave situations (Adelaide, Tasmania, Sydney and Perth) with two wave farm sizes (4 and 16). According to the experimental outcomes, the hybrid cooperative framework exhibits better performance in terms of both runtime and quality of obtained solutions.
Several real-world applications could be modeled as Mixed-Integer Non-Linear Programming (MINLP) problems, and some prominent examples include portfolio optimization, remote sensing technology, and so on. Most of the models for these applications are non-convex and always involve some conflicting objectives. The mathematical and heuristic methods have their advantages in solving this category of problems. In this work, we turn to Multi-Objective Evolutionary Algorithms (MOEAs) for finding elegant solutions for such problems. In this framework, we investigate a multi-objective constrained portfolio optimization problem, which can be cast as a classical financial problem and can also be naturally modeled as an MINLP problem. Consequently, we point out one challenge, faced by a direct coding scheme for MOEAs, to this problem. It is that the dependence among variables, like the selection and weights for one same asset, will likely make the search difficult. We thus, propose a Compressed Coding Scheme (CCS), compressing the two dependent variables into one variable to utilize the dependence and thereby meeting this challenge. Subsequently, we carry out a detailed empirical study on two sets of instances. The first part consists of 5 instances from OR-Library, which is solvable for the general mathematical optimizer, like CPLEX, while the remaining 15 instances from NGINX are addressed only by MOEAs. The two benchmarks, involving the number of assets from 31 to 2235, consistently indicate that CCS is not only efficient but also robust for dealing with the constrained multi-objective portfolio optimization.
The possibility to use competitive evolutionary algorithms to generate long-term progress is normally prevented by the convergence on limit cycle dynamics in which the evolving agents keep progressing against their current competitors by periodically rediscovering solutions adopted previously over and over again. This leads to local but not to global progress, i.e. progress against all possible competitors. We propose a new competitive algorithm that produces long-term global progress by identifying and by filtering out opportunistic variations, i.e. variations leading to progress against current competitors and retrogression against other competitors. The efficacy of the method is validated on the co-evolution of predator and prey robots, a classic problem that has been used in other related researches. The accumulation of global progress over many generations leads to effective solutions that involve the production of rather articulated behaviors. The complexity of the behavior displayed by the evolving robots increases across generations although progresses in performance are not always accompanied by behavior complexification.
Water distribution system design is a challenging optimisation problem with a high number of search dimensions and constraints. In this way, Evolutionary Algorithms (EAs) have been widely applied to optimise WDS to minimise cost subject whilst meeting pressure constraints. This paper proposes a new hybrid evolutionary framework that consists of three distinct phases. The first phase applied CMA-ES, a robust adaptive meta-heuristic for continuous optimisation. This is followed by an upward-greedy search phase to remove pressure violations. Finally, a downward greedy search phase is used to reduce oversized pipes. To assess the effectiveness of the hybrid method, it was applied to five well-known WDSs case studies. The results reveal that the new framework outperforms CMA-ES by itself and other previously applied heuristics on most benchmarks in terms of both optimisation speed and network cost.
Many-objective evolutionary algorithms (MOEAs), especially the decomposition-based MOEAs, have attracted wide attention in recent years. Recent studies show that a well designed combination of the decomposition method and the domination method can improve the performance ,i.e., convergence and diversity, of a MOEA. In this paper, a novel way of combining the decomposition method and the domination method is proposed. More precisely, a set of weight vectors is employed to decompose a given many-objective optimization problem(MaOP), and a hybrid method of the penalty-based boundary intersection function and dominance is proposed to compare local solutions within a subpopulation defined by a weight vector. A MOEA based on the hybrid method is implemented and tested on problems chosen from two famous test suites, i.e., DTLZ and WFG. The experimental results show that our algorithm is very competitive in dealing with MaOPs. Subsequently, our algorithm is extended to solve constraint MaOPs, and the constrained version of our algorithm also shows good performance in terms of convergence and diversity. These reveals that using dominance locally and combining it with the decomposition method can effectively improve the performance of a MOEA.
When globally optimal solutions of complicated optimization problems cannot be located by evolutionary algorithms (EAs) in polynomial expected running time, the hitting time/running time analysis is not flexible enough to accommodate the requirement of theoretical study, because sometimes we have no idea on what approximation ratio is available in polynomial expected running time. Thus, it is necessary to propose an alternative routine for the theoretical analysis of EAs. To bridge the gap between theoretical analysis and algorithm implementation, in this paper we perform an error analysis where expected approximation error is estimated to evaluate performances of randomized search heuristics (RSHs). Based on the Markov chain model of RSHs, the multi-step transition matrix can be computed by diagonalizing the one-step transition matrix, and a general framework for estimation of expected approximation errors is proposed. Case studies indicate that the error analysis works well for both uni- and multi-modal benchmark problems. It leads to precise estimations of approximation error instead of asymptotic results on fitness values, which demonstrates its competitiveness to fixed budget analysis.
A common view in evolutionary biology is that mutation rates are minimised. However, studies in combinatorial optimisation and search have shown a clear advantage of using variable mutation rates as a control parameter to optimise the performance of evolutionary algorithms. Much biological theory in this area is based on Ronald Fisher's work, who used Euclidean geometry to study the relation between mutation size and expected fitness of the offspring in infinite phenotypic spaces. Here we reconsider this theory based on the alternative geometry of discrete and finite spaces of DNA sequences. First, we consider the geometric case of fitness being isomorphic to distance from an optimum, and show how problems of optimal mutation rate control can be solved exactly or approximately depending on additional constraints of the problem. Then we consider the general case of fitness communicating only partial information about the distance. We define weak monotonicity of fitness landscapes and prove that this property holds in all landscapes that are continuous and open at the optimum. This theoretical result motivates our hypothesis that optimal mutation rate functions in such landscapes will increase when fitness decreases in some neighbourhood of an optimum, resembling the control functions derived in the geometric case. We test this hypothesis experimentally by analysing approximately optimal mutation rate control functions in 115 complete landscapes of binding scores between DNA sequences and transcription factors. Our findings support the hypothesis and find that the increase of mutation rate is more rapid in landscapes that are less monotonic (more rugged). We discuss the relevance of these findings to living organisms.
This paper provides an in-depth review of the optimal design of type-1 and type-2 fuzzy inference systems (FIS) using five well known computational frameworks: genetic-fuzzy systems (GFS), neuro-fuzzy systems (NFS), hierarchical fuzzy systems (HFS), evolving fuzzy systems (EFS), and multi-objective fuzzy systems (MFS), which is in view that some of them are linked to each other. The heuristic design of GFS uses evolutionary algorithms for optimizing both Mamdani-type and Takagi-Sugeno-Kang-type fuzzy systems. Whereas, the NFS combines the FIS with neural network learning systems to improve the approximation ability. An HFS combines two or more low-dimensional fuzzy logic units in a hierarchical design to overcome the curse of dimensionality. An EFS solves the data streaming issues by evolving the system incrementally, and an MFS solves the multi-objective trade-offs like the simultaneous maximization of both interpretability and accuracy. This paper offers a synthesis of these dimensions and explores their potentials, challenges, and opportunities in FIS research. This review also examines the complex relations among these dimensions and the possibilities of combining one or more computational frameworks adding another dimension: deep fuzzy systems.
In [1], we have explored the theoretical aspects of feature selection and evolutionary algorithms. In this chapter, we focus on optimization algorithms for enhancing data analytic process, i.e., we propose to explore applications of nature-inspired algorithms in data science. Feature selection optimization is a hybrid approach leveraging feature selection techniques and evolutionary algorithms process to optimize the selected features. Prior works solve this problem iteratively to converge to an optimal feature subset. Feature selection optimization is a non-specific domain approach. Data scientists mainly attempt to find an advanced way to analyze data n with high computational efficiency and low time complexity, leading to efficient data analytics. Thus, by increasing generated/measured/sensed data from various sources, analysis, manipulation and illustration of data grow exponentially. Due to the large scale data sets, Curse of dimensionality (CoD) is one of the NP-hard problems in data science. Hence, several efforts have been focused on leveraging evolutionary algorithms (EAs) to address the complex issues in large scale data analytics problems. Dimension reduction, together with EAs, lends itself to solve CoD and solve complex problems, in terms of time complexity, efficiently. In this chapter, we first provide a brief overview of previous studies that focused on solving CoD using feature extraction optimization process. We then discuss practical examples of research studies are successfully tackled some application domains, such as image processing, sentiment analysis, network traffics / anomalies analysis, credit score analysis and other benchmark functions/data sets analysis.
This paper extends the runtime analysis of non-elitist evolutionary algorithms (EAs) with fitness-proportionate selection from the simple OneMax function to the linear functions. Not only does our analysis cover a larger class of fitness functions, it also holds for a wider range of mutation rates. We show that with overwhelmingly high probability, no linear function can be optimised in less than exponential time, assuming bitwise mutation rate $\Theta(1/n)$ and population size $\lambda=n^k$ for any constant $k>2$. In contrast to this negative result, we also show that for any linear function with polynomially bounded weights, the EA achieves a polynomial expected runtime if the mutation rate is reduced to $\Theta(1/n^2)$ and the population size is sufficiently large. Furthermore, the EA with mutation rate $\chi/n=\Theta(1/n)$ and modest population size $\lambda=\Omega(\ln n)$ optimises the scaled fitness function $e^{(\chi+\varepsilon)f(x)}$ for any linear function $f$ and any $\varepsilon>0$ in expected time $O(n\lambda\ln\lambda+n^2)$. These upper bounds also extend to some additively decomposed fitness functions, such as the Royal Road functions. We expect that the obtained results may be useful not only for the development of the theory of evolutionary algorithms, but also for biological applications, such as the directed evolution.
he greatest weakness of evolutionary algorithms, widely used today, is the premature convergence due to the loss of population diversity over generations. To overcome this problem, several algorithms have been proposed, such as the Graph-based Evolutionary Algorithm (GEA) \cite{1} which uses graphs to model the structure of the population, but also memetic or differential evolution algorithms \cite{2,3}, or diversity-based ones \cite{4,5} have been designed. These algorithms are based on multi-populations, or often rather focus on the self-tuning parameters, however, they become complex to tune because of their high number of parameters. In this paper, our approach consists of an evolutionary algorithm that allows a dynamic adaptation of the search operators based on a graph in order to limit the loss of diversity and reduce the design complexity.
A large number of engineering, science and computational problems have yet to be solved in a computationally efficient way. One of the emerging challenges is how evolving technologies grow towards autonomy and intelligent decision making. This leads to collection of large amounts of data from various sensing and measurement technologies, e.g., cameras, smart phones, health sensors, smart electricity meters, and environment sensors. Hence, it is imperative to develop efficient algorithms for generation, analysis, classification, and illustration of data. Meanwhile, data is structured purposefully through different representations, such as large-scale networks and graphs. We focus on data science as a crucial area, specifically focusing on a curse of dimensionality (CoD) which is due to the large amount of generated/sensed/collected data. This motivates researchers to think about optimization and to apply nature-inspired algorithms, such as evolutionary algorithms (EAs) to solve optimization problems. Although these algorithms look un-deterministic, they are robust enough to reach an optimal solution. Researchers do not adopt evolutionary algorithms unless they face a problem which is suffering from placement in local optimal solution, rather than global optimal solution. In this chapter, we first develop a clear and formal definition of the CoD problem, next we focus on feature extraction techniques and categories, then we provide a general overview of meta-heuristic algorithms, its terminology, and desirable properties of evolutionary algorithms.
Along with the development of manufacture and services, the problem of distribution network optimization has been growing in importance, thus receiving much attention from the research community. One of the most recently introduced network optimization problems is the Clustered Shortest-Path Tree Problem (CluSTP). Since the problem is NP-Hard, recent approaches often prefer to use approximation algorithms to solve it, several of which used Evolutionary Algorithms (EAs) and have been proven to be effective. However, most of the prior studies directly applied EAs to the whole CluSTP problem, which leads to a great amount of resource consumption, especially when the problem size is large. To overcome these limitations, this paper suggests a method for reducing the search space of the EAs applied to CluSTP by decomposing the original problem into two sub-problems, the solution to one of which is found by an EAs and that to the other is found by another method. The goal of the first sub-problem is to determine a spanning tree which connects among the clusters, while the goal of the second sub-problem is to determine the best spanning tree for each cluster. In addition, this paper proposes a new EAs, which can be applied to solve the first sub-problem and suggests using the Dijkstra's algorithm to solve the second sub-problem. The proposed approach is comprehensively experimented and compared with existing methods. Experimental results prove that our method is more efficient and more importantly, it can obtain results which are close to the optimal results.