Seeking multiple solutions:an updated survey on niching methods and their applications

Multi-Modal Optimization (MMO) aiming to locate multiple optimal (or near-optimal) solutions in a single simulation run has practical relevance to problem solving across many fields. Population-based meta-heuristics have been shown particularly effective in solving MMO problems, if equipped with specificallydesigned diversity-preserving mechanisms, commonly known as niching methods. This paper provides an updated survey on niching methods. The paper first revisits the fundamental concepts about niching and its most representative schemes, then reviews the most recent development of niching methods, including novel and hybrid methods, performance measures, and benchmarks for their assessment. Furthermore, the paper surveys previous attempts at leveraging the capabilities of niching to facilitate various optimization tasks (e.g., multi-objective and dynamic optimization) and machine learning tasks (e.g., clustering, feature selection, and learning ensembles). A list of successful applications of niching methods to real-world problems is presented to demonstrate the capabilities of niching methods in providing solutions that are difficult for other optimization methods to offer. The significant practical value of niching methods is clearly exemplified through these applications. Finally, the paper poses challenges and research questions on niching that are yet to be appropriately addressed. Providing answers to these questions is crucial before we can bring more fruitful benefits of niching to real-world problem solving

Building nearest prototype classifiers using a Michigan approach PSO

IEEE Swarm Intelligence Symposium. Honolulu, HI, 1-5 april 2007This paper presents an application of particle swarm optimization (PSO) to continuous classification problems, using a Michigan approach. In this work, PSO is used to process training data to find a reduced set of prototypes to be used to classify the patterns, maintaining or increasing the accuracy of the nearest neighbor classifiers. The Michigan approach PSO represents each prototype by a particle and uses modified movement rules with particle competition and cooperation that ensure particle diversity. The result is that the particles are able to recognize clusters, find decision boundaries and achieve stable situations that also retain adaptation potential. The proposed method is tested both with artificial problems and with three real benchmark problems with quite promising results

Uncertainty evaluation of reservoir simulation models using particle swarms and hierarchical clustering

History matching production data in finite difference reservoir simulation models has been and always will be a challenge for the industry. The principal hurdles that need to be overcome are finding a match in the first place and more importantly a set of matches that can capture the uncertainty range of the simulation model and to do this in as short a time as possible since the bottleneck in this process is the length of time taken to run the model. This study looks at the implementation of Particle Swarm Optimisation (PSO) in history matching finite difference simulation models. Particle Swarms are a class of evolutionary algorithms that have shown much promise over the last decade. This method draws parallels from the social interaction of swarms of bees, flocks of birds and shoals of fish. Essentially a swarm of agents are allowed to search the solution hyperspace keeping in memory each individual’s historical best position and iteratively improving the optimisation by the emergent interaction of the swarm. An intrinsic feature of PSO is its local search capability. A sequential niching variation of the PSO has been developed viz. Flexi-PSO that enhances the exploration and exploitation of the hyperspace and is capable of finding multiple minima. This new variation has been applied to history matching synthetic reservoir simulation models to find multiple distinct history 3 matches to try to capture the uncertainty range. Hierarchical clustering is then used to post-process the history match runs to reduce the size of the ensemble carried forward for prediction. The success of the uncertainty modelling exercise is then assessed by checking whether the production profile forecasts generated by the ensemble covers the truth case

Bio-inspired computation: where we stand and what's next

In recent years, the research community has witnessed an explosion of literature dealing with the adaptation of behavioral patterns and social phenomena observed in nature towards efficiently solving complex computational tasks. This trend has been especially dramatic in what relates to optimization problems, mainly due to the unprecedented complexity of problem instances, arising from a diverse spectrum of domains such as transportation, logistics, energy, climate, social networks, health and industry 4.0, among many others. Notwithstanding this upsurge of activity, research in this vibrant topic should be steered towards certain areas that, despite their eventual value and impact on the field of bio-inspired computation, still remain insufficiently explored to date. The main purpose of this paper is to outline the state of the art and to identify open challenges concerning the most relevant areas within bio-inspired optimization. An analysis and discussion are also carried out over the general trajectory followed in recent years by the community working in this field, thereby highlighting the need for reaching a consensus and joining forces towards achieving valuable insights into the understanding of this family of optimization techniques

Bio-inspired computation: where we stand and what's next

In recent years, the research community has witnessed an explosion of literature dealing with the adaptation of behavioral patterns and social phenomena observed in nature towards efficiently solving complex computational tasks. This trend has been especially dramatic in what relates to optimization problems, mainly due to the unprecedented complexity of problem instances, arising from a diverse spectrum of domains such as transportation, logistics, energy, climate, social networks, health and industry 4.0, among many others. Notwithstanding this upsurge of activity, research in this vibrant topic should be steered towards certain areas that, despite their eventual value and impact on the field of bio-inspired computation, still remain insufficiently explored to date. The main purpose of this paper is to outline the state of the art and to identify open challenges concerning the most relevant areas within bio-inspired optimization. An analysis and discussion are also carried out over the general trajectory followed in recent years by the community working in this field, thereby highlighting the need for reaching a consensus and joining forces towards achieving valuable insights into the understanding of this family of optimization techniques

Effective Simulation and Optimization of a Laser Peening Process

Laser peening (LP) is a surface enhancement technique that has been applied to improve fatigue and corrosion properties of metals. The ability to use a high energy laser pulse to generate shock waves, inducing a compressive residual stress field in metallic materials, has applications in multiple fields such as turbomachinery, airframe structures, and medical appliances. In the past, researchers have investigated the effects of LP parameters experimentally and performed a limited number of simulations on simple geometries. However, monitoring the dynamic, intricate relationships of peened materials experimentally is time consuming, expensive, and challenging. With increasing applications of LP on complex geometries, these limited experimental and simulation capabilities are not sufficient for an effective LP process design. Due to high speed, dynamic process parameters, it is difficult to achieve a consistent residual stress field in each treatment and constrain detrimental effects. With increased computer speed as well as increased sophistication in non-linear finite element analysis software, it is now possible to develop simulations that can consider several LP parameters. In this research, a finite element simulation capability of the LP process is developed. These simulations are validated with the available experimental results. Based on the validated model, simplifications to complex models are developed. These models include quarter symmetric 3D model, a cylindrical coupon, a parametric plate, and a bending coupon model. The developed models can perform simulations incorporating the LP process parameters, such as pressure pulse properties, spot properties, number of shots, locations, sequences, overlapping configurations, and complex geometries. These models are employed in parametric investigations and residual stress profile optimization at single and multiple locations. In parametric investigations, quarter symmetric 3D model is used to investigate temporal variations of pressure pulse, pressure magnitude, and shot shape and size. The LP optimization problem is divided into two parts: single and multiple locations peening optimization. The single-location peening optimization problems have mixed design variables and multiple optimal solutions. In the optimization literature, many researchers have solved problems involving mixed variables or multiple optima, but it is difficult to find multiple solutions for mixed-variable problems. A mixed-variable Niche Particle Swarm Optimization (MNPSO) is proposed that incorporates a mixed-variable handling technique and a niching technique to solve the problem. Designing an optimal residual stress profile for multiple-location peening is a challenging task due to the computational cost and the nonlinear behavior of LP. A Progressive Multifidelity Optimization Strategy (PMOS) is proposed to solve the problem. The three-stage PMOS, combines low- and high- fidelity simulations and respective surrogate models and a mixed-variable handling strategy. This strategy employs comparatively low computational-intensity models in the first two stages to locate the design space that may contain the optimal solution. The third stage employs high fidelity simulation and surrogate models to determine the optimal solution. The overall objective of this research is to employ finite element simulations and effective optimization techniques to achieve optimal residual stress fields

Derating NichePSO

The search for multiple solutions is applicable to many fields (Engineering [54][67], Science [75][80][79][84][86], Economics [13][59], and others [51]). Multiple solutions allow for human judgement to select the best solution from a group of solutions that best match the search criteria. Finding multiple solutions to an optimisation problem has shown to be difficult to solve. Evolutionary computation (EC) and more recently Particle Swarm Optimisation (PSO) algorithms have been used in this field to locate and maintain multiple solutions with fair success. This thesis develops and empirically analyses a new method to find multiple solutions within a convoluted search space. The method is a hybrid of the NichePSO [14] and the sequential niche technique (SNT)[8]. The original SNT was developed using a Genetic Algorithm (GA). It included restrictions such as knowing or approximating the number of solutions that exist. A further pitfall of the SNT is that it introduces false optima after modifying the search space, thereby reducing the accuracy of the solutions. However, this can be resolved with a local search in the unmodified search space. Other sequential niching algorithms require that the search be repeated sequentially until all solutions are found without considering what was learned in previous iterations, resulting in a blind and wasteful search. The NichePSO has shown to be more accurate than GA based algorithms [14][15]. It does not require knowledge of the number of solutions in the search space prior to the search process. However, the NichePSO does not scale well for problems with many optima [16]. The method developed in this thesis, referred to as the derating NichePSO, combines SNT with the NichePSO. The main objective of the derating NichePSO is to eliminate the inaccuracy of SNT and to improve the scalability of the NichePSO. The derating NichePSO is compared to the NichePSO, deterministic crowding [23] and the original SNT using various multimodal functions. The performance of the derating NichePSO is analysed and it is shown that the derating NichePSO is more accurate than SNT and more scalable than the NichePSO.Dissertation (MSc)--University of Pretoria, 2007.Computer ScienceMScUnrestricte

Nature-inspired algorithms for solving some hard numerical problems

Optimisation is a branch of mathematics that was developed to find the optimal solutions, among all the possible ones, for a given problem. Applications of optimisation techniques are currently employed in engineering, computing, and industrial problems. Therefore, optimisation is a very active research area, leading to the publication of a large number of methods to solve specific problems to its optimality. This dissertation focuses on the adaptation of two nature inspired algorithms that, based on optimisation techniques, are able to compute approximations for zeros of polynomials and roots of non-linear equations and systems of non-linear equations. Although many iterative methods for finding all the roots of a given function already exist, they usually require: (a) repeated deflations, that can lead to very inaccurate results due to the problem of accumulating rounding errors, (b) good initial approximations to the roots for the algorithm converge, or (c) the computation of first or second order derivatives, which besides being computationally intensive, it is not always possible. The drawbacks previously mentioned served as motivation for the use of Particle Swarm Optimisation (PSO) and Artificial Neural Networks (ANNs) for root-finding, since they are known, respectively, for their ability to explore high-dimensional spaces (not requiring good initial approximations) and for their capability to model complex problems. Besides that, both methods do not need repeated deflations, nor derivative information. The algorithms were described throughout this document and tested using a test suite of hard numerical problems in science and engineering. Results, in turn, were compared with several results available on the literature and with the well-known Durand–Kerner method, depicting that both algorithms are effective to solve the numerical problems considered.A Optimização é um ramo da matemática desenvolvido para encontrar as soluções óptimas, de entre todas as possíveis, para um determinado problema. Actualmente, são várias as técnicas de optimização aplicadas a problemas de engenharia, de informática e da indústria. Dada a grande panóplia de aplicações, existem inúmeros trabalhos publicados que propõem métodos para resolver, de forma óptima, problemas específicos. Esta dissertação foca-se na adaptação de dois algoritmos inspirados na natureza que, tendo como base técnicas de optimização, são capazes de calcular aproximações para zeros de polinómios e raízes de equações não lineares e sistemas de equações não lineares. Embora já existam muitos métodos iterativos para encontrar todas as raízes ou zeros de uma função, eles usualmente exigem: (a) deflações repetidas, que podem levar a resultados muito inexactos, devido ao problema da acumulação de erros de arredondamento a cada iteração; (b) boas aproximações iniciais para as raízes para o algoritmo convergir, ou (c) o cálculo de derivadas de primeira ou de segunda ordem que, além de ser computacionalmente intensivo, para muitas funções é impossível de se calcular. Estas desvantagens motivaram o uso da Optimização por Enxame de Partículas (PSO) e de Redes Neurais Artificiais (RNAs) para o cálculo de raízes. Estas técnicas são conhecidas, respectivamente, pela sua capacidade de explorar espaços de dimensão superior (não exigindo boas aproximações iniciais) e pela sua capacidade de modelar problemas complexos. Além disto, tais técnicas não necessitam de deflações repetidas, nem do cálculo de derivadas. Ao longo deste documento, os algoritmos são descritos e testados, usando um conjunto de problemas numéricos com aplicações nas ciências e na engenharia. Os resultados foram comparados com outros disponíveis na literatura e com o método de Durand–Kerner, e sugerem que ambos os algoritmos são capazes de resolver os problemas numéricos considerados

Structural optimization using evolutionary multimodal and bilevel optimization techniques

This research aims to investigate the multimodal properties of structural optimization using techniques from the field of evolutionary computation, specifically niching and bilevel techniques. Truss design is a well-known structural optimization problem which has important practical applications in many fields. Truss design problems are typically multimodal by nature, meaning that it offers multiple equally good design solutions with respect to the topology and/or sizes of the members, but they are evaluated to have similar or equally good objective function values. From a practical standpoint, it is desirable to find as many alternative designs as possible, rather than finding a single design, as often practiced. Niching is an intuitive way of finding multiple optimal solutions in a single optimization run. Literature shows that existing niching methods are largely designed for handling continuous optimization problems. There does not exist a well-studied niching method for constrained discrete optimization problems like truss design problems. In addition, there are no well-defined multimodal discrete benchmark problems that can be used to evaluate the reliability and robustness of such a niching method. This thesis fills the identified research gaps by means of five major contributions. In the first contribution, we design a test suite for producing a diverse set of challenging multimodal discrete benchmark problems, which can be used for evaluating the discrete niching methods. In the second contribution, we develop a binary speciation-based PSO (B-SPSO) niching method using the concept of speciation in nature along with the binary PSO (BPSO). The results show that the proposed multimodal discrete benchmark problems are useful for the evaluation of the discrete niching methods like B-SPSO. In light of this study, a time-varying transfer function based binary PSO (TVT-BPSO) is developed for the B-SPSO which is the third contribution of this thesis. We propose this TVT-BPSO for maintaining a better balance between exploration/exploitation during the search process of the BPSO. The results show that the TVT-BPSO outperforms the state-of-the-art discrete optimization methods on the large-scale 0-1 knapsack problems. The fourth contribution is to consider and formulate the truss design problem as a bilevel optimization problem. With this new formulation, truss topology can be optimized in the upper level, at the same time the size of that truss topology can be optimized in the lower level. The proposed bilevel formulation is a precursor to the development of a bilevel niching method (Bi-NM) which constitutes the fifth contribution of this thesis. The proposed Bi-NM method performs niching at the upper level and a local search at the lower level to further refine the solutions. Extensive empirical studies are carried out to examine the accuracy, robustness, and efficiency of the proposed bilevel niching method in finding multiple topologies and their size solutions. Our results confirm that the proposed bilevel niching method is superior in all these three aspects over the state-of-the-art methods on several low to high-dimensional truss design problems

Multi self-adapting particle swarm optimization algorithm (MSAPSO).

The performance and stability of the Particle Swarm Optimization algorithm depends on parameters that are typically tuned manually or adapted based on knowledge from empirical parameter studies. Such parameter selection is ineffectual when faced with a broad range of problem types, which often hinders the adoption of PSO to real world problems. This dissertation develops a dynamic self-optimization approach for the respective parameters (inertia weight, social and cognition). The effects of self-adaption for the optimal balance between superior performance (convergence) and the robustness (divergence) of the algorithm with regard to both simple and complex benchmark functions is investigated. This work creates a swarm variant which is parameter-less, which means that it is virtually independent of the underlying examined problem type. As PSO variants always have the issue, that they can be stuck-in-local-optima, as second main topic the MSAPSO algorithm do have a highly flexible escape-lmin-strategy embedded, which works dimension-less. The MSAPSO algorithm outperforms other PSO variants and also other swarm inspired approaches such as Memetic Firefly algorithm with these two major algorithmic elements (parameter-less approach, dimension-less escape-lmin-strategy). The average performance increase in two dimensions is at least fifteen percent with regard to the compared swarm variants. In higher dimensions (≥ 250) the performance gain accumulates to about fifty percent in average. At the same time the error-proneness of MSAPSO is in average similar or even significant better when converging to the respective global optima’s