Memetic particle swarm optimization

We propose a new Memetic Particle Swarm Optimization scheme that incorporates local search techniques in the standard Particle Swarm Optimization algorithm, resulting in an efficient and effective optimization method, which is analyzed theoretically. The proposed algorithm is applied to different unconstrained, constrained, minimax and integer programming problems and the obtained results are compared to that of the global and local variants of Particle Swarm Optimization, justifying the superiority of the memetic approach.     

Operation strategy optimization of desulfurization system based on data mining

Desulfurization systems in coal-fired power stations often suffer the problem of high operating costs caused by a rule-of-thumb control strategy, which implies great potential for optimization of the operation. Due to the complex desulfurization mechanism, frequently fluctuating unit load, and severe disturbance, it is challenging to determine the optimal operating parameters based on the traditional mechanistic models, and the operating parameters are closely related to the operational efficiency of the flue gas desulfurization system. In this paper, an operation strategy optimization method for the desulfurization process is proposed based on a data mining framework, which is able to determine online the optimal operating parameter settings from a large amount of historical data. First, Principal Component Analysis (PCA) is used to reduce data redundancy by mapping the data into a new vector space. Based on the new vector space, an enhanced fuzzy C-means clustering (Enhanced-FCM) is developed to cluster the historical data into groups sharing similar characteristics. Taking sulfur dioxide emission concentration as a constraint condition, the system is optimized with economic benefits and desulfurization efficiency as the objective function. When performing optimization, the group that current operating conditions belong to is determined first, then the operating parameters of the best performance are searched within the group and provided as the optimization results. The method is validated and tested based on the data from a wet flue gas desulfurization (WFGD) system of a 1000 MWe supercritical coal-fired power plant in China. The results indicate that the proposed operation strategy can appropriately obtain operating parameter settings at different conditions, and effectively reduce the desulfurization cost under the constraint of meeting emission requirements.     

Unsupervised and supervised data classification via nonsmooth and global optimization

We examine various methods for data clustering and data classification that are based on the minimization of the so-called cluster function and its modications. These functions are nonsmooth and nonconvex. We use Discrete Gradient methods for their local minimization. We consider also a combination of this method with the cutting angle method for global minimization. We present and discuss results of numerical experiments. This research was supported by the Australian Research Council.     

A network-based data mining approach to portfolio selection via weighted clique relaxations

We introduce a new network-based data mining approach to selecting diversified portfolios by modeling the stock market as a network and utilizing combinatorial optimization techniques to find maximum-weight s-plexes in the obtained networks. The considered approach is based on the weighted market graph model, which is used for identifying clusters of stocks according to a correlation-based criterion. The proposed techniques provide a new framework for selecting profitable diversified portfolios, which is verified by computational experiments on historical data over the past decade. In addition, the proposed approach can be used as a complementary tool for narrowing down a set of “candidate” stocks for a diversified portfolio, which can potentially be analyzed using other known portfolio selection techniques.     

Handling equality constraints in evolutionary optimization

Over the last few decades several methods have been proposed for handling functional constraints while solving optimization problems using evolutionary algorithms (EAs). However, the presence of equality constraints makes the feasible space very small compared to the entire search space. As a consequence, the handling of equality constraints has long been a difficult issue for evolutionary optimization methods. This paper presents a Hybrid Evolutionary Algorithm (HEA) for solving optimization problems with both equality and inequality constraints. In HEA, we propose a new local search technique with special emphasis on equality constraints. The basic concept of the new technique is to reach a point on the equality constraint from the current position of an individual solution, and then explore on the constraint landscape. We believe this new concept will influence the future research direction for constrained optimization using population based algorithms. The proposed algorithm is tested on a set of standard benchmark problems. The results show that the proposed technique works very well on those benchmark problems.     

Embedding evolutionary strategy in ordinal optimization for hard optimization problems

This work proposes a method for embedding evolutionary strategy (ES) in ordinal optimization (OO), abbreviated as ESOO, for solving real-time hard optimization problems with time-consuming evaluation of the objective function and a huge discrete solution space. Firstly, an approximate model that is based on a radial basis function (RBF) network is utilized to evaluate approximately the objective value of a solution. Secondly, ES associated with the approximate model is applied to generate a representative subset from a huge discrete solution space. Finally, the optimal computing budget allocation (OCBA) technique is adopted to select the best solution in the representative subset as the obtained “good enough” solution. The proposed method is applied to a hotel booking limits (HBL) problem, which is formulated as a stochastic combinatorial optimization problem with a huge discrete solution space. The good enough booking limits, obtained by the proposed method, have promising solution quality, and the computational efficiency of the method makes it suitable for real-time applications. To demonstrate the computational efficiency of the proposed method and the quality of the obtained solution, it is compared with two competing methods – the canonical ES and the genetic algorithm (GA). Test results demonstrate that the proposed approach greatly outperforms the canonical ES and GA.     

Improving biorefinery planning: Integration of spatial data using exact optimization nested in an evolutionary strategy

Biorefineries can provide a product portfolio from renewable biomass similar to that of crude oil refineries. To operate biorefineries of any kind, however, the availability of biomass inputs is crucial and must be considered during planning. Here, we develop a planning approach that uses Geographic Information Systems (GIS) to account for spatially scattered biomass when optimizing a biorefinery’s location, capacity, and configuration. To deal with the challenges of a non-smooth objective function arising from the geographic data, higher dimensionality, and strict constraints, the planning problem is repeatedly decomposed by nesting an exact nonlinear program (NLP) inside an evolutionary strategy (ES) heuristic, which handles the spatial data from the GIS. We demonstrate the functionality of the algorithm and show how including spatial data improves the planning process by optimizing a synthesis gas biorefinery using this new planning approach.     

Hierarchical visual data mining for large-scale data

Summary  An increasingly important problem in exploratory data analysis and visualization is that of scale; more and more data sets are much too large to analyze using traditional techniques, either in terms of the number of variables or the number of records. One approach to addressing this problem is the development and use of multiresolution strategies, where we represent the data at different levels of abstraction or detail through aggregation and summarization. In this paper we present an overview of our recent and current activities in the development of a multiresolution exploratory visualization environment for large-scale multivariate data. We have developed visualization, interaction, and data management techniques for effectively dealing with data sets that contain millions of records and/or hundreds of dimensions, and propose methods for applying similar approaches to extend the system to handle nominal as well as ordinal data.     

Robustness in multi-objective optimization using evolutionary algorithms

This work discusses robustness assessment during multi-objective optimization with a Multi-Objective Evolutionary Algorithm (MOEA) using a combination of two types of robustness measures. Expectation quantifies simultaneously fitness and robustness, while variance assesses the deviation of the original fitness in the neighborhood of the solution. Possible equations for each type are assessed via application to several benchmark problems and the selection of the most adequate is carried out. Diverse combinations of expectation and variance measures are then linked to a specific MOEA proposed by the authors, their selection being done on the basis of the results produced for various multi-objective benchmark problems. Finally, the combination preferred plus the same MOEA are used successfully to obtain the fittest and most robust Pareto optimal frontiers for a few more complex multi-criteria optimization problems.     

Evacuation planning using multiobjective evolutionary optimization approach

In an emergency situation, evacuation is conducted in order to displace people from a dangerous place to a safer place, and it usually needs to be done in a hurry. It is necessary to prepare evacuation plans in order to have a good response in an emergency situation. A central challenge in developing an evacuation plan is in determining the distribution of evacuees into the safe areas, that is, deciding where and from which road each evacuee should go. To achieve this aim, several objective functions should be brought into consideration and need to be satisfied simultaneously, though these objective functions may often conflict with each other.     

Hyper-spherical inversion transformations in multi-objective evolutionary optimization

Multi-objective evolutionary algorithms (MOEAs) are widely considered to have two goals: convergence towards the true Pareto front and maintaining a diverse set of solutions. The primary concern here is with the first goal of convergence, in particular when one or more variables must converge to a constant value. Using a number of well known test problems, the difficulties that are currently impeding convergence are discussed and then a new method is proposed that transforms the decision space using the geometric properties of hyper-spherical inversions to converge towards/onto the true Pareto front. Future extensions of this work and its application to multi-objective optimisation is discussed.     

A metamodel-assisted evolutionary algorithm for expensive optimization

Expensive optimization aims to find the global minimum of a given function within a very limited number of function evaluations. It has drawn much attention in recent years. The present expensive optimization algorithms focus their attention on metamodeling techniques, and call existing global optimization algorithms as subroutines. So it is difficult for them to keep a good balance between model approximation and global search due to their two-part property. To overcome this difficulty, we try to embed a metamodel mechanism into an efficient evolutionary algorithm, low dimensional simplex evolution (LDSE), in this paper. The proposed algorithm is referred to as the low dimensional simplex evolution extension (LDSEE). It is inherently parallel and self-contained. This renders it very easy to use. Numerical results show that our proposed algorithm is a competitive alternative for expensive optimization problems.     

Using multi-objective evolutionary algorithms for single-objective optimization

In recent decades, several multi-objective evolutionary algorithms have been successfully applied to a wide variety of multi-objective optimization problems. Along the way, several new concepts, paradigms and methods have emerged. Additionally, some authors have claimed that the application of multi-objective approaches might be useful even in single-objective optimization. Thus, several guidelines for solving single-objective optimization problems using multi-objective methods have been proposed. This paper offers a survey of the main methods that allow the use of multi-objective schemes for single-objective optimization. In addition, several open topics and some possible paths of future work in this area are identified.     

A metamodel-assisted evolutionary algorithm for expensive optimization

Expensive optimization aims to find the global minimum of a given function within a very limited number of function evaluations. It has drawn much attention in recent years. The present expensive optimization algorithms focus their attention on metamodeling techniques, and call existing global optimization algorithms as subroutines. So it is difficult for them to keep a good balance between model approximation and global search due to their two-part property. To overcome this difficulty, we try to embed a metamodel mechanism into an efficient evolutionary algorithm, low dimensional simplex evolution (LDSE), in this paper. The proposed algorithm is referred to as the low dimensional simplex evolution extension (LDSEE). It is inherently parallel and self-contained. This renders it very easy to use. Numerical results show that our proposed algorithm is a competitive alternative for expensive optimization problems.     

A novel three-phase trajectory informed search methodology for global optimization

A new deterministic method for solving a global optimization problem is proposed. The proposed method consists of three phases. The first phase is a typical local search to compute a local minimum. The second phase employs a discrete sup-local search to locate a so-called sup-local minimum taking the lowest objective value among the neighboring local minima. The third phase is an attractor-based global search to locate a new point of next descent with a lower objective value. The simulation results through well-known global optimization problems are shown to demonstrate the efficiency of the proposed method.     

Operations research and data mining

With the rapid growth of databases in many modern enterprises data mining has become an increasingly important approach for data analysis. The operations research community has contributed significantly to this field, especially through the formulation and solution of numerous data mining problems as optimization problems, and several operations research applications can also be addressed using data mining methods. This paper provides a survey of the intersection of operations research and data mining. The primary goals of the paper are to illustrate the range of interactions between the two fields, present some detailed examples of important research work, and provide comprehensive references to other important work in the area. The paper thus looks at both the different optimization methods that can be used for data mining, as well as the data mining process itself and how operations research methods can be used in almost every step of this process. Promising directions for future research are also identified throughout the paper. Finally, the paper looks at some applications related to the area of management of electronic services, namely customer relationship management and personalization.     

Variational optimization via chattering

We develop a chattering approach to solve variational problems that lack traditional properties such as differentiable everywhere and convexity conditions. We prove that our chattering approximation approaches the true relaxed solution as the intervals get smaller. Our chattering approach suggests a nonlinear optimization problem that can be easily solved to recover the optimal trajectory. A numerical example demonstrates our approach.     

Interactive evolutionary multi-objective optimization for quasi-concave preference functions

We present a new hybrid approach to interactive evolutionary multi-objective optimization that uses a partial preference order to act as the fitness function in a customized genetic algorithm. We periodically send solutions to the decision maker (DM) for her evaluation and use the resulting preference information to form preference cones consisting of inferior solutions. The cones allow us to implicitly rank solutions that the DM has not considered. This technique avoids assuming an exact form for the preference function, but does assume that the preference function is quasi-concave. This paper describes the genetic algorithm and demonstrates its performance on the multi-objective knapsack problem.