On decomposition methods in interactive user-preference based optimization

Evolutionary multi-objective optimization (EMO) methodologies have been widely applied to find a well-distributed trade-off solutions approximating to the Pareto-optimal front in the past decades. However, integrating the user-preference into the optimization to find the region of interest (ROI) [1] or preferred Pareto-optimal solutions could be more efficient and effective for the decision maker (DM) straightforwardly. In this paper, we propose several methods by combining preference-based strategy (like the reference points) with the decomposition-based multi-objective evolutionary algorithm (MOEA/D) [2], and demonstrate how preferred sets or ROIs near the different reference points specified by the DM can be found simultaneously and interactively. The study is based on the experiments conducted on a set of test problems with objectives ranging from two to fifteen objectives. Experiments have proved that the proposed approaches are more efficient and effective especially on many-objective problems to provide a set of solutions to the DM's preference, so that a better and a more reliable decision can be made.     

Closed-loop evolutionary multiobjective optimization

Artificial evolution has been used for more than 50 years as a method of optimization in engineering, operations research and computational intelligence. In closed-loop evolution (a term used by the statistician, George Box) or, equivalently, evolutionary experimentation (Ingo Rechenberg?s terminology), the ?phenotypes? are evaluated in the real world by conducting a physical experiment, whilst selection and breeding is simulated. Well-known early work on artificial evolution?design engineering problems in fluid dynamics, and chemical plant process optimization? was carried out in this experimental mode. More recently, the closed-loop approach has been successfully used in much evolvable hardware and evolutionary robotics research, and in some microbiology and biochemistry applications. In this article, several further new targets for closed-loop evolutionary and multiobjective optimization are considered. Four case studies from my own collaborative work are described: (i) instrument optimization in analytical biochemistry; (ii) finding effective drug combinations in vitro; (iii) onchip synthetic biomolecule design; and (iv) improving chocolate production processes. Accurate simulation in these applications is not possible due to complexity or a lack of adequate analytical models. In these and other applications discussed, optimizing experimentally brings with it several challenges: noise; nuisance factors; ephemeral resource constraints; expensive evaluations, and evaluations that must be done in (large) batches. Evolutionary algorithms (EAs) are largely equal to these vagaries, whilst modern multiobjective EAs also enable tradeoffs among conflicting optimization goals to be explored. Nevertheless, principles from other disciplines, such as statistics, Design of Experiments, machine learning and global optimization are also relevant to aspects of the closed-loop problem, and may inspire futher development of multiobjective EAs.     

Managing approximation models in multiobjective optimization

In engineering problems, computationally intensive high-fidelity models or expensive computer simulations hinder the use of standard optimization techniques because they should be invoked repeatedly during optimization, despite the tremendous growth of computer capability. Therefore, these expensive analyses are often replaced with approximation models that can be evaluated at considerably less effort. However, due to their limited accuracy, it is practically impossible to exactly find an actual optimum (or a set of actual noninferior solutions) of the original single (or multi) objective optimization problem. Significant efforts have been made to overcome this limitation. The model management framework is one of such endeavours. The approximation models are sequentially updated during the iterative optimization process in such a way that their capability to accurately model the original functions especially in the region of our interests can be improved. The models are modified and improved by using one or several sample points generated by making a good use of the predictive ability of the approximation models. However, these approaches have been restricted to a single objective optimization problem. It seems that there is no reported management framework that can handle a multi-objective optimization problem. This paper will suggest strategies that can successfully treat not only a single objective but also multiple objectives by extending the concept of sequentially managing approximation models and combining this extended concept with a genetic algorithm which can treat multiple objectives (MOGA). Consequently, the number of exact analyses required to converge to an actual optimum or to generate a sufficiently accurate Pareto set can be reduced considerably. Especially, the approach for multiple objectives will lead to a surprising reduction in number. We will confirm these effects through several illustrative examples.     

On approximate starshapedness in multiobjective optimization

In this paper, we give the vector versions of the concepts of approximate starshapedness, equi-subdifferentiability and pseudo-equi-subdifferentiability and establish relationships among approximate vector starshapedness, vector-equi-subdifferentiability and vector-pseudo-equi-subdifferentiability. We extend the concept of ε-quasi-efficient solutions in the context of multiobjective optimization problems involving approximately starshaped functions and use approximate vector variational inequalities of Stampacchia and Minty type in terms of Fréchet subdifferentials to characterize approximate efficient solutions.     

Expert models of multiobjective optimization

An approach is proposed to solve a vector optimization problem for complex engineering and economic systems where the information about experimental and statistical data necessary to set up regression models is insufficient (or absent). To solve this problem, multiobjective optimization with nonlinear trade-off scheme is employed.     

Hyperspectral image classification using multiobjective optimization

Hyperspectral images constitute a substantial amount of data in the form of spectral bands. This information is used for land cover analysis, specifically in classifying a hyperspectral pixel, which is a popular domain in remote sensing. This paper proposed an efficient framework to classify spectral-spatial hyperspectral images by employing multiobjective optimization. Spectral-spatial features of hyperspectral images are passed for optimization. As hyperspectral images have a high dimensional feature set, many classifiers cannot perform well. Multiobjective optimization reduces the feature set without affecting the discrimination ability of the classifier. The proposed work is validated on a standard hyperspectral image set, Pavia University and Kennedy Space Centre.

     

多目标混沌差分进化算法

将差分进化算法用于多目标优化问题,提出了多目标混沌差分进化算法(CDEMO).该算法利用混沌序列初始化种群,并用混沌备用种群进行替换操作.该操作不仅起到了维持非劣最优解集均匀性的作用,而且增强了算法的搜索功能.对CDEMO的性能进行研究,数值实验结果表明了CDEMO的有效性.     

多模态多目标优化综述

随着工业生产和日常生活需求的多样化,单个解决方案己经无法满足生产生活的需求.多模态优化可以为决策者提供多个可行方案,但是早期对多模态优化的研究局限在单目标优化中.在多目标优化中也存在多模态优化问题,其存在多个全局或局部帕累托最优解集,找到这些最优解集具有重大的理论和实际意义.鉴于此,首先,介绍多模态多目标优化问题的特点...     

Immune optimization algorithm for constrained nonlinear multiobjective optimization problems

A new dynamical immune optimization algorithm for constrained nonlinear multiobjective optimization problems over continuous domains is proposed based on both the concept of Pareto optimality and simple interactive metaphors between antibody population and multiple antigens as well as ideas of T cell regulation. The focus of design is concentrated on constructing one constraint-handling technique associated with uniform design reported and designing one antibody evolution mechanism through utilizing simplified metaphors of humoral immune response of the immune system. The former is to provide an alternative feasible solution set for dealing with constraints and infeasible solutions created during the execution of the algorithm, while helping for rapidly finding Pareto-optimal solutions; the latter generates multiple excellent feasible solutions so that the desired solutions will be gradually obtained. Theoretically, its weak convergence is proven by using Markov theory, while the experimental results demonstrate its strong convergence. Through application to difficult test problems, comparative results illustrate it is potential for the algorithm to cope with high dimensional complex optimization problems with multiple constraints.     

Combining convergence and diversity in evolutionary multiobjective optimization

Over the past few years, the research on evolutionary algorithms has demonstrated their niche in solving multiobjective optimization problems, where the goal is to find a number of Pareto-optimal solutions in a single simulation run. Many studies have depicted different ways evolutionary algorithms can progress towards the Pareto-optimal set with a widely spread distribution of solutions. However, none of the multiobjective evolutionary algorithms (MOEAs) has a proof of convergence to the true Pareto-optimal solutions with a wide diversity among the solutions. In this paper, we discuss why a number of earlier MOEAs do not have such properties. Based on the concept of epsilon-dominance, new archiving strategies are proposed that overcome this fundamental problem and provably lead to MOEAs that have both the desired convergence and distribution properties. A number of modifications to the baseline algorithm are also suggested. The concept of epsilon-dominance introduced in this paper is practical and should make the proposed algorithms useful to researchers and practitioners alike.     

On some multiobjective optimization problems arising in biology

In this paper, we discuss modelling and solving some multiobjective optimization problems arising in biology. A class of comparison problems for string selection in molecular biology and a relocation problem in conservation biology are modelled as multiobjective optimization programmes. Some discussions about applications, solvability and different variants of the obtained models are given, as well. A crucial part of the study is based upon the Pareto optimization which refers to the Pareto solutions of multiobjective optimization problems. For such solution, improvement of some objective function can only be obtained at the expense of the deterioration of at least one other objective function.     

A problem space genetic algorithm in multiobjective optimization

In this study, a problem space genetic algorithm (PSGA) is used to solve bicriteria tool management and scheduling problems simultaneously in flexible manufacturing systems. The PSGA is used to generate approximately efficient solutions minimizing both the manufacturing cost and total weighted tardiness. This is the first implementation of PSGA to solve a multiobjective optimization problem (MOP). In multiobjective search, the key issues are guiding the search towards the global Pareto-optimal set and maintaining diversity. A new fitness assignment method, which is used in PSGA, is proposed to find a well-diversified, uniformly distributed set of solutions that are close to the global Pareto set. The proposed fitness assignment method is a combination of a nondominated sorting based method which is most commonly used in multiobjective optimization literature and aggregation of objectives method which is popular in the operations research literature. The quality of the Pareto-optimal set is evaluated by using the performance measures developed for multiobjective optimization problems.     

Incremental user-interface development for interactive multiobjective optimization

Interactive multiobjective optimization (IMO) is a subfield of multiple criteria decision making. In multiobjective optimization, the optimization problem is formulated with a mathematical model containing several conflicting objectives and constraints depending on decision variables. By using IMO methods, a decision maker progressively provides preference information in order to find the most satisfactory compromise between the conflicting objectives. In this paper, we consider implementation challenges of IMO methods. In particular, we consider what kind of interaction techniques can support the decision making process and information exchange between IMO methods and the decision maker. The implementation of an IMO method called Pareto Navigator is used as an example to demonstrate concrete challenges of interaction design. This paper focuses on describing the incremental development of the user interface for Pareto Navigator including empirical validation by user testing evaluation.     

Performance evaluation of evolutionary multiobjective optimization algorithms for multiobjective fuzzy genetics-based machine learning

Recently, evolutionary multiobjective optimization (EMO) algorithms have been utilized for the design of accurate and interpretable fuzzy rule-based systems. This research area is often referred to as multiobjective genetic fuzzy systems (MoGFS), where EMO algorithms are used to search for non-dominated fuzzy rule-based systems with respect to their accuracy and interpretability. In this paper, we examine the ability of EMO algorithms to efficiently search for Pareto optimal or near Pareto optimal fuzzy rule-based systems for classification problems. We use NSGA-II (elitist non-dominated sorting genetic algorithm), its variants, and MOEA/D (multiobjective evolutionary algorithm based on decomposition) in our multiobjective fuzzy genetics-based machine learning (MoFGBML) algorithm. Classification performance of obtained fuzzy rule-based systems by each EMO algorithm is evaluated for training data and test data under various settings of the available computation load and the granularity of fuzzy partitions. Experimental results in this paper suggest that reported classification performance of MoGFS in the literature can be further improved using more computation load, more efficient EMO algorithms, and/or more antecedent fuzzy sets from finer fuzzy partitions.     

Infine functions and nonsmooth multiobjective optimization problems

In this paper, we consider notion of infine functions and we establish necessary and sufficient optimality conditions for a feasible solution of a multiobjective optimization problem involving mixed constraints (equality and inequality) to be an efficient or properly efficient solution. We also obtain duality theorems for Wolf type and Mond-Weir type duals under the generalized invexity assumptions.     

Bilevel multiobjective packaging optimization for automotive design

The successful application of multiobjective optimization to engineering problems has motivated studies of more complex systems involving multiple subsystems and design disciplines, each with multiple design criteria. Complex system design requires participation of different teams that are highly specialized within each discipline and subsystem. Such a high differentiation results in limited sharing of information among the design teams. The mathematical modeling and the solution algorithm proposed in this paper address the issue of coordinating multiple design problems that negotiate according to conflicting criteria. The design of the layout of hybrid vehicles is formulated as a bilevel decomposed problem including a vehicle level and a battery level in concert with the specialization of the respective design teams required at each level. An iterative algorithm, the Multiobjective Decomposition Algorithm (MODA) is proposed, whose generated sequences are shown to converge to efficient designs for the overall design problem under certain conditions examined in the context of the block coordinate descent method and the method of multipliers. MODA applied to the hybrid electric design problem captures the bilevel tradeoffs originating by the conflicting objectives at the vehicle and battery levels.     

Using unconstrained elite archives for multiobjective optimization

Multiobjective evolutionary algorithms (MOEAs) have been the subject of numerous studies over the past 20 years. Recent work has highlighted the use of an active archive of elite, nondominated solutions to improve the optimization speed of these algorithms. However, preserving all elite individuals is costly in time (due to the linear comparison with all archived solutions needed before a new solution can be inserted into the archive). Maintaining an elite population of a fixed maximum size (by clustering or other means) alleviates this problem, but can cause retreating (or oscillitory) and shrinking estimated Pareto fronts - which can affect the efficiency of the search process. New data structures are introduced to facilitate the use of an unconstrained elite archive, without the need for a linear comparison to the elite set for every new individual inserted. The general applicability of these data structures is shown by their use in an evolution-strategy-based MOEA and a genetic-algorithm-based MOEA. It is demonstrated that MOEAs using the new data structures run significantly faster than standard, unconstrained archive MOEAs, and result in estimated Pareto fronts significantly ahead of MOEAs using a constrained archive. It is also shown that the use of an unconstrained elite archive permits robust criteria for algorithm termination to be used, and that the use of the data structure can also be used to increase the speed of algorithms using /spl epsi/-dominance methods.     

A novel micro-population immune multiobjective optimization algorithm

In this paper, we present a novel immune multiobjective optimization algorithm based on micro-population, which adopts a novel adaptive mutation operator for local search and an efficient fine-grained selection operator for archive update. With the external archive for storing nondominated individuals, the population diversity can be well preserved using an efficient fine-grained selection procedure performed on the micro-population. The adaptive mutation operator is executed according to the fitness values, which promotes to use relatively large steps for boundary and less-crowded individuals in high probability. Therefore, the exploratory capabilities are enhanced. When comparing the proposed algorithm with a recently proposed immune multiobjective algorithm and a scatter search multiobjective algorithm in various benchmark functions, simulations show that the proposed algorithm not only improves convergence ability but also preserves population diversity adequately in most cases.