New mechanism for archive maintenance in PSO-based multi-objective feature selection

In classification problems, a large number of features are typically used to describe the problem’s instances. However, not all of these features are useful for classification. Feature selection is usually an important pre-processing step to overcome the problem of “curse of dimensionality”. Feature selection aims to choose a small number of features to achieve similar or better classification performance than using all features. This paper presents a particle swarm Optimization (PSO)-based multi-objective feature selection approach to evolving a set of non-dominated feature subsets which achieve high classification performance. The proposed algorithm uses local search techniques to improve a Pareto front and is compared with a pure multi-objective PSO algorithm, three well-known evolutionary multi-objective algorithms and a current state-of-the-art PSO-based multi-objective feature selection approach. Their performances are examined on 12 benchmark datasets. The experimental results show that in most cases, the proposed multi-objective algorithm generates better Pareto fronts than all other methods.     

A Length-Adaptive Non-Dominated Sorting Genetic Algorithm for Bi-Objective High-Dimensional Feature Selection

As a crucial data preprocessing method in data mining, feature selection (FS) can be regarded as a bi-objective optimization problem that aims to maximize classification accuracy and minimize the number of selected features. Evolutionary computing (EC) is promising for FS owing to its powerful search capability. However, in traditional EC-based methods, feature subsets are represented via a length-fixed individual encoding. It is ineffective for high-dimensional data, because it results in a huge search space and prohibitive training time. This work proposes a length-adaptive non-dominated sorting genetic algorithm (LA-NSGA) with a length-variable individual encoding and a length-adaptive evolution mechanism for bi-objective high-dimensional FS. In LA-NSGA, an initialization method based on correlation and redundancy is devised to initialize individuals of diverse lengths, and a Pareto dominance-based length change operator is introduced to guide individuals to explore in promising search space adaptively. Moreover, a dominance-based local search method is employed for further improvement. The experimental results based on 12 high-dimensional gene datasets show that the Pareto front of feature subsets produced by LA-NSGA is superior to those of existing algorithms.     

A multiobjective approach for maximizing the reach or GRP of different brands in TV advertising

This paper focuses on a multiobjective optimization problem in TV advertising from an advertising agency's perspective, which involves deciding on which commercial breaks to air the ads of various brands to jointly maximize reach or gross rating point (GRP) for the different brands subject to budget constraints, brand competition constraints, and other scheduling constraints. We present a multiobjective integer programming formulation of this problem and develop and implement algorithms for generating provably Pareto‐optimal solutions. We also develop reduction and visualization procedures to aid a decision maker in choosing suitable subsets of the Pareto‐optimal solutions obtained. Numerical experiments on five TV advertising problems involving 20–40 objective functions and thousands of decision variables and constraints demonstrate the effectiveness of the proposed formulation and solution methods in generating Pareto‐optimal objective vectors that reflect brand priorities and that are well distributed along the Pareto front.     

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.     

Balance between genetic search and local search in memetic algorithms for multiobjective permutation flowshop scheduling

This paper shows how the performance of evolutionary multiobjective optimization (EMO) algorithms can be improved by hybridization with local search. The main positive effect of the hybridization is the improvement in the convergence speed to the Pareto front. On the other hand, the main negative effect is the increase in the computation time per generation. Thus, the number of generations is decreased when the available computation time is limited. As a result, the global search ability of EMO algorithms is not fully utilized. These positive and negative effects are examined by computational experiments on multiobjective permutation flowshop scheduling problems. Results of our computational experiments clearly show the importance of striking a balance between genetic search and local search. In this paper, we first modify our former multiobjective genetic local search (MOGLS) algorithm by choosing only good individuals as initial solutions for local search and assigning an appropriate local search direction to each initial solution. Next, we demonstrate the importance of striking a balance between genetic search and local search through computational experiments. Then we compare the modified MOGLS with recently developed EMO algorithms: the strength Pareto evolutionary algorithm and revised nondominated sorting genetic algorithm. Finally, we demonstrate that a local search can be easily combined with those EMO algorithms for designing multiobjective memetic algorithms.     

Hybrid sampling strategy-based multiobjective evolutionary algorithm for process planning and scheduling problem

Process planning and scheduling (PPS) is an important and practical topic but very intractable problem in manufacturing systems. Many research studies used multiobjective evolutionary algorithm (MOEA) to solve such problems; however, they cannot achieve satisfactory results in both quality and computational speed. This paper proposes a hybrid sampling strategy-based multiobjective evolutionary algorithm (HSS-MOEA) to deal with the PPS problem. HSS-MOEA tactfully combines the advantages of vector evaluated genetic algorithm (VEGA) and a sampling strategy according to a new Pareto dominating and dominated relationship-based fitness function (PDDR-FF). The sampling strategy of VEGA prefers the edge region of the Pareto front and PDDR-FF-based sampling strategy has the tendency converging toward the central area of the Pareto front. These two mechanisms preserve both the convergence rate and the distribution performance. The numerical comparisons state that the HSS-MOEA is better than a generalized Pareto-based scale-independent fitness function based genetic algorithm combing with VEGA in efficacy (convergence and distribution) performance, while the efficiency is closely equivalent. Moreover, the efficacy performance of HSS-MOEA is also better than NSGA-II and SPEA2, and the efficiency is obviously better than their performance.     

Dominance-Based Multiobjective Simulated Annealing

Simulated annealing is a provably convergent optimizer for single-objective problems. Previously proposed multiobjective extensions have mostly taken the form of a single-objective simulated annealer optimizing a composite function of the objectives. We propose a multiobjective simulated annealer utilizing the relative dominance of a solution as the system energy for optimization, eliminating problems associated with composite objective functions. We also propose a method for choosing perturbation scalings promoting search both towards and across the Pareto front. We illustrate the simulated annealer's performance on a suite of standard test problems and provide comparisons with another multiobjective simulated annealer and the NSGA-II genetic algorithm. The new simulated annealer is shown to promote rapid convergence to the true Pareto front with a good coverage of solutions across it comparing favorably with the other algorithms. An application of the simulated annealer to an industrial problem, the optimization of a code-division-multiple access (CDMA) mobile telecommunications network's air interface, is presented and the simulated annealer is shown to generate nondominated solutions with an even and dense coverage that outperforms single objective genetic algorithm optimizers.     

采用遗传算法求解多跳分组无线网服务质量路由优化模型

采用多目标遗传算法来确定多跳无线网服务质量路由优化问题的Pareto最优解集。通过计算表明,多目标遗传算法能够在一次运行中搜索到优化问题的近似Pareto最优解集,这为决策者进行目标折衷决策提供了充分的依据,此算法是有效可行的。     

MOTGA: A multiobjective Tchebycheff based genetic algorithm for the multidimensional knapsack problem

This paper presents a new multiobjective genetic algorithm based on the Tchebycheff scalarizing function, which aims to generate a good approximation of the nondominated solution set of the multiobjective problem. The algorithm performs several stages, each one intended for searching potentially nondominated solutions in a different part of the Pareto front. Pre-defined weight vectors act as pivots to define the weighted-Tchebycheff scalarizing functions used in each stage. Therefore, each stage focuses the search on a specific region, leading to an iterative approximation of the entire nondominated set.     

A multiobjective hybrid ant colony optimization approach applied to the assignment and scheduling problem

The assignment and scheduling problem is inherently multiobjective. It generally involves multiple conflicting objectives and large and highly complex search spaces. The problem allows the determination of an efficient allocation of a set of limited and shared resources to perform tasks, and an efficient arrangement scheme of a set of tasks over time, while fulfilling spatiotemporal constraints. The main objective is to minimize the project makespan as well as the total cost. Finding a good approximation set is the result of trade‐offs between diversity of solutions and convergence toward the Pareto‐optimal front. It is difficult to achieve such a balance with NP‐hard problems. In this respect, and in order to efficiently explore the search space, a hybrid bidirectional ant‐based approach is proposed in this paper, which is an improvement of a bi‐colony ant‐based approach. Its main characteristic is that it combines a solution construction developed for a more complicated problem with a Pareto‐guided local search engine.     

Method of Inequality-Based Multiobjective Genetic Algorithm for Domestic Daily Aircraft Routing

This study proposes a method of inequality-based multiobjective genetic algorithm (MMGA) to solve the aircraft routing problem. The proposed algorithm includes the following features: 1) a method of inequality to confine a genetic algorithm to search a Pareto optimal set in regions of interest with little computing effort; 2) an improved rank-based fitness assignment method to significantly increase the speed of fitness evaluation; and 3) a repairing strategy to relax the infeasible flight schedules to help reduce violations of solutions. The MMGA is successfully applied to solve the aircraft routing problems in a local airline company.     

基于精英进化导向的多目标PID参数优化

在多目标优化问题中,决策者必须对Pareto前沿的众多非劣解做出选择.本文将决策偏好融入Pareto优化过程,提出一种基于精英导向机制的多目标遗传算法,根据决策偏好选择Pareto最优解为精英,利用无损有限精度法和归一增量距离保持种群多样性,通过多种群进化机制将决策偏好的影响传播到整个种群.该方法成功应用于自动导引车(AGV)伺服系统的PID参数优化,可根据决策偏好快速有效地定向搜索Pareto最优解,保证伺服控制达到路径跟踪要求的速度响应性能.     

A Multiobjective Evolutionary-Simplex Hybrid Approach for the Optimization of Differential Equation Models of Gene Networks

This paper describes genetic and hybrid approaches for multiobjective optimization using a numerical measure called fuzzy dominance. Fuzzy dominance is used when implementing tournament selection within the genetic algorithm (GA). In the hybrid version, it is also used to carry out a Nelder-Mead simplex-based local search. The proposed GA is shown to perform better than NSGA-II and SPEA-2 on standard benchmarks, as well as for the optimization of a genetic model for flowering time control in rice. Adding the local search achieves faster convergence, an important feature in computationally intensive optimization of gene networks. The hybrid version also compares well with ParEGO on a few other benchmarks. The proposed hybrid algorithm is then applied to estimate the parameters of an elaborate gene network model of flowering time control in Arabidopsis. Overall solution quality is quite good by biological standards. Tradeoffs are discussed between accuracy in gene activity levels versus in the plant traits that they influence. These tradeoffs suggest that data mining the Pareto front may be useful in bioinformatics.     

多目标资源优化分配问题的Memetic 算法

针对传统算法求解多目标资源优化分配问题收敛慢、Pareto解不能有效分布在Pareto 前沿面的问题, 提出一种新的Memetic 算法. 在遗传算法的交叉算子中引入模拟退火算法, 加强了遗传算法的局部搜索能力, 加快了收敛速度. 为了使Pareto 最优解均匀分布在Pareto 前沿面, 在染色体编码中引入禁忌表, 增加了种群的多样性, 避免了传统遗传算法后期Pareto 解集过于集中的缺点. 通过与已有的遗传算法、蚁群算法、粒子群算法进行比较, 仿真实验表明了所提出算法的有效性, 并分析了禁忌表长度和模拟退火参数对算法收敛性的影响.

     

Adaptive weighted-sum method for bi-objective optimization: Pareto front generation

This paper presents a new method that effectively determines a Pareto front for bi-objective optimization with potential application to multiple objectives. A traditional method for multiobjective optimization is the weighted-sum method, which seeks Pareto optimal solutions one by one by systematically changing the weights among the objective functions. Previous research has shown that this method often produces poorly distributed solutions along a Pareto front, and that it does not find Pareto optimal solutions in non-convex regions. The proposed adaptive weighted sum method focuses on unexplored regions by changing the weights adaptively rather than by using a priori weight selections and by specifying additional inequality constraints. It is demonstrated that the adaptive weighted sum method produces well-distributed solutions, finds Pareto optimal solutions in non-convex regions, and neglects non-Pareto optimal solutions. This last point can be a potential liability of Normal Boundary Intersection, an otherwise successful multiobjective method, which is mainly caused by its reliance on equality constraints. The promise of this robust algorithm is demonstrated with two numerical examples and a simple structural optimization problem.     

Evolutionary algorithms with dynamic population size and localexploration for multiobjective optimization

Evolutionary algorithms have been recognized to be well suited for multiobjective optimization. These methods, however, need to "guess" for an optimal constant population size in order to discover the usually sophisticated tradeoff surface. This paper addresses the issue by presenting a novel incrementing multiobjective evolutionary algorithm (IMOEA) with dynamic population size that is computed adaptively according to the online discovered tradeoff surface and its desired population distribution density. It incorporates the method of fuzzy boundary local perturbation with interactive local fine tuning for broader neighborhood exploration. This achieves better convergence as well as discovering any gaps or missing tradeoff regions at each generation. Other advanced features include a proposed preserved strategy to ensure better stability and diversity of the Pareto front and a convergence representation based on the concept of online population domination to provide useful information. Extensive simulations are performed on two benchmark and one practical engineering design problems     

混合互信息和粒子群算法的多目标特征选择方法

在数据挖掘中,由于数据集中含有大量的冗余和不相关的特征,因此特征选择是一个重要的预处理过程。提出了一个基于混合互信息和粒子群算法的过滤式-封装式的多目标特征选择方法(HMIPSO)。根据粒子的pbest距离上次更新的迭代次数,提出了自适应突变策略去扰动种群,避免种群陷入局部最优。同时基于帕累托前沿面和外部文档提出了一个新的集合概念。结合互信息和新的集合知识提出了一个局部搜索策略,使得帕累托前沿面中的粒子可以删除不相关和冗余的特征,然后通过精英策略更新学习前和学习后的帕累托前沿面。最后将提出的算法和另外4种多目标算法在15个UCI数据集上进行了测试,实验结果表明提出的算法能够更好地降低特征个数和分类错误率。     

基于精英选择和个体迁移的多目标遗传算法

提出基于遗传算法求解多目标优化问题的方法,将多目标问题分解成多个单目标优化问题,用遗传算法分别在每个单目标种群中并行搜索.在进化过程中的每一代,采用精英选择和个体迁移策略加快多个目标的并行搜索,提出了控制Pareto最优解数量并保持个体多样性的有限精度法,同时还提出了多目标遗传算法的终止条件.数值实验说明所提出的算法能较快地找到一组分布广泛且均匀的Pareto最优解.     

Wrapper–Filter Feature Selection Algorithm Using a Memetic Framework

This correspondence presents a novel hybrid wrapper and filter feature selection algorithm for a classification problem using a memetic framework. It incorporates a filter ranking method in the traditional genetic algorithm to improve classification performance and accelerate the search in identifying the core feature subsets. Particularly, the method adds or deletes a feature from a candidate feature subset based on the univariate feature ranking information. This empirical study on commonly used data sets from the University of California, Irvine repository and microarray data sets shows that the proposed method outperforms existing methods in terms of classification accuracy, number of selected features, and computational efficiency. Furthermore, we investigate several major issues of memetic algorithm (MA) to identify a good balance between local search and genetic search so as to maximize search quality and efficiency in the hybrid filter and wrapper MA     

Bi-objective scheduling for reentrant hybrid flow shop using Pareto genetic algorithm

This paper deals with a scheduling problem for reentrant hybrid flowshop with serial stages where each stage consists of identical parallel machines. In a reentrant flowshop, a job may revisit any stage several times. Local-search based Pareto genetic algorithms with Minkowski distance-based crossover operator is proposed to approximate the Pareto optimal solutions for the minimization of makespan and total tardiness in a reentrant hybrid flowshop. The Pareto genetic algorithms are compared with existing multi-objective genetic algorithm, NSGA-II in terms of the convergence to optimal solution, the diversity of solution and the dominance of solution. Experimental results show that the proposed crossover operator and local search are effective and the proposed algorithm outperforms NSGA-II by statistical analysis.