Multiobjective evolutionary optimization of DNA sequences for reliable DNA computing

DNA computing relies on biochemical reactions of DNA molecules and may result in incorrect or undesirable computations. Therefore, much work has focused on designing the DNA sequences to make the molecular computation more reliable. Sequence design involves with a number of heterogeneous and conflicting design criteria and traditional optimization methods may face difficulties. In this paper, we formulate the DNA sequence design as a multiobjective optimization problem and solve it using a constrained multiobjective evolutionary algorithm (EA). The method is implemented into the DNA sequence design system, NACST/Seq, with a suite of sequence-analysis tools to help choose the best solutions among many alternatives. The performance of NACST/Seq is compared with other sequence design methods, and analyzed on a traveling salesman problem solved by bio-lab experiments. Our experimental results show that the evolutionary sequence design by NACST/Seq outperforms in its reliability the existing sequence design techniques such as conventional EAs, simulated annealing, and specialized heuristic methods.     

A multiobjective swarm intelligence approach based on artificial bee colony for reliable DNA sequence design

The design of reliable DNA sequences is crucial in many engineering applications which depend on DNA-based technologies, such as nanotechnology or DNA computing. In these cases, two of the most important properties that must be controlled to obtain reliable sequences are self-assembly and self-complementary hybridization. These processes have to be restricted to avoid undesirable reactions, because in the specific case of DNA computing, undesirable reactions usually lead to incorrect computations. Therefore, it is important to design robust sets of sequences which provide efficient and reliable computations. The design of reliable DNA sequences involves heterogeneous and conflicting design criteria that do not fit traditional optimization methods. In this paper, DNA sequence design has been formulated as a multiobjective optimization problem and a novel multiobjective approach based on swarm intelligence has been proposed to solve it. Specifically, a multiobjective version of the Artificial Bee Colony metaheuristics (MO-ABC) is developed to tackle the problem. MO-ABC takes in consideration six different conflicting design criteria to generate reliable DNA sequences that can be used for bio-molecular computing. Moreover, in order to verify the effectiveness of the novel multiobjective proposal, formal comparisons with the well-known multiobjective standard NSGA-II (fast non-dominated sorting genetic algorithm) were performed. After a detailed study, results indicate that our artificial swarm intelligence approach obtains satisfactory reliable DNA sequences. Two multiobjective indicators were used in order to compare the developed algorithms: hypervolume and set coverage. Finally, other relevant works published in the literature were also studied to validate our results. To this respect the conclusion that can be drawn is that the novel approach proposed in this paper obtains very promising DNA sequences that significantly surpass other results previously published.     

Efficient shape parameterization method for multidisciplinary global optimization and application to integrated ship hull shape optimization workflow

Multidisciplinary global shape optimization requires a geometric parameterization method that keeps the shape generality while lowering the number of free variables. This paper presents a reduced parameter set parameterization method based on integral B-spline surface capable of both shape and topology variations and suitable for global multidisciplinary optimization. The objective of the paper is to illustrate the advantages of the proposed method in comparison to standard parameterization and to prove that the proposed method can be used in an integrated multidisciplinary workflow. Non-linear fitting is used to test the proposed parameterization performance before the actual optimization. The parameterization method can in this way be tested and pre-selected based on previously existing geometries. Fitting tests were conducted on three shapes with dissimilar geometrical features, and great improvement in shape generality while reducing the number of shape parameters was achieved. The best results are obtained for a small number (up to 50) of optimization variables, where a classical applying of parameterization method requires about two times as many optimization variables to obtain the same fitting capacity.The proposed shape parameterization method was tested in a multidisciplinary ship hull optimization workflow to confirm that it can actually be used in multiobjective optimization problems. The workflow integrates shape parameterization with hydrodynamic, structural and geometry analysis tools. In comparison to classical local and global optimization methods, the evolutionary algorithm allows for fully autonomous design with an ability to generate a wide Pareto front without a need for an initial solution.     

Solving multiobjective problems using cat swarm optimization

This paper proposes a new multiobjective evolutionary algorithm (MOEA) by extending the existing cat swarm optimization (CSO). It finds the nondominated solutions along the search process using the concept of Pareto dominance and uses an external archive for storing them. The performance of our proposed approach is demonstrated using standard test functions. A quantitative assessment of the proposed approach and the sensitivity test of different parameters is carried out using several performance metrics. The simulation results reveal that the proposed approach can be a better candidate for solving multiobjective problems (MOPs).     

基于目标空间划分的自适应多目标进化算法

目前,多目标进化算法在众多领域具有极高的应用价值,是优化领域的研究热点之一.分析已有多目标进化算法在保持种群多样性方面的不足并提出一种基于解空间划分的自适应多目标进化算法（space division basedadaptive multiobjective evolutionary algorithm,简称SDA-MOEA）来解决多目标优化问题.该方法首先将多目标优化问题的解空间划分为大量子空间,在算法进化过程中,每个子空间都保留一个非支配解集,以保证种群的多样性.另外,该方法根据每个子空间推进种群前进的距离,自适应地为每个子空间分配进化机会,以提高种群的进化速度.最后,利用3组共14个多目标优化问题检验SDA-MOEA的性能,并将SDA-MOEA与其他5个已有多目标进化算法进行对比分析.实验结果表明：在10个问题上,算法SDA-MOEA显著优于其他对比算法.     

A new multiobjective clustering technique based on the concepts of stability and symmetry

Most clustering algorithms operate by optimizing (either implicitly or explicitly) a single measure of cluster solution quality. Such methods may perform well on some data sets but lack robustness with respect to variations in cluster shape, proximity, evenness and so forth. In this paper, we have proposed a multiobjective clustering technique which optimizes simultaneously two objectives, one reflecting the total cluster symmetry and the other reflecting the stability of the obtained partitions over different bootstrap samples of the data set. The proposed algorithm uses a recently developed simulated annealing-based multiobjective optimization technique, named AMOSA, as the underlying optimization strategy. Here, points are assigned to different clusters based on a newly defined point symmetry-based distance rather than the Euclidean distance. Results on several artificial and real-life data sets in comparison with another multiobjective clustering technique, MOCK, three single objective genetic algorithm-based automatic clustering techniques, VGAPS clustering, GCUK clustering and HNGA clustering, and several hybrid methods of determining the appropriate number of clusters from data sets show that the proposed technique is well suited to detect automatically the appropriate number of clusters as well as the appropriate partitioning from data sets having point symmetric clusters. The performance of AMOSA as the underlying optimization technique in the proposed clustering algorithm is also compared with PESA-II, another evolutionary multiobjective optimization technique.     

A niched genetic algorithm to solve a pollutant emission reduction problem in the manufacturing industry: A case study

A multiobjective optimization approach to deal with a pollutant emission reduction problem in the manufacturing industry, through implementation of the best available technical options, is presented in this paper. More specifically, attention is focused on the industrial painting of wood and the problem under investigation is formulated as a bicriteria combinatorial optimization problem. A niched Pareto genetic algorithm based approach is used to determine sets of methods, tools and technologies, applicable both in the design and in the production phase, allowing to simultaneously minimize the total cost and maximize the total pollutant emission reduction.     

分层多目标最优化进化算法

文章用进化算法给出了求解二层字典分层多目标最优化的方法,该算法把求解问题转化为多目标最优化,并研究了这两个问题的解集之间的联系。对多目标最优化定义了一个新的选择算子和适应值函数,这样定义的选择算子和适应值函数结合均匀设计能有效地引导搜索,直接求出问题的解而不用逐层求解。数值模拟表明该方法十分有效。     

Multiobjective firefly algorithm for continuous optimization

Design problems in industrial engineering often involve a large number of design variables with multiple objectives, under complex nonlinear constraints. The algorithms for multiobjective problems can be significantly different from the methods for single objective optimization. To find the Pareto front and non-dominated set for a nonlinear multiobjective optimization problem may require significant computing effort, even for seemingly simple problems. Metaheuristic algorithms start to show their advantages in dealing with multiobjective optimization. In this paper, we extend the recently developed firefly algorithm to solve multiobjective optimization problems. We validate the proposed approach using a selected subset of test functions and then apply it to solve design optimization benchmarks. We will discuss our results and provide topics for further research.     

一种基于免疫原理的多目标优化方法

借鉴生物免疫原理中抗体多样性产生及保持的机理，建立了一种多目标优化方法．该方法定义了多目标选择熵和浓度调节选择概率的概念，采用了抗体克隆选择策略和高度变异策略．最后采用四种典型的多目标优化函数，将本方法同几种常用的多目标遗传算法进行了比较研究，证明了所建立的基于免疫原理的多目标优化方法能有效解决多目标优化问题且具有一定的优越性．     

Three-objective subgraph mining using multiobjective evolutionary programming

The existing methods for graph-based data mining (GBDM) follow the basic approach of applying a single-objective search with a user-defined threshold to discover interesting subgraphs. This obliges the user to deal with simple thresholds and impedes her/him from evaluating the mined subgraphs by defining different “goodness” (i.e., multiobjective) criteria regarding the characteristics of the subgraphs. In previous papers, we defined a multiobjective GBDM framework to perform bi-objective graph mining in terms of subgraph support and size maximization. Two different search methods were considered with this aim, a multiobjective beam search and a multiobjective evolutionary programming (MOEP). In this contribution, we extend the latter formulation to a three-objective framework by incorporating another classical graph mining objective, the subgraph diameter. The proposed MOEP method for multiobjective GBDM is tested on five synthetic and real-world datasets and its performance is compared against single and multiobjective subgraph mining approaches based on the classical Subdue technique in GBDM. The results highlight the application of multiobjective subgraph mining allows us to discover more diversified subgraphs in the objective space.     

Interactive Evolutionary Multiobjective Search and Optimization of Set-Based Concepts

This paper deals with interactive concept-based multiobjective problems (IC-MOPs) and their solution by an evolutionary computation approach. The presented methodology is motivated by the need to support engineers during the conceptual design stage. IC-MOPs are based on a nontraditional concept-based approach to search and optimization. It involves conceptual solutions, which are represented by sets of particular solutions, with each concept having a one-to-many relation with the objective space. Such a set-based concept representation is most suitable for human–computer interaction. Here, a fundamental type of IC-MOPs, namely, the Pareto-directed one, is formally defined, and its solution is presented. Next, a new interactive concept-based multiobjective evolutionary algorithm is introduced, and measures to assess its resulting fronts are devised. Finally, the proposed approach and the suggested search algorithm are studied using both academic test functions and an engineering problem.      

An efficient multiobjective differential evolution algorithm for engineering design

Solving engineering design and resources optimization via multiobjective evolutionary algorithms (MOEAs) has attracted much attention in the last few years. In this paper, an efficient multiobjective differential evolution algorithm is presented for engineering design. Our proposed approach adopts the orthogonal design method with quantization technique to generate the initial archive and evolutionary population. An archive (or secondary population) is employed to keep the nondominated solutions found and it is updated by a new relaxed form of Pareto dominance, called Pareto-adaptive ϵ-dominance (paϵ-dominance), at each generation. In addition, in order to guarantee to be the best performance produced, we propose a new hybrid selection mechanism to allow the archive solutions to take part in the generating process. To handle the constraints, a new constraint-handling method is employed, which does not need any parameters to be tuned for constraint handling. The proposed approach is tested on seven benchmark constrained problems to illustrate the capabilities of the algorithm in handling mathematically complex problems. Furthermore, four well-studied engineering design optimization problems are solved to illustrate the efficiency and applicability of the algorithm for multiobjective design optimization. Compared with Nondominated Sorting Genetic Algorithm II, one of the best MOEAs available at present, the results demonstrate that our approach is found to be statistically competitive. Moreover, the proposed approach is very efficient and is capable of yielding a wide spread of solutions with good coverage and convergence to true Pareto-optimal fronts.     

A gene-level hybrid search framework for multiobjective evolutionary optimization

This paper proposes a general framework of gene-level hybrid search (GLHS) for multiobjective evolutionary optimization. Regarding the existing hybrid search methods, most of them usually combine different search strategies and only select one search strategy to generate child solution. This kind of hybrid search is called as a chromosome-level approach in this paper. However, in GLHS, every gene bit of the child solution can be produced using different search strategies and such operation provides the enhanced exploration capability. As an example, two different DE mutation strategies are used in this paper as the variance candidate pool to implement the proposed GLHS framework, named GLHS-DE. To validate the effectiveness of GLHS-DE, it is embedded into one state-of-the-art algorithmic framework of MOEA/D, and is compared to a basic DE operator and two competitive hybrid search operators, i.e., FRRMAB and CDE, on 80 test problems with two to fifteen objectives. The experimental results show GLHS-DE obtains a superior performance over DE, FRRMAB and CDE on about 70 out of 80 test problems, indicating the promising application of our approach for multiobjective evolutionary optimization.

     

Multiobjective optimization using population-based extremal optimization

In recent years, a general-purpose local-search heuristic method called Extremal Optimization (EO) has been successfully applied in some NP-hard combinatorial optimization problems. In this paper, we present a novel Pareto-based algorithm, which can be regarded as an extension of EO, to solve multiobjective optimization problems. The proposed method, called Multiobjective Population-based Extremal Optimization (MOPEO), is validated by using five benchmark functions and metrics taken from the standard literature on multiobjective evolutionary optimization. The experimental results demonstrate that MOPEO is competitive with the state-of-the-art multiobjective evolutionary algorithms. Thus MOPEO can be considered as a viable alternative to solve multiobjective optimization problems.     

Running time analysis of multiobjective evolutionary algorithms on pseudo-Boolean functions

This paper presents a rigorous running time analysis of evolutionary algorithms on pseudo-Boolean multiobjective optimization problems. We propose and analyze different population-based algorithms, the simple evolutionary multiobjective optimizer (SEMO), and two improved versions, fair evolutionary multiobjective optimizer (FEMO) and greedy evolutionary multiobjective optimizer (GEMO). The analysis is carried out on two biobjective model problems, leading ones trailing zeroes (LOTZ) and count ones count zeroes (COCZ), as well as on the scalable m-objective versions mLOTZ and mCOCZ. Results on the running time of the different population-based algorithms and for an alternative approach, a multistart (1+1)-EA based on the /spl epsi/-constraint method, are derived. The comparison reveals that for many problems, the simple algorithm SEMO is as efficient as this (1+1)-EA. For some problems, the improved variants FEMO and GEMO are provably better. For the analysis, we propose and apply two general tools, an upper bound technique based on a decision space partition and a randomized graph search algorithm, which facilitate the analysis considerably.     

Handling multiple objectives with particle swarm optimization

This paper presents an approach in which Pareto dominance is incorporated into particle swarm optimization (PSO) in order to allow this heuristic to handle problems with several objective functions. Unlike other current proposals to extend PSO to solve multiobjective optimization problems, our algorithm uses a secondary (i.e., external) repository of particles that is later used by other particles to guide their own flight. We also incorporate a special mutation operator that enriches the exploratory capabilities of our algorithm. The proposed approach is validated using several test functions and metrics taken from the standard literature on evolutionary multiobjective optimization. Results indicate that the approach is highly competitive and that can be considered a viable alternative to solve multiobjective optimization problems.     

The balance between proximity and diversity in multiobjective evolutionary algorithms

Over the last decade, a variety of evolutionary algorithms (EAs) have been proposed for solving multiobjective optimization problems. Especially more recent multiobjective evolutionary algorithms (MOEAs) have been shown to be efficient and superior to earlier approaches. An important question however is whether we can expect such improvements to converge onto a specific efficient MOEA that behaves best on a large variety of problems. In this paper, we argue that the development of new MOEAs cannot converge onto a single new most efficient MOEA because the performance of MOEAs shows characteristics of multiobjective problems. While we point out the most important aspects for designing competent MOEAs in this paper, we also indicate the inherent multiobjective tradeoff in multiobjective optimization between proximity and diversity preservation. We discuss the impact of this tradeoff on the concepts and design of exploration and exploitation operators. We also present a general framework for competent MOEAs and show how current state-of-the-art MOEAs can be obtained by making choices within this framework. Furthermore, we show an example of how we can separate nondomination selection pressure from diversity preservation selection pressure and discuss the impact of changing the ratio between these components.     

Coupling dynamic simulation and interactive multiobjective optimization for complex problems: An APROS-NIMBUS case study

Dynamic process simulators for plant-wide process simulation and multiobjective optimization tools can be used by industries as a means to cut costs and enhance profitability. Specifically, dynamic process simulators are useful in the process plant design phase, as they provide several benefits such as savings in time and costs. On the other hand, multiobjective optimization tools are useful in obtaining the best possible process designs when multiple conflicting objectives are to be optimized simultaneously. Here we concentrate on interactive multiobjective optimization. When multiobjective optimization methods are used in process design, they need an access to dynamic process simulators, hence it is desirable for them to coexist on the same software platform. However, such a co-existence is not common. Hence, users need to couple multiobjective optimization software and simulators, which may not be trivial. In this paper, we consider APROS, a dynamic process simulator and couple it with IND-NIMBUS, an interactive multiobjective optimization software. Specifically, we: (a) study the coupling of interactive multiobjective optimization with a dynamic process simulator; (b) bring out the importance of utilizing interactive multiobjective optimization; (c) propose an augmented interactive multiobjective optimization algorithm; and (d) apply an APROS-NIMBUS coupling for solving a dynamic optimization problem in a two-stage separation process.