ML-MOEA/SOM : A Manifold-Learning-Based Multiobjective Evolutionary Algorithm Via Self-Organizing Maps

Wei Cao,Wei Zhan,ZhiQiang Chen 보안공학연구지원센터 2016 International Journal of Signal Processing, Image Vol.9 No.7

Under mild conditions, it can be induced from the Karush–Kuhn–Tucker condition that the Pareto set, in the decision space, of a continuous Multiobjective Optimization Problems(MOPs) is a piecewise continuous (m 1)  D manifold(where m is the number of objectives). One hand, the traditional Multiobjective Optimization Algorithms(EMOAs) cannot utilize this regularity property; on the other hand, the Regular Model-Based Multiobjective Estimation of Distribution Algorithm(RM-MEDA) only able to build the linear model of decision space using linear modelling algorithm, such as: the local principal component analysis algorithm(Local PCA).Aim at the shortcomings of EMOAs and RM-MEDA, the Manifold-Learning-Based Multiobjective Evolutionary Algorithm Via Self-Organizing Maps(ML-MOEA/SOM) is proposed for continuous multiobjective optimization problems. At each generation, first, via Self-Organizing Maps, the proposed algorithm learns such a nonlinear manifold in the decision space; then, new trial solutions is built through expanding the neurons of SOM with random noise; at the end, a nondominated sorting-based selection is used for choosing solutions for the next generation. Systematic experiments have shown that, overall, ML-MOEA/SOM outperforms NSGA-II, and is competitive with RM-MEDA in terms of convergence and diversity, on a set of test instances with variable linkages. We have demonstrated that, compared with NSGA-II and RM-MEDA, via self-Organizing maps, ML-MOEA/SOM can dig nonlinear manifold hidden in the decision space of multiobjective optimization problems.

Recent advances in hybrid evolutionary algorithms for multiobjective manufacturing scheduling

Gen, Mitsuo,Zhang, Wenqiang,Lin, Lin,Yun, YoungSu Elsevier 2017 COMPUTERS & INDUSTRIAL ENGINEERING Vol.112 No.-

<P><B>Abstract</B></P> <P>In real manufacturing systems there are many combinatorial optimization problems (COP) imposing on more complex issues with multiple objectives. However it is very difficult for solving the intractable COP problems by the traditional approaches because of NP-hard problems. For developing effective and efficient algorithms that are in a sense “good,” <I>i.e.</I>, whose computational time is small as within 3min, we have to consider three issues: quality of solution, computational time and effectiveness of the nondominated solutions for multiobjective optimization problem (MOP).</P> <P>In this paper, we focus on recent <I>hybrid evolutionary algorithms</I> (HEA) to solve a variety of single or multiobjective scheduling problems in manufacturing systems to get a best solution with a smaller computational time. Firstly we summarize <I>multiobjective hybrid genetic algorithm</I> (Mo-HGA) and <I>hybrid sampling strategy-based multiobjective evolutionary algorithm</I> (HSS-MoEA) and then propose <I>HSS-MoEA combining with differential evolution</I> (HSS-MoEA-DE). We also demonstrate those hybrid evolutionary algorithms to <I>bicriteria automatic guided vehicle</I> (B-AGV) dispatching problem, <I>robot-based assembly line balancing problem</I> (R-ALB), <I>bicriteria flowshop scheduling problem</I> (B-FSP), multiobjective scheduling problem in <I>thin-film transistor-liquid crystal display</I> (TFT-LCD) module assembly and <I>bicriteria process planning and scheduling</I> (B-PPS) problem. Also we demonstrate their effectiveness of the proposed hybrid evolutionary algorithms by several empirical examples.</P> <P><B>Highlights</B></P> <P> <UL> <LI> Various real manufacturing systems are considered. </LI> <LI> Multiobjective scheduling problems in manufacturing systems are considered. </LI> <LI> Recent hybrid evolutionary algorithms are proposed. </LI> </UL> </P>

Multiobjective Optimal Reactive Power Flow Using Elitist Nondominated Sorting Genetic Algorithm

Zhihuan Li,Yinhong Li,Xianzhong Duan 대한전기학회 2010 Journal of Electrical Engineering & Technology Vol.5 No.1

Elitist nondominated sorting genetic algorithm (NSGA-II) is adopted and improved for multiobjective optimal reactive power flow (ORPF) problem. Multiobjective ORPF, formulated as a multiobjective mixed integer nonlinear optimization problem, minimizes real power loss and improves voltage profile of power grid by determining reactive power control variables. NSGA-II-based ORPF is tested on standard IEEE 30-bus test system and compared with four other state-of-the-art multiobjective evolutionary algorithms (MOEAs). Pareto front and outer solutions achieved by the five MOEAs are analyzed and compared. NSGA-II obtains the best control strategy for ORPF, but it suffers from the lower convergence speed at the early stage of the optimization. Several problem-specific local search strategies (LSSs) are incorporated into NSGA-II to promote algorithm’s exploiting capability and then to speed up its convergence. This enhanced version of NSGA-II (ENSGA) is examined on IEEE 30 system. Experimental results show that the use of LSSs clearly improved the performance of NSGA-II. ENSGA shows the best search efficiency and is proved to be one of the efficient potential candidates in solving reactive power optimization in the real-time operation systems.

Multiobjective Optimal Reactive Power Flow Using Elitist Nondominated Sorting Genetic Algorithm: Comparison and Improvement

Li, Zhihuan,Li, Yinhong,Duan, Xianzhong The Korean Institute of Electrical Engineers 2010 Journal of Electrical Engineering & Technology Vol.5 No.1

Elitist nondominated sorting genetic algorithm (NSGA-II) is adopted and improved for multiobjective optimal reactive power flow (ORPF) problem. Multiobjective ORPF, formulated as a multiobjective mixed integer nonlinear optimization problem, minimizes real power loss and improves voltage profile of power grid by determining reactive power control variables. NSGA-II-based ORPF is tested on standard IEEE 30-bus test system and compared with four other state-of-the-art multiobjective evolutionary algorithms (MOEAs). Pareto front and outer solutions achieved by the five MOEAs are analyzed and compared. NSGA-II obtains the best control strategy for ORPF, but it suffers from the lower convergence speed at the early stage of the optimization. Several problem-specific local search strategies (LSSs) are incorporated into NSGA-II to promote algorithm's exploiting capability and then to speed up its convergence. This enhanced version of NSGA-II (ENSGA) is examined on IEEE 30 system. Experimental results show that the use of LSSs clearly improved the performance of NSGA-II. ENSGA shows the best search efficiency and is proved to be one of the efficient potential candidates in solving reactive power optimization in the real-time operation systems.

Online Multiobjective Evolutionary Approach for Navigation of Humanoid Robots

Ki-Baek Lee,Hyun Myung,Jong-Hwan Kim Institute of Electrical and Electronics Engineers 2015 IEEE transactions on industrial electronics Vol. No.

<P>This paper proposes a novel online multiobjective evolutionary approach for the navigation of humanoid robots. In the proposed approach, the humanoid robot navigation problem is decomposed into a series of small multiobjective optimization problems (MOPs) with corresponding local information. Using multiobjective evolutionary algorithms (MOEAs), the MOPs can be successively solved while the robot is walking. In addition, to achieve significant reductions in the processing time of the MOEAs for online implementation while maintaining robustness and scalability, a novel homogeneous parallel computing method is devised for the MOEAs. Multiobjective particle swarm optimization with preference-based sort (MOPSO-PS) is employed as the MOEA to reflect the user-defined preference for each objective during navigation. The effectiveness of the proposed online approach is demonstrated through well-known benchmark problems and a robot simulator. In both the simulation and the experiment, a humanoid robot successfully navigates to the goal, satisfying the preferences for various objectives, with local information in an environment without a global map.</P>

Multidimensional visualization and clustering for multiobjective optimization of artificial satellite heat pipe design

Min-Joong Jeong,Takashi Kobayashi,Shinobu Yoshimura 대한기계학회 2007 JOURNAL OF MECHANICAL SCIENCE AND TECHNOLOGY Vol.21 No.12

This study presents a newly developed approach for visualization of Pareto and quasi-Pareto solutions of a multiobjective design problem for the heat piping system in an artificial satellite. Given conflicting objective functions, multiobjective optimization requires both a search algorithm to find optimal solutions and a decision-making process for finalizing a design solution. This type of multiobjective optimization problem may easily induce equally optimized multple solutions such as Pareto solutions, quasi-Pareto solutions, and feasible solutions. Here, a multidimensional visualization and clustering technique is used for visualization of Pareto solutions. The proposed approach can support engineering decisions in the design of the heat piping system in artificial satellites. Design considerations for heat piping system need to simultaneously satisfy dual conditions such as thermal robustness and overall limitation of the total weight of the system. The proposed visualization and clustering technique can be a valuable design tool for the heat piping system, in which reliable decision-making has been frequently hindered by the conflicting nature of objective functions in conventional approaches.

다중목적함수 진화 알고리즘을 이용한 마이크로어레이 프로브 디자인

이인희(In-Hee Lee),신수용(Soo-Yong Shin),조영민(Youngmin Cho),양경애(Kyung-Ae Yang),장병탁(Byoung-Tak Zhang) 한국정보과학회 2008 정보과학회논문지 : 소프트웨어 및 응용 Vol.35 No.8

프로브(probe) 디자인은 성공적인 DNA 마이크로어레이(DNA microarray) 실험을 위해서 필수적인 작업이다. 프로브가 만족시켜야 하는 조건은 마이크로어레이 실험의 목적이나 방법에 따라 다양하게 정의될 수 있는데, 대부분의 기존 연구에서는 각각의 조건에 대하여 각각 독립적으로 정해진 한계치(threshold) 값을 넘지 않는 프로브를 탐색하는 방법을 취하고 있다. 그러나, 본 연구에서는 프로브 디자인을 두가지 목적함수를 지닌 다중목적함수 최적화 문제(multiobjective optimization problem)로 정의하고, ε -다중목적함수 진화 알고리즘(ε -multiobjective evolutionary algorithm)을 이용하여 해결하는 방법을 제시한다. 제시된 방법은 19종류의 고위험군 인유두종 바이러스(Human Papillomavirus) 유전자들에 대한 프로브 디자인과 52종류의 애기장대 칼모듈린 유전자군(Arabidopsis Calmodulin multigene family)에 대한 프로브 디자인에 각각 적용되었다. 제안한 방법론을 사용하여 기존의 공개 프로브 디자인 프로그램인 OligoArray 및 OligoWiz에 비해 목표유전자에 더 적합한 프로브를 찾을 수 있었다. Probe design is one of the essential tasks in successful DNA microarray experiments. The requirements for probes vary as the purpose or type of microarray experiments. In general, most previous works use the simple filtering approach with the fixed threshold value for each requirement. Here, we formulate the probe design as a multiobjective optimization problem with the two objectives and solve it using ε -multiobjective evolutionary algorithm. The suggested approach was applied in designing probes for 19 types of Human Papillomavirus and 52 genes in Arabidopsis Calmodulin multigene family and successfully produced more target specific probes compared to well-known probe design tools such as OligoArray and OligoWiz.

텐세그리티 구조물 설계를 위한다목적 최적화 기법에 관한 연구

Makoto Ohsaki,Jingyao Zhang,김재열 한국공간구조학회 2008 한국공간구조학회지 Vol.8 No.1

A multiobjective optimization approach is presented for force design of tensegrity structures. The geometry of the structure is given a priori. The design variables are the member forces, and the objective functions are the lowest eigenvalue of the tangent stiffness matrix that is to be maximized, and the deviation of the member forces from the target values that is to be minimized. The multiobjective programming problem is converted to a series of single-objective programming problems by using the constraint approach. A set of Pareto optimal solutions are generated for a tensegrity grid to demonstrate the validity of the proposed method.

Interval Valued Solution of Multiobjective Problem with Interval Cost, Source and Destination Parameters

홍덕헌 한국지능시스템학회 2009 INTERNATIONAL JOURNAL of FUZZY LOGIC and INTELLIGE Vol.9 No.1

Das etal.[EJOR117(1999)100-112]discussed the real valued solution procedure of the multiobjective transportation problem(MOTP)where the cost coefficients of the objective functions, and the source and destination parameters have been expressed as interval values by the decision maker. In this note, we consider the interval valued solution procedure of the same problem. This problem has been transformed into a classical multiobjective transportation problem where the constraints with interval source and destination parameters have been converted into deterministic ones. Numerical examples have been provided to illustrate the solution procedure for this case.

Higher order duality in multiobjective programming with cone constraints

Kim, Do Sang,Kang, Hun Suk,Lee, Yu Jung,Seo, You Young Taylor Francis 2010 Optimization Vol.59 No.1

<P> We consider the nonlinear multiobjective programming problems involving cone constraints. For this program, we construct higher order dual problems and establish weak, strong and converse duality theorems for an efficient solution by using higher order generalized invexity conditions due to Zhang (Higher order convexity and duality in multiobjective programming, in “Progress in Optimization”, Contributions from Australasia, Applied Optimization, Vol. 30, eds. A. Eberhard, R. Hill, D. Ralph and B.M. Glover, Kluwer Academic Publishers, Dordrecht, 1999, 101-116). As special cases of our duality relations, we give some known duality results.</P>