Knowledge extraction in multi-objective optimization problem based on visualization of Pareto solutions

Optimizing the cost and benefit allocation among multiple players in a public-private partnership (PPP) project is recognized to be a multi-objective optimization problem (MOP). When the least present value of revenue (LPVR) mechanism is adopted in the competitive procurement of PPPs, the MOP presents asymmetry in objective levels, control variables and action orders. This paper characterizes this asymmetrical MOP in Stackelberg theory and builds a bi-level programing model to solve it in order to support the decision-making activities of both the public and private sectors in negotiation. An intuitive algorithm based on the non-dominated sorting genetic algorithm III (NSGA III) framework is designed to generate Pareto solutions that allow decision-makers to choose optimal strategies from their own criteria. The effectiveness of the model and algorithm is validated via a real case of a highway PPP project. The results reveal that the PPP project will be financially infeasible without the transfer of certain amounts of exterior benefits into supplementary income for the private sector. Besides, the strategy of transferring minimum exterior benefits is more beneficial to the public sector than to users.

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Some Preliminary Results on the Development and Comparison of a New Multi-Objective Genetic Algorithm

Volume 2A: 27th Design Automation Conference ◽

10.1115/detc2001/dac-21021 ◽

2001 ◽

Author(s):

A. Farhang-Mehr ◽

J. Wu ◽

S. Azarm

Keyword(s):

Genetic Algorithm ◽

Optimization Problem ◽

Quality Metrics ◽

Initial Population ◽

Multi Objective Optimization ◽

Pareto Solutions ◽

Preliminary Results ◽

Multi Objective ◽

Multi Objective Genetic Algorithm ◽

Speed Reducer

Abstract Some preliminary results for a new multi-objective genetic algorithm (MOGA) are presented. This new algorithm aims at obtaining the fullest possible representation of observed Pareto solutions to a multi-objective optimization problem. The algorithm, hereafter called entropy-based MOGA (or E-MOGA), is based on an application of the concepts from the statistical theory of gases to a MOGA. A few set quality metrics are introduced and used for a comparison of the E-MOGA to a previously published MOGA. Due to the stochastic nature of the MOGA, confidence intervals with a 95% confidence level are calculated for the quality metrics based on the randomness in the initial population. An engineering example, namely the design of a speed reducer is used to demonstrate the performance of E-MOGA when compared to the previous MOGA.

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MCDM towards knowledge incorporation in ANN models for phase transformation in continuous cooling of steel

Multidiscipline Modeling in Materials and Structures ◽

10.1108/mmms-01-2018-0002 ◽

2019 ◽

Vol 15 (1) ◽

pp. 170-186 ◽

Cited By ~ 2

Author(s):

Subhamita Chakraborty ◽

Prasun Das ◽

Naveen Kumar Kaveti ◽

Partha Protim Chattopadhyay ◽

Shubhabrata Datta

Keyword(s):

Optimization Problem ◽

Multi Objective Optimization ◽

Pareto Solutions ◽

Single Model ◽

Content Type ◽

Multi Objective ◽

Ann Models ◽

Knowledge Incorporation ◽

Single Objective ◽

System Knowledge

Purpose The purpose of this paper is to incorporate prior knowledge in the artificial neural network (ANN) model for the prediction of continuous cooling transformation (CCT) diagram of steel, so that the model predictions become valid from materials engineering point of view. Design/methodology/approach Genetic algorithm (GA) is used in different ways for incorporating system knowledge during training the ANN. In case of training, the ANN in multi-objective optimization mode, with prediction error minimization as one objective and the system knowledge incorporation as the other, the generated Pareto solutions are different ANN models with better performance in at least one objective. To choose a single model for the prediction of steel transformation, different multi-criteria decision-making (MCDM) concepts are employed. To avoid the problem of choosing a single model from the non-dominated Pareto solutions, the training scheme also converted into a single objective optimization problem. Findings The prediction results of the models trained in multi and single objective optimization schemes are compared. It is seen that though conversion of the problem to a single objective optimization problem reduces the complexity, the models trained using multi-objective optimization are found to be better for predicting metallurgically justifiable result. Originality/value ANN is being used extensively in the complex materials systems like steel. Several works have been done to develop ANN models for the prediction of CCT diagram. But the present work proposes some methods to overcome the inherent problem of data-driven model, and make the prediction viable from the system knowledge.

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Search Acceleration of Evolutionary Multi-Objective Optimization Using an Estimated Convergence Point

Mathematics ◽

10.3390/math7020129 ◽

2019 ◽

Vol 7 (2) ◽

pp. 129 ◽

Cited By ~ 4

Author(s):

Yan Pei ◽

Jun Yu ◽

Hideyuki Takagi

Keyword(s):

Parameter Space ◽

Statistical Tests ◽

Distribution Characteristic ◽

Multi Objective Optimization ◽

Pareto Improvement ◽

Pareto Solutions ◽

Pareto Solution ◽

Multi Objective ◽

Objective Space ◽

Convergence Point

We propose a method to accelerate evolutionary multi-objective optimization (EMO) search using an estimated convergence point. Pareto improvement from the last generation to the current generation supports information of promising Pareto solution areas in both an objective space and a parameter space. We use this information to construct a set of moving vectors and estimate a non-dominated Pareto point from these moving vectors. In this work, we attempt to use different methods for constructing moving vectors, and use the convergence point estimated by using the moving vectors to accelerate EMO search. From our evaluation results, we found that the landscape of Pareto improvement has a uni-modal distribution characteristic in an objective space, and has a multi-modal distribution characteristic in a parameter space. Our proposed method can enhance EMO search when the landscape of Pareto improvement has a uni-modal distribution characteristic in a parameter space, and by chance also does that when landscape of Pareto improvement has a multi-modal distribution characteristic in a parameter space. The proposed methods can not only obtain more Pareto solutions compared with the conventional non-dominant sorting genetic algorithm (NSGA)-II algorithm, but can also increase the diversity of Pareto solutions. This indicates that our proposed method can enhance the search capability of EMO in both Pareto dominance and solution diversity. We also found that the method of constructing moving vectors is a primary issue for the success of our proposed method. We analyze and discuss this method with several evaluation metrics and statistical tests. The proposed method has potential to enhance EMO embedding deterministic learning methods in stochastic optimization algorithms.

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Braille Block Detection via Multi-Objective Optimization from an Egocentric Viewpoint

Sensors ◽

10.3390/s21082775 ◽

2021 ◽

Vol 21 (8) ◽

pp. 2775

Author(s):

Tsubasa Takano ◽

Takumi Nakane ◽

Takuya Akashi ◽

Chao Zhang

Keyword(s):

Optimization Problem ◽

Line Pair ◽

Objective Functions ◽

Multi Objective Optimization ◽

Multi Objective ◽

Optimization Framework ◽

Visually Impaired People ◽

Comprehensive Comparison ◽

Basic Characteristics ◽

Support Devices

In this paper, we propose a method to detect Braille blocks from an egocentric viewpoint, which is a key part of many walking support devices for visually impaired people. Our main contribution is to cast this task as a multi-objective optimization problem and exploits both the geometric and the appearance features for detection. Specifically, two objective functions were designed under an evolutionary optimization framework with a line pair modeled as an individual (i.e., solution). Both of the objectives follow the basic characteristics of the Braille blocks, which aim to clarify the boundaries and estimate the likelihood of the Braille block surface. Our proposed method was assessed by an originally collected and annotated dataset under real scenarios. Both quantitative and qualitative experimental results show that the proposed method can detect Braille blocks under various environments. We also provide a comprehensive comparison of the detection performance with respect to different multi-objective optimization algorithms.

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Auto-sharing parameters for transfer learning based on multi-objective optimization

Integrated Computer-Aided Engineering ◽

10.3233/ica-210655 ◽

2021 ◽

pp. 1-13

Author(s):

Hailin Liu ◽

Fangqing Gu ◽

Zixian Lin

Keyword(s):

Transfer Learning ◽

Optimization Problem ◽

Data Sets ◽

Multi Objective Optimization ◽

Particle Swarm Optimizer ◽

Real World Data ◽

Data Set ◽

Target Task ◽

Main Research ◽

Multi Objective

Transfer learning methods exploit similarities between different datasets to improve the performance of the target task by transferring knowledge from source tasks to the target task. “What to transfer” is a main research issue in transfer learning. The existing transfer learning method generally needs to acquire the shared parameters by integrating human knowledge. However, in many real applications, an understanding of which parameters can be shared is unknown beforehand. Transfer learning model is essentially a special multi-objective optimization problem. Consequently, this paper proposes a novel auto-sharing parameter technique for transfer learning based on multi-objective optimization and solves the optimization problem by using a multi-swarm particle swarm optimizer. Each task objective is simultaneously optimized by a sub-swarm. The current best particle from the sub-swarm of the target task is used to guide the search of particles of the source tasks and vice versa. The target task and source task are jointly solved by sharing the information of the best particle, which works as an inductive bias. Experiments are carried out to evaluate the proposed algorithm on several synthetic data sets and two real-world data sets of a school data set and a landmine data set, which show that the proposed algorithm is effective.

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On the use of filters to facilitate the post-optimal analysis of the Pareto solutions in multi-objective optimization

Computers & Chemical Engineering ◽

10.1016/j.compchemeng.2014.12.012 ◽

2015 ◽

Vol 74 ◽

pp. 48-58 ◽

Cited By ~ 23

Author(s):

E. Antipova ◽

C. Pozo ◽

G. Guillén-Gosálbez ◽

D. Boer ◽

L.F. Cabeza ◽

...

Keyword(s):

Multi Objective Optimization ◽

Pareto Solutions ◽

Multi Objective ◽

Optimal Analysis

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multi-Multi-Objective Optimization Problem and Its Solution by a MOEA

Lecture Notes in Computer Science - Evolutionary Multi-Criterion Optimization ◽

10.1007/978-3-540-70928-2_63 ◽

2007 ◽

pp. 847-861 ◽

Cited By ~ 2

Author(s):

Gideon Avigad

Keyword(s):

Optimization Problem ◽

Multi Objective Optimization ◽

Multi Objective

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Dynamic Particle Swarm Optimization to Solve Multi-objective Optimization Problem

Procedia Technology ◽

10.1016/j.protcy.2012.10.034 ◽

2012 ◽

Vol 6 ◽

pp. 283-290 ◽

Cited By ~ 9

Author(s):

Hemlata S. Urade ◽

Rahila Patel

Keyword(s):

Particle Swarm Optimization ◽

Optimization Problem ◽

Particle Swarm ◽

Multi Objective Optimization ◽

Swarm Optimization ◽

Multi Objective

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Walking with EMO

Multi-Objective Optimization in Computational Intelligence ◽

10.4018/978-1-59904-498-9.ch011 ◽

2011 ◽

pp. 300-332

Author(s):

Jason Teo ◽

Lynnie D. Neri ◽

Minh H. Nguyen ◽

Hussein A. Abbass

Keyword(s):

Legged Locomotion ◽

Operational Performance ◽

Multi Objective Optimization ◽

Pareto Solutions ◽

Uncertain Environments ◽

Multi Objective ◽

Limb Dynamics

This chapter will demonstrate the various robotics applications that can be achieved using evolutionary multi-objective optimization (EMO) techniques. The main objective of this chapter is to demonstrate practical ways of generating simple legged locomotion for simulated robots with two, four and six legs using EMO. The operational performance as well as complexities of the resulting evolved Pareto solutions that act as controllers for these robots will then be analyzed. Additionally, the operational dynamics of these evolved Pareto controllers in noisy and uncertain environments, limb dynamics and effects of using a different underlying EMO algorithm will also be discussed.

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