Wenji Li

An improved epsilon constraint handling method embedded in MOEA/D for constrained multi-objective optimization problems

This paper proposes an improved epsilon constraint handling method embedded in the multi-objective evolutionary algorithm based on decomposition (MOEA/D) to solve constrained multi-objective optimization problems (CMOPs). More specifically, it dynamically adjusts the epsilon level, which is a critical parameter in the epsilon constraint method, according to the feasible ratio of solutions in the current population. In order to verify the effect of the improved epsilon constraint handling method, three algorithms - MOEA/D-CDP, MOEA/D-Epsilon, and MOEA/D-IEpsilon (MOEA/D with the improved epsilon constraint handling mechanism) are tested on nine CMOPs (CMOP1-CMOP9). The comprehensive experimental results indicate that the proposed epsilon constraint handling method is very effective on the performance of both convergence and diversity.

Hybridizing Infeasibility Driven and Constrained-Domination Principle with MOEA/D for Constrained Multiobjective Evolutionary Optimization

This paper presents a novel multiobjective constraint handling approach, named as MOEA/D-CDP-ID, to tackle constrained optimization problems. In the proposed method, two mechanisms, namely infeasibility driven (ID) and constrained-domination principle (CDP) are embedded into a prominent multiobjective evolutionary algorithm called MOEA/D. Constrained-domination principle defined a domination relation of two solutions in constraint handling problem. Infeasibility driven preserves a proportion of marginally infeasible solutions to join the searching process to evolve offspring. Such a strategy allows the algorithm to approach the constraint boundary from both the feasible and infeasible side of the search space, thus resulting in gaining a Pareto solution set with better distribution and convergence. The efficiency and effectiveness of the proposed approach are tested on several well-known benchmark test functions. In addition, the proposed MOEA/D-CDP-ID is applied to a real world application, namely design optimization of the two-stage planetary gear transmission system. Experimental results suggest that MOEA/D-CDP-ID can outperform other state-of-the-art algorithms for constrained multiobjective evolutionary optimization.

Optic Disk Detection in Fundus Image Based on Structured Learning

Automated optic disk (OD) detection plays an important role in developing a computer aided system for eye diseases. In this paper, we propose an algorithm for the OD detection based on structured learning. A classifier model is trained based on structured learning. Then, we use the model to achieve the edge map of OD. Thresholding is performed on the edge map, thus a binary image of the OD is obtained. Finally, circle Hough transform is carried out to approximate the boundary of OD by a circle. The proposed algorithm has been evaluated on three public datasets and obtained promising results. The results (an area overlap and Dices coefficients of 0.8605 and 0.9181, respectively, an accuracy of 0.9777, and a true positive and false positive fraction of 0.9183 and 0.0102) show that the proposed method is very competitive with the state-of-the-art methods and is a reliable tool for the segmentation of OD.

Difficulty Controllable and Scalable Constrained Multi-objective Test Problems

In this paper, we propose a general toolkit to construct constrained multi-objective optimisation problems (CMOPs) with three different kinds of constraint functions. Based on this toolkit, we suggested eight constrained multi-objective optimisation problems named CMOP1-CMOP8. As the ratio of feasible regions in the whole search space determines the difficulty of a constrained multi-objective optimisation problem, we propose four test instances CMOP3-6, which have very low ratio of feasible regions. To study the difficulties of proposed test instances, we make some experiments with two popular CMOEAs - MOEA/D-CDP and NSGA-II-CDP, and analysed their performances.

A comparative study of constrained multi-objective evolutionary algorithms on constrained multi-objective optimization problems

Solving constrained multi-objective optimization problems is a difficult task, it needs to simultaneously optimize multiple conflicting objectives and a number of constraints. This paper first reviews a number of popular constrained multi-objective evolutionary algorithms (CMOEAs) and twenty-three widely used constrained multi-objective optimization problems (CMOPs) (including CF1-10, CTP1-8, BNH, CONSTR, OSY, SRN and TNK problems). Then eight popular CMOEAs with simulated binary crossover (SBX) and differential evolution (DE) operators are selected to test their performance on the twenty-three CMOPs. The eight CMOEAs can be classified into domination-based CMOEAs (including ATM, IDEA, NSGA-II-CDP and SP) and decomposition-based CMOEAs (including CMOEA/D, MOEA/D-CDP, MOEA/D-SR and MOEA/D-IEpsilon). The comprehensive experimental results indicate that IDEA has the best performance in the domination-based CMOEAs and MOEA/D-IEpsilon has the best performance in the decomposition-based CMOEAs. Among the eight CMOEAs, MOEA/D-IEpsilon with both SBX and DE operators has the best performance on the twenty-three test problems.

Angle-based constrained dominance principle in MOEA/D for constrained multi-objective optimization problems

This paper proposes a new constraint handling method named Angle-based Constrained Dominance Principle (ACDP). Unlike the original Constrained Dominance Principle (CDP), this approach adopts the angle information of the objective functions to enhance the populations diversity in the infeasible region. To be more specific, given two infeasible solutions, if the angle of the solutions is greater than a given threshold, they are considered to be non-dominated by each other. For a feasible solution and an infeasible solution, if the angle of the solutions is less than a given threshold, the feasible solution is better, otherwise they are non-dominated. To verify the proposed constraint handling approach ACDP, eight test problems CMOP1 to CMOP8 are introduced. The suggested algorithm MOEA/D-ACDP is compared with MOEA/D-CDP and NSGA-II-CDP on CMOP1 to CMOP8. The experimental results demonstrate that ACDP performs better than CDP in the framework of MOEA/D, and MOEA/D-ACDP is significantly better than NSGA-II-CDP, especially on the test instances with the very low ratio of feasible region against the whole objective space.

Detecting optic disk based on structured learning

Optic Disk (OD) detection plays an important role for fundus image analysis. In this paper, we propose an algorithm for detecting OD mainly based on a classifier model trained by structured learning. Then we use the model to achieve the edge map of OD. Thresholding is performed on the edge map to obtain a binary image. Finally, circle Hough transform is carried out to approximate the boundary of OD by a circle. The proposed algorithm has been evaluated on the public database and obtained promising results. The results (an area overlap and Dices coefficients of 0.8636 and 0.9196, respectively, an accuracy of 0.9770, and a true positive and false positive fraction of 0.9212 and 0.0106) show that the proposed method is a robust tool for the segmentation of OD and is very competitive with the stage-of-the-art methods.

An opposition-based repair operator for multi-objective evolutionary algorithm in constrained optimization problems

In this paper, we design a set of multi-objective constrained optimization problems (MCOPs) and propose a new repair operator to address them. The proposed repair operator is used to fix the solutions that violate the box constraints. More specifically, it employs a reversed correction strategy that can effectively avoid the population falling into local optimum. In addition, we integrate the proposed repair operator into two classical multi-objective evolutionary algorithms MOEA/D and NSGA-II. The proposed repair operator is compared with other two kinds of commonly used repair operators on benchmark problems CTPs and MCOPs. The experiment results demonstrate that our proposed approach is very effective in terms of convergence and diversity.

An Improved Ideal Point Setting in Multiobjective Evolutionary Algorithm Based on Decomposition

In this paper, we propose an improved ideal point setting method in the framework of MOEA/D. MOEA/D decomposes a multi-objective optimisation problem into a number of scalar optimisation problems and optimise them simultaneously. The performance of MOEA/D is highly relate to its decomposition method, and the proposed ideal point setting approach is used in the weighted Tchebycheff (TCH) and penalty-based boundary intersection (PBI) decomposition approach. It expands the region of search in the objective space by transforming the original ideal point into its symmetric point and changes the search direction of each subproblems in MOEA/D. In order to address the proposed ideal point setting method, we design a set of multi-objective problems(MOPs). The proposed method is compared with original MOEA/D-TCH and MOEA/D-PBI on MOPs. The experimental results demonstrate that our proposed ideal point setting method is very effective in terms of both diversity and convergence.

Detecting optic disk based on AdaBoost and active geometric shape model

Detecting the optic disk (OD) is very important in the fundus image analysis. In this paper, we propose a new OD detection algorithm consisting of four main steps: first, obtaining the sub-image which includes the OD from the fundus image based on the saliency map; second, generating the super-pixel from the sub-image with a simple linear iterative clustering (SLIC) algorithm; third, classifying the super-pixel into OD or non-OD based on the AdaBoost algorithm; fourth, fitting the detected OD region with a circle based on the active geometric shape model. The proposed method has been evaluated on the Digital Retinal Images for Optic Nerve Segmentation (DRIONS) database. Experimental results show that our algorithm is very competitive with the state-of-the-art method.