Hai-Lin Liu

Decomposition of a Multiobjective Optimization Problem Into a Number of Simple Multiobjective Subproblems

This letter suggests an approach for decomposing a multiobjective optimization problem (MOP) into a set of simple multiobjective optimization subproblems. Using this approach, it proposes MOEA/D-M2M, a new version of multiobjective optimization evolutionary algorithm-based decomposition. This proposed algorithm solves these subproblems in a collaborative way. Each subproblem has its own population and receives computational effort at each generation. In such a way, population diversity can be maintained, which is critical for solving some MOPs. Experimental studies have been conducted to compare MOEA/D-M2M with classic MOEA/D and NSGA-II. This letter argues that population diversity is more important than convergence in multiobjective evolutionary algorithms for dealing with some MOPs. It also explains why MOEA/D-M2M performs better.

Selected Papers from the Ninth International Conference on Computational Intelligence and Security

The 2012 International Conference on Computational Intelligence and Security (CIS) is the ninth one focusing on all areas of two crucial fields in information processing: computational intelligence (CI) and information security (IS). In particular, the CIS Conference provides a platform to explore the potential applications of CI models, algorithms, and technologies to IS.

A Multi-Objective Evolutionary Algorithm Using Min-Max Strategy And Sphere Coordinate Transformation

Abstract Multi-objective evolutionary algorithms using the weighted sum of the objectives as the fitness functions feature simple execution and effectiveness in multi-objective optimization. However, they cannot fmd the Pareto solutions on the non-convex part of the Pareto frontier, and thus aze difficult to find evenly distributed solutions. Under the circumstances, this paper proposes anew evolutionary algorithm using multiple fitness functions. Although the weights generated via the sphere coordinate transformation and uniform design are used to define the fitness, the fitness is not defined by the weighted sum of the objectives. Instead, it is defined by the maximum value of the weighted normalized objectives using amin-max strategy. In this manner, the proposed algorithm can overcome the drawbacks of the algorithms using the weighted sum of the objectives, and explore the objective space to fmd approximate uniformly distributed solutions on the Pareto front gradually. The numerical simulations show t...

T-MOEA/D: MOEA/D with Objective Transform in Multi-objective Problems

To approximate the Pareto optimal solutions of a multi-objective optimization problem, Zhang and Li [8] have recently developed a novel multi-objective evolutionary algorithm based on decomposition(MOEA/D). It can work well if the curve shape of the Pareto-optimalfront is friendly. Otherwise, it might fail. In this paper, we propose an improved MOEA/D algorithm (denoted as TMOEA/D), which utilizes a monotonic increasing function to transform each individual objective function into the one so that the curve shape of the non-dominant solutions of the transformed multi-objective problem is close to the hyper-plane whose intercept of coordinate axes is equal to one in the original objective function space. Consequently, we can approximate the Pareto optimal solutions that are uniformly distributed over the Pareto front using the advanced decomposition technique of MOEA/D. Numerical results show that the proposed algorithm has a good performance.

A Lip Contour Extraction Method Using Localized Active Contour Model with Automatic Parameter Selection

Lip contour extraction is crucial to the success of a lipreading system. This paper presents a lip contour extraction algorithm using localized active contour model with the automatic selection of proper parameters. The proposed approach utilizes a minimum-bounding ellipse as the initial evolving curve to split the local neighborhoods into the local interior region and the local exterior region, respectively, and then compute the localized energy for evolving and extracting. This method is robust against the uneven illumination, rotation, deformation, and the effects of teeth and tongue. Experiments show its promising result in comparison with the existing methods.

On Solving WCDMA Network Planning Using Iterative Power Control Scheme and Evolutionary Multiobjective Algorithm [Application Notes]

Due to the increasing demand for mobile radio services, 3G wireless network planning has been becoming one of the most important research f ields. 3G system, e.g. WCDMA, is based on Code Division Multiple Access [1], which is quite different from Time Division Multiple Access (TDMA) as used in 2G system.In the 3G network planning, not only are coverage, capacity and quality of the signal interrelated, but multi-rate and mixed-business also utilize the common carrier at the same time. As a result, it makes the 3G network planning become more challenging. In this paper, we will only concentrate on the WCDMA network planning. Since the WCDMA systems have self-interference and the effects of cell-breathing, it makes the coverage, capacity and interference of the base stations (BSs) restrain each other [2], [3]. That is, the area actually covered by a BS depends on the Quality of Service (QoS) and the traffic demand distribution. Therefore, the relationship between coverage, capacity and interference should be fully taken into account in the planning process.

Objective Extraction for Many-Objective Optimization Problems: Algorithm and Test Problems

For many-objective optimization problems (MaOPs), in which the number of objectives is greater than three, the performance of most existing evolutionary multi-objective optimization algorithms generally deteriorates over the number of objectives. As some MaOPs may have redundant or correlated objectives, it is desirable to reduce the number of the objectives in such circumstances. However, the Pareto solution of the reduced MaOP obtained by most of the existing objective reduction methods, based on objective selection, may not be the Pareto solution of the original MaOP. In this paper, we propose an objective extraction method (OEM) for MaOPs. It formulates the reduced objective as a linear combination of the original objectives to maximize the conflict between the reduced objectives. Subsequently, the Pareto solution of the reduced MaOP obtained by the proposed algorithm is that of the original MaOP, and the proposed algorithm can thus preserve the dominance structure as much as possible. Moreover, we propose a novel framework that features both simple and complicated Pareto set shapes for many-objective test problems with an arbitrary number of essential objectives. Within this framework, we can control the importance of essential objectives. As there is no direct performance metric for the objective reduction algorithms on the benchmarks, we present a new metric that features simplicity and usability for the objective reduction algorithms. We compare the proposed OEM with three objective reduction methods, i.e., REDGA, L-PCA, and NL-MVU-PCA, on the proposed test problems and benchmark DTLZ5 with different numbers of objectives and essential objectives. Our numerical studies show the effectiveness and robustness of the proposed approach.

An evolutionary algorithm based on Covariance Matrix Leaning and Searching Preference for solving CEC 2014 benchmark problems

In this paper, we propose a single objective optimization evolutionary algorithm (EA) based on Covariance Matrix Learning and Searching Preference (CMLSP) and design a switching method which is used to combine CMLSP and Covariance Matrix Adaptation Evolution Strategy (CMAES). Then we investigate the performance of the switch method on a set of 30 noiseless optimization problems designed for the special session on real-parameter optimization of CEC 2014. The basic idea of the proposed CMLSP is that it is more likely to find a better individual around a good individual. That is to say, the better an individual is, the more resources should be invested to search the region around the individual. To achieve it, we discard the traditional crossover and mutation and design a novel method based on the covariance matrix leaning to generate high quality solutions. The best individual found so far is used as the mean of a Gaussian distribution and the covariance of the best λ individuals in the population are used as the evaluation of its covariance matrix and we sample the next generation individual from the Gaussian distribution other than using crossover and mutation. In the process of generating new individuals, the best individual is changed if ever a better one is found. This search strategy emphasizes the region around the best individual so that a faster convergence can be achieved. The use of switch method is to make best use of the proposed CMLSP and existing CMAES. At last, we report the results.

Investigating the Effect of Imbalance Between Convergence and Diversity in Evolutionary Multiobjective Algorithms

There are two main tasks involved in addressing a multiobjective optimization problem (MOP) by evolutionary multiobjective (EMO) algorithms: 1) make the population converge close to the Pareto-optimal front and 2) maintain adequate population diversity. However, most state-of-the-art EMO algorithms are designed based on the “convergence first and diversity second” principle. It has been observed that although these EMO algorithms have been successful in optimizing many real-world MOPs, they fail to solve certain problems that feature a severe imbalance between diversity preservation and achieving convergence. This paper characterizes an imbalanced MOP by clearly defining properties and indicating the reasons for the existing EMO algorithms’ difficulties in solving them. We then present 14 imbalanced problems, with and without constraints. Computational results using four existing EMO algorithms—elitist non-dominated sorting genetic algorithm (NSGA-II), multiobjective evolutionary algorithm based on decomposition (MOEA/D), strength Pareto evolutionary algorithm 2 (SPEA2), and S metric selection EMO algorithm (SMS-EMOA) and a proposed generalized vector-evaluated genetic algorithm are then presented. It is seen that these EMO algorithms cannot solve these imbalanced problems, but they are able to solve the problems when augmented by multiobjective to multiobjective (M2M), an approach that decomposes the population into several interacting subpopulations. These results and the successful application of the EMO methods with the M2M approach even on standard so-called balanced problems indicate the usefulness of using the M2M approach.

An evolutionary many-objective optimisation algorithm with adaptive region decomposition

When optimizing an multiobjective optimization problem, the evolution of population can be regarded as a approximation to the Pareto Front (PF). Motivated by this idea, we propose an adaptive region decomposition framework: MOEA/D-AM2M for the degenerated Many-Objective optimization problem (MaOP), where degenerated MaOP refers to the optimization problem with a degenerated PF in a subspace of the objective space. In this framework, a complex MaOP can be adaptively decomposed into a number of many-objective optimization subproblems, which is realized by the adaptively direction vectors design according to the present populations distribution. A new adaptive weight vectors design method based on this adaptive region decomposition is also proposed for selection in MOEA/D-AM2M. This strategy can timely adjust the regions and weights according to the populations tendency in the evolutionary process, which serves as a remedy for the inefficiency of fixed and evenly distributed weights when solving MaOP with a degenerated PF. Five degenerated MaOPs with disconnected PFs are generated to identify the effectiveness of proposed MOEA/D-AM2M. Contrast experiments are conducted by optimizing those MaOPs using MOEA/D-AM2M, MOEA/D-DE and MOEA/D-M2M. Simulation results have shown that the proposed MOEA/D-AM2M outperforms MOEA/D-DE and MOEA/D-M2M.