Fangqing Gu

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.

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.

Online objective reduction for many-objective optimization problems

For many-objective optimization problems, i.e. the number of objectives is greater than three, the performance of most of the existing Evolutionary Multi-objective Optimization algorithms will deteriorate to a certain degree. It is therefore desirable to reduce many objectives to fewer essential objectives, if applicable. Currently, most of the existing objective reduction methods are based on objective selection, whose computational process is, however, laborious. In this paper, we will propose an online objective reduction method based on objective extraction for the many-objective optimization problems. It formulates the essential objective as a linear combination of the original objectives with the combination weights determined based on the correlations of each pair of the essential objectives. Subsequently, we will integrate it into NSGA-II. Numerical studies have show the efficacy of the proposed approach.

Self-Organizing Map-Based Weight Design for Decomposition-Based Many-Objective Evolutionary Algorithm

Many-objective optimization problems (MaOPs), in which the number of objectives is greater than three, are undoubtedly more challenging compared with the bi- and tri-objective optimization problems. Currently, the decomposition-based evolutionary algorithms have shown promising performance in dealing with MaOPs. Nevertheless, these algorithms need to design the weight vectors, which has significant effects on the performance of the algorithms. In particular, when the Pareto front of problems is incomplete, these algorithms cannot obtain a set of uniformly distribution solutions by using the conventional weight design methods. In the literature, it is well-known that the self-organizing map (SOM) can preserve the topological properties of the input data by using the neighborhood function, and its display is more uniform than the probability density of the input data. This phenomenon is advantageous to generate a set of uniformly distributed weight vectors based on the distribution of the individuals. Therefore, we will propose a novel weight design method based on SOM, which can be integrated with most of the decomposition-based algorithms for solving MaOPs. In this paper, we choose the existing state-of-the-art decomposition-based algorithms as examples for such integration. This integrated algorithms are then compared with some state-of-the-art algorithms on eleven redundancy problems and eight nonredundancy problems, respectively. The experimental results show the effectiveness of the proposed approach.

An evolutionary algorithm based on decomposition for multimodal optimization problems

This paper presents a non-parameter method to identify the peaks of the multi-modal optimization problems provided that the peaks are characterized by a smaller objective values than their neighbors and by a relatively large distance from points with smaller objective value. Using the identified peaks as the seeds, we decompose the population into some subpopulations and dynamically allocate the computational effort to different subpopulations. We evaluate the proposed approach on the CEC2015 single objective multi-niche optimization problems. The promising experimental results show its efficacy.

A novel multiobjective differential evolutionary algorithm based on subregion search

A novel multiobjective DE algorithm using the subregion and external set strategy (MOEA/S-DE) is proposed in this paper, in which the objective space is divided into some subregions and then independently optimize each subregion. An external set is introduced for each subregion to save some individuals ever found in this subregion. An alternative of mutation operators based the idea of direct simplex method of mathematical programming are proposed: local and global mutation operator. The local mutation operator is applied to improve the local search performance of the algorithm and the global mutation operator to explore a wider area. Additionally, a reusing strategy of difference vector also is proposed. It reuses the difference vector of the better individuals according to a given probability. Compared with traditional DE, the crossover operator also is improved. In order to demonstrate the performance of the proposed algorithm, it is compared with the MOEA/D-DE and the hybrid-NSGA-II-DE. The result indicates that the proposed algorithm is efficient.

Optimization of Spectrum-Energy Efficiency in Heterogeneous Communication Network

Green communication has become a hot topic in the field of wireless communication. This paper aims to improve the Quality of Service (QoS) of the system and minimizes the energy consumption by the spectrum-energy cooperation between adjacent base stations. We formulate the proposed spectrum-energy cooperation model as a hybrid constrained many-objective optimization problem (MaOP). To improve the efficiency of optimization algorithm, an alternate optimization algorithm is presented to address the proposed complex MaOP. The evolutionary multiobjective algorithm is employed for spectrum cooperation optimization which is discrete optimization problem, meanwhile classical optimization method is employed for energy consumption optimization and energy cooperation optimization that are continuous optimization problems. Simulation results show the effectiveness of the algorithm.

A supervised correlation analysis for score-level calibration of cross-device fingerprint recognition

As the usage of fingerprint systems is rolled out on a large scale, scenarios have cross-device matching to allow information exchange and provide compatibility to the existing systems. A score-level calibration for device interoperability will require normalizing scores obtained from different devices so that they can be matched meaningfully and effectively. Conventional methods either assume a homogeneous distribution or model score distribution based on assumptions that may not be valid. In this paper, we circumvent the problem by leveraging correlations among the scores and propose a novel method for biometric score normalization. Our experiments show the promising results.

A Fast Objective Reduction Algorithm Based on Dominance Structure for Many Objective Optimization

The performance of the most existing classical evolutionary multiobjective optimization (EMO) algorithms, especially for Pareto-based EMO algorithms, generally deteriorates over the number of objectives in solving many-objective optimization problems (MaOPs), in which the number of objectives is greater than three. Objective reduction methods that transform an MaOP into the one with few objectives, are a promising way for solving MaOPs. The dominance-based objective reduction methods, e.g. k-EMOSS and \(\delta \)-MOSS, omitting an objective while preserving the dominant structure of the individuals as much as possible, can achieve good performance. However, these algorithms have higher computational complexity. Therefore, this paper presents a novel measure for measuring the capacity of preserving the dominance structure of an objective set, i.e., the redundancy of an objective to an objective set. Subsequently, we propose a fast algorithm to find a minimum set of objectives preserving the dominance structure as much as possible. We compare the proposed algorithm with its counterparts on eleven test instances. Numerical studies show the effectiveness of the proposed algorithm.