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.
© Springer International Publishing AG 2017. k-means is one of the fundamental and most well-known algorithms in data mining. It has been widely used in clustering tasks, but suffers from a number of limitations on large or complex datasets. Genetic Programming (GP) has been used to improve performance of data mining algorithms by performing feature construction—the process of combining multiple attributes (features) of a dataset together to produce more powerful constructed features. In this paper, we propose novel representations for using GP to perform feature construction to improve the clustering performance of the k-means algorithm. Our experiments show significant performance improvement compared to k-means across a variety of difficult datasets. Several GP programs are also analysed to provide insight into how feature construction is able to improve clustering performance.
© Springer International Publishing AG 2017. Image descriptors are very important components in computer vision and pattern recognition that play critical roles in a wide range of applications. The main task of an image descriptor is to automatically detect micro-patterns in an image and generate a feature vector. A domain expert is often needed to undertake the process of developing an image descriptor. However, such an expert, in many cases, is difficult to find or expensive to employ. In this paper, a multitree genetic programming representation is adopted to automatically evolve image descriptors. Unlike existing hand-crafted image descriptors, the proposed method does not rely on predetermined features, instead, it automatically identifies a set of features using a few instances of each class. The performance of the proposed method is assessed using seven benchmark texture classification datasets and compared to seven state-of-the-art methods. The results show that the new method has significantly outperformed its counterpart methods in most cases.
In this paper we introduce ACOP, a novel ACO algorithm for solving permutation based optimization problems. The main novelty is in how ACOP ants construct a permutation by navigating the space of partial orders and considering precedence relations as solution components. Indeed, a permutation is built up by iteratively adding precedence relations to a partial order of items until it becomes a total order, thus the corresponding permutation is obtained. The pheromone model and the heuristic function assign desirability values to precedence relations. An ACOP implementation for the Linear Ordering Problem (LOP) is proposed. Experiments have been held on a large set of widely adopted LOP benchmark instances. The experimental results show that the approach is very competitive and it clearly outperforms previous ACO proposals for LOP.
This paper presents a generalized hybrid evolutionary optimization structure that not only combines both nondeterministic and deterministic algorithms on their individual merits and distinct advantages, but also offers behaviors of the three originating classes of evolutionary algorithms (EAs). In addition, a robust mutation operator is developed in place of the necessity of mutation adaptation, based on the mutation properties of binary-coded individuals in a genetic algorithm. The behaviour of this mutation operator is examined in full and its performance is compared with adaptive mutations. The results show that the new mutation operator outperforms adaptive mutation operators while reducing complications of extra adaptive parameters in an EA representation.
Fuzzy cognitive maps (FCMs) are inference networks, which are the combination of fuzzy logic and neural networks. Various evolutionary-based learning algorithms have been proposed to learn FCMs. However, evolutionary algorithms have shortcomings, such as easy to become premature and the local search ability is weak where the search may trap into local optima. Decision-making trial and evaluation laboratory (DEMATEL) has been widely accepted as one of the best tools to analyze the causal and effect relationships between concepts. Therefore, we combine real-coded genetic algorithm (RCGA) with DEMATEL method, termed as RCGADEMATEL-FCM, to learn FCM models. In RCGADEMATEL-FCM, the DEMATEL method is used as a directed neighborhood search operator to steer the search to the right direction in the objective space, which can overcome the premature problem and make the search jump out of the local optimum. Experimental results on both synthetic and real life data demonstrate the efficiency of the proposed algorithm. The comparison with existing learning algorithms shows that RCGADEMATEL-FCM can learn FCMs with higher accuracy without expert knowledge.
This paper proposes a decomposition-based multi-objective multi-factorial evolutionary algorithm (MFEA/D-M2M). The MFEA/D-M2M adopts the M2M approach to decompose multi-objective optimization problems into multiple constrained sub-problems for enhancing the diversity of population and convergence of sub-regions. An machine learning model augmented version is also been implemented, which utilized discriminative models for pre-selecting solutions. Experimental studies on nine multi-factorial optimization (MFO) problem sets are conducted. The experimental results demonstrated that MFEA/D-M2M outperforms the vanilla MFEA on six MFO benchmark problem sets and achieved comparable results on the other three problem sets with partial intersection of global optimal.
A multi-objective optimization problem (MOP) involves simultaneous minimization or maximization of more than one conflicting objectives. Such problems are commonly encountered in a number of domains, such as engineering, finance, operations research, etc. In the recent years, algorithms based on decomposition have shown commendable success in solving MOPs. In particular they have been helpful in overcoming the limitation of Pareto-dominance based ranking when the number of objectives is large. Decomposition based evolutionary algorithms divide an MOP into a number of simpler sub-problems and solve them simultaneously in a cooperative manner. In order to define the sub-problems, a reference point is needed to construct reference vectors in the objective space to guide the corresponding sub-populations. However, the effect of the choice of this reference point has been scarcely studied in literature. Most of the existing works simply construct the reference point using the minimum objective values in the current nondominated population. Some of the recent studies have gone beyond and suggested the use of optimistic, pessimistic or dynamic reference point specification. In this study, we first qualitatively examine the implications of using different strategies to construct the reference points. Thereafter, we suggest an alternative method which relies on identifying promising reference points rather than specifying them. In the proposed approach, each objective is individually minimized in order to estimate a point close to the true ideal point to identify such reference points. Some initial results and analysis are presented to demonstrate the potential benefits and limitations of the approach. Overall, the approach demonstrates promising results but needs further development for achieving more significant improvements in solving MOPs.
The traveling salesman problem with neighborhoods (TSPN) is a generalization of TSP and can be regarded as a combination of TSP and TPP (Touring Polygons Problem). In this paper, we propose a hybrid TSPN solution named ACO-iRBA in which the TSP and TPP tasks are tackled simultaneously by ACO (Ant Colony Optimization) and iRBA, an improved version of RBA (Rubber Band Algorithm), respectively. A major feature of ACO-iRBA is that it can properly handle situations where the neighborhoods are heavily overlapped. Experiment results on benchmark problems composed of random ellipses show that ACO-iRBA can solve TSPN instances with up to 70 regions effectively and generally produce higher quality solutions than a recent heuristic method CIH.
Evolutionary algorithms (EAs) are a kind of population-based meta-heuristic optimization methods, which have proven to have superiorities in solving NP-complete and NP-hard optimization problems. But until now, there is lacking in the researches of effective representation method to describe the collective search behavior of the Evolutionary Algorithm, while it is useful for researchers and engineers to understand and compare different EAs better. In the past, most of the theoretical researches cannot directly guide for practical applications. To bridge the gap between theoretical research and practice, we present a generic and reusable framework for learning features to describe collective behavior of EAs in this paper. Firstly, we represent the collective behavior of EAs with a parent-child difference of population distribution encoded by self-organizing map (SOM). Then, we train a Convolutional Neural Network (CNN) to learn problem-invariant features from the samples of EAs’ collective behavior. Lastly, experiment results demonstrate that our framework can effectively learn discriminative features representing collective behavior of EAs. In the behavioral feature space stretched by the obtained features, the collective behavior samples of various EAs on various testing problems exhibit obvious aggregations that highly correlated with EAs but very weakly related to testing problems. We believe that the learned features are meaningful in analyzing EAs, i.e. it can be used to measure the similarity of EAs according to their inner behavior in solution space, and further guide in selecting an appropriate combination of sub-algorithm of a hybrid algorithm according to the diversity of candidate sub-algorithm instead of blind.
The majority of real-world problems involve not only finding the optimal solution, but also this solution must satisfy one or more constraints. Differential evolution (DE) algorithm with constraints handling has been proposed to solve one of the most fundamental problems in cellular network design. This proposed method has been applied to solve the radio network planning (RNP) in the forthcoming 5G Long Term Evolution (5G LTE) wireless cellular network, that satisfies both deployment cost and energy savings by reducing the number of deployed micro base stations (BSs) in an area of interest. Practically, this has been implemented using constrained strategy that must guarantee good coverage for the users as well. Three differential evolution variants have been adopted to solve the 5G RNP problem. Experimental results have shown that the constrained DE/best/1/bin has achieved best results over other variants in terms of deployment cost, coverage rate and quality of service (QoS).
Maximizing the lifetime of Wireless Sensor Network (WSN) with a mobile sink is a challenging and important problem that has attracted increasing research attentions. In the literature, heuristic based approaches have been proposed to solve the problem, such as the Greedy Maximum Residual Energy (GMRE) based method. However, existing heuristic based approaches highly rely on expert knowledge, which makes them inconvenient for practical applications. Taking this cue, in this paper, we propose an automatic method to construct heuristic for sink routing based on Genetic Programming (GP) approach. Empirical study shows that the proposed method can generate promising heuristics that achieve superior performance against existing methods with respect to the global lifetime of WSN.
Constrained multiobjective optimization problem (CMOP) is an important research topic in the field of evolutionary computation. In terms of constraint handling, most of the existing evolutionary algorithms consider more about the proportion of infeasible solutions in population, but less concern about the distribution of infeasible solutions. Therefore, we propose a constraint partitioning method based on minimax strategy (CPM/MS) to solve CMOP. Firstly, we analyze the impact of the distribution of infeasible solutions on selecting solutions and give a preconditioning method for infeasible solutions. Secondly, we divide the preconditioned solutions into different regions by minimax strategy. Finally, we update individuals based on feasibility criteria method in each region. The effectiveness of CPM/MS algorithm is extensively evaluated on a suite of 10 bound-constrained numerical optimization problems, where the results show that CPM/MS algorithm is able to obtain considerably better fronts for some of the problems compared with some the state-of-the-art multiobjective evolutionary algorithms.
Setting proper parameters is vital for using Evolutionary Algorithms (EAs) to optimize problems, while parameter tuning is a time-consuming task. Previous approaches focus on tuning parameter configurations that are suitable for multiple problems or problem instances. However, according to the No Free Lunch (NFL) theorem, there is no generic parameter configuration that is fit for all problems. Moreover, practitioners are usually concerned with their particular optimization problem at hand and desire to obtain an acceptable result with less computational cost. Therefore, in this paper, the KW-Race framework is first proposed for solving the parameter tuning task of EAs on certain black-box optimization problem. Then a measure of convergence speed is embedded in the preceding framework to form the Fast KW-Race (F-KW-Race) framework for further reducing the computational cost of the tuning procedure. Experimental studies illustrate remarkable results and further demonstrate the validity and efficiency of the proposed frameworks.
Evolutionary multitasking optimization has recently emerged as an effective framework to solve different optimization problems simultaneously. Different from the classic evolutionary algorithms, multi-task optimization (MTO) is designed to take advantage of implicit genetic transfer in a multitasking environment. It deals with multiple tasks simultaneously by leveraging similarities and differences across different tasks. However, MTO still suffers from a few issues. In this paper, a multifactorial memetic algorithm is introduced to solve the single-objective MTO problems. Particularly, the proposed algorithm introduces a local search method based on quasi-Newton, reinitializes a port of worse individuals, and suggests a self-adapt parent selection strategy. The effectiveness of the proposed algorithm is validated by comparing with the multifactorial evolutionary algorithm proposed in CEC’17 competition.
Many evolutionary and constructive heuristic approaches have been introduced in order to solve the Travelling Thief Problem (TTP). However, the accuracy of such approaches is unknown due to their inability to find global optima. In this paper, we propose three exact algorithms and a hybrid approach to the TTP. We compare these with state-of-the-art approaches to gather a comprehensive overview on the accuracy of heuristic methods for solving small TTP instances.
This paper proposed a novel method for unsupervised change detection of remote sensing images using principal component analysis and differential evolution (PDECD). PDECD consists of two main steps. Firstly, an eigenvector space is generated by principal component analysis (PCA) of image blocks. Difference image is projected onto the eigenvector space to extract image local features, which is essentially composed of local smoothing feature and edge fidelity features. Then PDECD regards change detection as an optimal clustering problem and utilizes the differential evolution algorithm (DE) to search for the optimal change detection results without any priori knowledge. Compared with the existing methods, PDECD is not only robust to image noise, but also sensitive to small changed details. In addition, PDECD can avoid tracking to the local optima in change detection process and improve the detection performance due to the powerful global optimization capability of DE. Considering the image data belonging to two clusters cannot separated by sharp boundaries, so the Jm index of standard fuzzy clustering method is used as the objective function of DE. In order to improve the robustness and automatic detection capability of PDECD, control parameters of DE have been adjusted adaptively. Experiments conducted on real SAR and optical remote sensing images demonstrate the effectiveness of the proposed method.
This article proposes an efficient method for Restricted Boltzmann Machine (RBM) to learn sparse feature. Deep learning algorithms are used more and more often. The Deep Belief Network (DBN) model, which is composed of RBM, is considered as one of the most effective deep learning algorithms. RBM or auto-encoder (AE) is the basic model to build deep networks. However, RBM may produce redundant features without any constraints, then much improved RBM were proposed by added a regularization term to control sparsity of hidden units. Most of the proposed algorithms need a parameter to control the sparseness of the code. In this paper, we proposed a multiobjective optimization model to avoid user-defined constant that is a trade-off between the regularization term and the reconstruction error based on SR-RBM. We employ evolutionary algorithm to optimize the distortion function and the sparsity of hidden units simultaneously. Experimental results show that our novel approach can learn useful sparse feature without a user-define constant and it performs better than other feature learning models.
Pareto Local Search (PLS) is a basic building block in many state-of-the-art multiobjective combinatorial optimization algorithms. However, the basic PLS requires a long time to find high-quality solutions. In this paper, we propose and investigate several parallel strategies to speed up PLS. These strategies are based on a parallel multi-search framework. In our experiments, we investigate the performances of different parallel variants of PLS on the multiobjective unconstrained binary quadratic programming problem. Each PLS variant is a combination of the proposed parallel strategies. The experimental results show that the proposed approaches can significantly speed up PLS while maintaining about the same solution quality. In addition, we introduce a new way to visualize the search process of PLS on two-objective problems, which is helpful to understand the behaviors of PLS algorithms.
Nearly all solutions are Pareto non-dominated for multi-objective problems with more than three conflicting objectives. Thus, the comparison of solutions is a critical issue in many objective optimization. A simple but effective normalized ranking metric based method is proposed to compare solutions in this paper. All solutions are ranked by the sum of normalized fitness value of each objective. A solution with a small value is considered to be a good solution for minimum optimization problems. To enhance the population diversity of all solutions, the solutions with small values and the solutions with better fitness values on each objective are kept in an archive and updated per iteration. This ranking metric is further utilized in a particle swarm optimization algorithm to solve multiobjective and many objective problems. Four benchmark problems are utilized to test the proposed algorithm. Experimental results demonstrate that the proposed algorithm is a promising approach for solving the multiobjective and many objective optimization problems.
