Yutao Qi

Moea/d with adaptive weight adjustment

Recently, MOEA/D (multi-objective evolutionary algorithm based on decomposition) has achieved great success in the field of evolutionary multi-objective optimization and has attracted a lot of attention. It decomposes a multi-objective optimization problem (MOP) into a set of scalar subproblems using uniformly distributed aggregation weight vectors and provides an excellent general algorithmic framework of evolutionary multi-objective optimization. Generally, the uniformity of weight vectors in MOEA/D can ensure the diversity of the Pareto optimal solutions, however, it cannot work as well when the target MOP has a complex Pareto front (PF; i.e., discontinuous PF or PF with sharp peak or low tail). To remedy this, we propose an improved MOEA/D with adaptive weight vector adjustment (MOEA/D-AWA). According to the analysis of the geometric relationship between the weight vectors and the optimal solutions under the Chebyshev decomposition scheme, a new weight vector initialization method and an adaptive weight vector adjustment strategy are introduced in MOEA/D-AWA. The weights are adjusted periodically so that the weights of subproblems can be redistributed adaptively to obtain better uniformity of solutions. Meanwhile, computing efforts devoted to subproblems with duplicate optimal solution can be saved. Moreover, an external elite population is introduced to help adding new subproblems into real sparse regions rather than pseudo sparse regions of the complex PF, that is, discontinuous regions of the PF. MOEA/D-AWA has been compared with four state of the art MOEAs, namely the original MOEA/D, Adaptive-MOEA/D, -MOEA/D, and NSGA-II on 10 widely used test problems, two newly constructed complex problems, and two many-objective problems. Experimental results indicate that MOEA/D-AWA outperforms the benchmark algorithms in terms of the IGD metric, particularly when the PF of the MOP is complex.

A Multiobjective Evolutionary Algorithm Based on Decision Variable Analyses for Multiobjective Optimization Problems With Large-Scale Variables

State-of-the-art multiobjective evolutionary algorithms (MOEAs) treat all the decision variables as a whole to optimize performance. Inspired by the cooperative coevolution and linkage learning methods in the field of single objective optimization, it is interesting to decompose a difficult high-dimensional problem into a set of simpler and low-dimensional subproblems that are easier to solve. However, with no prior knowledge about the objective function, it is not clear how to decompose the objective function. Moreover, it is difficult to use such a decomposition method to solve multiobjective optimization problems (MOPs) because their objective functions are commonly conflicting with one another. That is to say, changing decision variables will generate incomparable solutions. This paper introduces interdependence variable analysis and control variable analysis to deal with the above two difficulties. Thereby, an MOEA based on decision variable analyses (DVAs) is proposed in this paper. Control variable analysis is used to recognize the conflicts among objective functions. More specifically, which variables affect the diversity of generated solutions and which variables play an important role in the convergence of population. Based on learned variable linkages, interdependence variable analysis decomposes decision variables into a set of low-dimensional subcomponents. The empirical studies show that DVA can improve the solution quality on most difficult MOPs. The code and supplementary material of the proposed algorithm are available at http://web.xidian.edu.cn/fliu/paper.html.

Multi-objective immune algorithm with Baldwinian learning

By replacing the selection component, a well researched evolutionary algorithm for scalar optimization problems (SOPs) can be directly used to solve multi-objective optimization problems (MOPs). Therefore, in most of existing multi-objective evolutionary algorithms (MOEAs), selection and diversity maintenance have attracted a lot of research effort. However, conventional reproduction operators designed for SOPs might not be suitable for MOPs due to the different optima structures between them. At present, few works have been done to improve the searching efficiency of MOEAs according to the characteristic of MOPs. Based on the regularity of continues MOPs, a Baldwinian learning strategy is designed for improving the nondominated neighbor immune algorithm and a multi-objective immune algorithm with Baldwinian learning (MIAB) is proposed in this study. The Baldwinian learning strategy extracts the evolving environment of current population by building a probability distribution model and generates a predictive improving direction by combining the environment information and the evolving history of the parent individual. Experimental results based on ten representative benchmark problems indicate that, MIAB outperforms the original immune algorithm, it performs better or similarly the other two outstanding approached NSGAII and MOEA/D in solution quality on most of the eight testing MOPs. The efficiency of the proposed Baldwinian learning strategy has also been experimentally investigated in this work.

MOEA/D with opposition-based learning for multiobjective optimization problem

Multiobjective evolutionary algorithm based on decomposition (MOEA/D) has attracted a great deal of attention and has obtained enormous success in the field of evolutionary multiobjective optimization. It converts a multiobjective optimization problem (MOP) into a set of scalar optimization subproblems and then uses the evolutionary algorithm (EA) to optimize these subproblems simultaneously. However, there is a great deal of randomness in MOEA/D. Researchers in the field of evolutionary algorithm, reinforcement learning and neural network have reported that the simultaneous consideration of randomness and opposition has an advantage over pure randomness. A new scheme, called opposition-based learning (OBL), has been proposed in the machine learning field. In this paper, OBL has been integrated into the framework of MOEA/D to accelerate its convergence speed. Hence, our proposed approach is called opposition-based learning MOEA/D (MOEA/D-OBL). Compared with MOEA/D, MOEA/D-OBL uses an opposition-based initial population and opposition-based learning strategy to generate offspring during the evolutionary process. It is compared with its parent algorithm MOEA/D on four representative kinds of MOPs and many-objective optimization problems. Experimental results indicate that MOEA/D-OBL outperforms or performs similar to MOEA/D. Moreover, the parameter sensitivity of generalization opposite point and the probable to use OBL is experimentally investigated.

MOEA/D with uniform decomposition measurement for many-objective problems

Many-objective problems (MAPs) have put forward a number of challenges to classical Pareto-dominance based multi-objective evolutionary algorithms (MOEAs) for the past few years. Recently, researchers have suggested that MOEA/D (multi-objective evolutionary algorithm based on decomposition) can work for MAPs. However, there exist two difficulties in applying MOEA/D to solve MAPs directly. One is that the number of constructed weight vectors is not arbitrary and the weight vectors are mainly distributed on the boundary of weight space for MAPs. The other is that the relationship between the optimal solution of subproblem and its weight vector is nonlinear for the Tchebycheff decomposition approach used by MOEA/D. To deal with these two difficulties, we propose an improved MOEA/D with uniform decomposition measurement and the modified Tchebycheff decomposition approach (MOEA/D-UDM) in this paper. Firstly, a novel weight vectors initialization method based on the uniform decomposition measurement is introduced to obtain uniform weight vectors in any amount, which is one of great merits to use our proposed algorithm. The modified Tchebycheff decomposition approach, instead of the Tchebycheff decomposition approach, is used in MOEA/D-UDM to alleviate the inconsistency between the weight vector of subproblem and the direction of its optimal solution in the Tchebycheff decomposition approach. The proposed MOEA/D-UDM is compared with two state-of-the-art MOEAs, namely MOEA/D and UMOEA/D on a number of MAPs. Experimental results suggest that the proposed MOEA/D-UDM outperforms or performs similarly to the other compared algorithms in terms of hypervolume and inverted generational distance metrics on different types of problems. The effects of uniform weight vector initializing method and the modified Tchebycheff decomposition are also studied separately.

A decomposition based memetic algorithm for multi-objective vehicle routing problem with time windows

Multi-objective evolutionary algorithm based on decomposition (MOEA/D) provides an excellent algorithmic framework for solving multi-objective optimization problems. It decomposes a target problem into a set of scalar sub-problems and optimizes them simultaneously. Due to its simplicity and outstanding performance, MOEA/D has been widely studied and applied. However, for solving the multi-objective vehicle routing problem with time windows (MO-VRPTW), MOEA/D faces a difficulty that many sub-problems have duplicated best solutions. It is well-known that MO-VRPTW is a challenging problem and has very few Pareto optimal solutions. To address this problem, a novel selection operator is designed in this work to enhance the original MOEA/D for dealing with MO-VRPTW. Moreover, three local search methods are introduced into the enhanced algorithm. Experimental results indicate that the proposed algorithm can obtain highly competitive results on Solomon?s benchmark problems. Especially for instances with long time windows, the proposed algorithm can obtain more diverse set of non-dominated solutions than the other algorithms. The effectiveness of the proposed selection operator is also demonstrated by further analysis. HighlightsWe develop a memetic algorithm following the framework of MOEA/D for MO-VRPTWA special selection operation is designed according to the character of MO-VRPTW.The proposed algorithm periodically employs three types of local search methods.The proposed algorithm performs well on Solomon?s problems with long time window.

An immune multi-objective optimization algorithm with differential evolution inspired recombination

Graphical abstractThis figure illustrates the two searching strategies of the proposed differential evolution inspired recombination operator: move towards the target Pareto set to improve the approximation and search along the current Pareto set to enhance the diversity. Display Omitted HighlightsA DE inspired recombination operator is developed for continuous MOPs.The proposed operator performs two complementary searching behaviors.The proposed operator can be integrated with any MOEAs. According to the regularity of continuous multi-objective optimization problems (MOPs), an immune multi-objective optimization algorithm with differential evolution inspired recombination (IMADE) is proposed in this paper. In the proposed IMADE, the novel recombination provides two types of candidate searching directions by taking three recombination parents which distribute along the current Pareto set (PS) within a local area. One of the searching direction provides guidance for finding new points along the current PS, and the other redirects the search away from the current PS and moves towards the target PS. Under the background of the SBX (Simulated binary crossover) recombination which performs local search combined with random search near the recombination parents, the new recombination operator utilizes the regularity of continuous MOPs and the distributions of current population, which helps IMADE maintain a more uniformly distributed PF and converge much faster. Experimental results have demonstrated that IMADE outperforms or performs similarly to NSGAII, NNIA, PESAII and OWMOSaDE in terms of solution quality on most of the ten testing MOPs. IMADE converges faster than NSGAII and OWMOSaDE. The efficiency of the proposed DE recombination and the contributions of DE and SBX recombination to IMADE have also been experimentally investigated in this work.

A hybrid multi-objective PSO-EDA algorithm for reservoir flood control operation

A hybrid multi-objective optimization algorithm is proposed.It combines particle swarm optimization with estimation of distribution algorithm.The algorithm is applied to solve reservoir flood control operation problem. Reservoir flood control operation (RFCO) is a complex multi-objective optimization problem (MOP) with interdependent decision variables. Traditionally, RFCO is modeled as a single optimization problem by using a certain scalar method. Few works have been done for solving multi-objective RFCO (MO-RFCO) problems. In this paper, a hybrid multi-objective optimization approach named MO-PSO-EDA which combines the particle swarm optimization (PSO) algorithm and the estimation of distribution algorithm (EDA) is developed for solving the MO-RFCO problem. MO-PSO-EDA divides the particle population into several sub-populations and builds probability models for each of them. Based on the probability model, each sub-population reproduces new offspring by using PSO based and EDA methods. In the PSO based method, a novel global best position selection method is designed. With the help of the EDA based reproduction, the algorithm can lean linkage between decision variables and hence have a good capability of solving complex multi-objective optimization problems, such as the MO-RFCO problem. Experimental studies on six benchmark problems and two typical multi-objective flood control operation problems of Ankang reservoir have indicated that the proposed MO-PSO-EDA performs as well as or superior to the other three competitive multi-objective optimization algorithms. MO-PSO-EDA is suitable for solving MO-RFCO problems.

Immune optimization algorithm for solving vertical handoff decision problem in heterogeneous wireless network

In heterogeneous wireless network environment, wireless local area network (WLAN) is usually deployed within the coverage of a cellular network to provide users with the convenience of seamless roaming among heterogeneous wireless access networks. Vertical handoffs between the WLAN and the cellular network maybe occur frequently. As for the vertical handoff performance, there is a critical requirement for developing algorithms for connection management and optimal resource allocation for seamless mobility. In this paper, we develop a mathematical model for vertical handoff decision problem, and propose a multi-objective optimization immune algorithm-based vertical handoff decision scheme. The proposed scheme can enable a wireless access network not only to balance the overall load among all base stations and access points but also maximize the collective battery lifetime of mobile terminals. Results based on a detailed performance evaluation study are also presented here to demonstrate the efficacy of the proposed scheme.

A Memetic Multi-objective Immune Algorithm for Reservoir Flood Control Operation

Reservoir flood control operation (RFCO) is a challenging optimization problem with multiple conflicting decision goals and interdependent decision variables. With the rapid development of multi-objective optimization techniques in recent years, more and more research efforts have been devoted to optimize the conflicting decision goals in RFCO problems simultaneously. However, most of these research works simply employ some existing multi-objective optimization algorithms for solving RFCO problem, few of them considers the characteristics of the RFCO problem itself. In this work, we consider the complexity of the RFCO problem in both objective space and decision space, and develop an immune inspired memetic algorithm, named M-NNIA2, to solve the multi-objective RFCO problem. In the proposed M-NNIA2, a Pareto dominance based local search operator and a differential evolution inspired local search operator are designed for the RFCO problem to guide the search towards the and along the Pareto set respectively. On the basis of inheriting the good diversity preserving in immune inspired optimization algorithm, M-NNIA2 can obtain a representative set of best trade-off scheduling plans that covers the whole Pareto front of the RFCO problem in the objective space. Experimental studies on benchmark problems and RFCO problem instances have illustrated the superiority of the proposed algorithm.