MOEA/D with Adaptative Number of Weight Vectors

A decomposition-based many-objective evolutionary algorithm updating weights when required

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

A triple‐objective optimal design method for AC filters in high voltage direct current (HVDC) system based on an improved multi‐objective evolutionary algorithm based on decomposition (MOEA/D) is proposed. A triple‐objective optimisation mathematical model including total harmonic distortion (THD) on AC side voltage, investment cost of AC filters and telephone harmonic form factor (THFF) is established. An improved MOEA/D is proposed to realise the triple‐objective optimal design for AC filters more efficiently. The improved MOEA/D adds a particular mutation operator, which can not only to prevent MOEA/D from getting stuck at local optimum but also accelerate the convergence to the optimum solution while the algorithm approaches the neighbourhood of the optimum solution. A three‐dimensional fuzzy evaluation system is designed to select the optimum solution of the triple‐objective optimisation. A case of ±500 kV HVDC system is simulated. Taking the ±500 kV HVDC system as the prototype system, a dynamic simulation experimental platform of the rectification system of the direct current transmission system with AC filters is designed and established based on the similarity principle. Both the simulation and experimental results verify that the proposed method have excellent performance.

Multi-Objective Evolutionary Algorithm based on decomposition (MOEA/D) has been proposed for a decade in solving complex multi-objective problems (MOP) by decomposing it into a set of single-objective problems. MOEA/D-AGR is one of the improved algorithm introduced recently to substitute the original replacement scheme in MOEA/D with a new adaptive global replacement (GR) scheme so that the neighborhood replacement size Tr is increased among the generation to achieve the shifting of focus from solution diversity to convergence. However, the new replacement scheme only considers the one-way convergence of the objective solutions among all sub-problems. It is hard to re-achieve the solution diversity once the algorithm reaches another steeper landscape of solution from a flatten one while it is focusing on convergence. This paper proposes a new adaptive GR scheme to prolong the period of Tr increment so that it can fit the re-increment of fitness landscape. To compensate the shorten period for solution convergence, local searching is adapted for those individuals which has stopped improving its solution value by Simulated Annealing (SA) algorithm. In order to suppress the degree of local searching at the early stage of focusing solution diversity, Fuzzy Logic is used here to coordinate the frequency of local searching according to the average change of objective solution values. To demonstrate the performance of the proposed algorithm, several common benchmark MOPs are used in this paper for comparing with the several state-of-the-art MOEA/D algorithms in terms of IGD. The performance investigation found that the performance of the proposed algorithm was generally better than the other compared algorithms.

An adaptive penalty-based boundary intersection method for many-objective optimization problem

This paper investigates the multi-objective uncertain multi-stage weapon target assignment (UMWTA) problem in which weapons' kill probabilities are considered to be uncertain from practical aspects. Here uncertainties are introduced by assuming that these probabilities depend on random parameters which are impacted by various factors. The multi-objective formulation of UMWTA problems covers the objectives of minimizing the risk of missing hostile targets measured by the conditional value-at-risk (CVaR) measure and minimizing the ammunition consumption. With the aim of determining referenced Pareto fronts, an approximated linear formulation of the UMWTA problem is put forward based on problem-specific characteristics. Two state-of-the-art decomposition-based multi-objective evolutionary algorithms (DMOEAs), i.e., MOEA/D-AWA and DMOEA -ɛC are used to solve the formulated problem. In view of the inefficiency of the standard comparison mechanism in DMOEAs, a hierarchical comparison strategy which takes into account Pareto dominance relationships and aggregated objective values simultaneously is proposed and embedded in MOEA/D-AWA and DMOEA-ɛC. MOEA/D-AWA and DMOEA-ɛC with the hierarchical comparison strategy are denoted as MOEA/D-AWA-H and DMOEA-ɛC-H, respectively. Numerical experiments have been performed on two sets of UMWTA instances. Experimental results confirm the effectiveness of the proposed hierarchical comparison strategy and demonstrate the superiority of DMOEA-ɛC-H over MOEA/D-AWA-H on the majority of test instances.

Multi-objective evolutionary algorithm based on decomposition (MOEA/D) uses crossover operator which often either breaks the building blocks or mix them ineffectively. Multi-objective estimation of distribution algorithm based on decomposition (MEDA/D) evolves a probability vector for each sub-problem to guide the search instead of using crossover operator.However, since the number of the weight vectors in the neighborhood of each weight vector is relatively small and MEDA/D does not provide a way to maintain diversity, the performance of MEDA/D is limited. To overcome the drawbacks of MEDA/D, we proposed a new reproduction operator. This operator could promote diversity. We introduced it into MOEA/D framework and the new algorithm is called s-MEDA/D. We also prove that the parameter newly introduced has physical significance and the reproduction operator is not susceptible to the scale of the problem. The s-MEDA/D was tested on nine instances of the 0/1 multi-objective knapsack problem. Empirical evaluation suggests that the proposed algorithm is effective and efficient.

Research on multiobjective optimization problems becomes one of the hottest topics of intelligent computation. In order to improve the search efficiency of an evolutionary algorithm and maintain the diversity of solutions, in this paper, the learning automata (LA) is first used for quantization orthogonal crossover (QOX), and a new fitness function based on decomposition is proposed to achieve these two purposes. Based on these, an orthogonal evolutionary algorithm with LA for complex multiobjective optimization problems with continuous variables is proposed. The experimental results show that in continuous states, the proposed algorithm is able to achieve accurate Pareto-optimal sets and wide Pareto-optimal fronts efficiently. Moreover, the comparison with the several existing well-known algorithms: nondominated sorting genetic algorithm II, decomposition-based multiobjective evolutionary algorithm, decomposition-based multiobjective evolutionary algorithm with an ensemble of neighborhood sizes, multiobjective optimization by LA, and multiobjective immune algorithm with nondominated neighbor-based selection, on 15 multiobjective benchmark problems, shows that the proposed algorithm is able to find more accurate and evenly distributed Pareto-optimal fronts than the compared ones.

Meta-Lamarckian learning in multi-objective optimization for mobile social network search

In this paper, we systematically study the influence of the main design elements of scalarizing function-based multiobjective evolutionary algorithms (MOEAs) on the performance of these algorithms. Such algorithms proved to be very successful in multiple computational experiments and practical applications. Well-known examples of this class of MOEAs are Jaszkiewicz’s multiobjecitve genetic local search and multiobjective evolutionary algorithm based on decomposition (MOEA/D). The two algorithms share the same common structure and differ in two aspects, i.e., the selection of parents for recombination and the selection of weight vectors of scalarizing functions. Using three different multiobjective combinatorial optimization problems, i.e., the multiobjective symmetric traveling salesperson problem, the traveling salesperson problem with profits, and the multiobjective set covering problem, we show that the design element with the highest influence on the performance is the choice of a mechanism for parents selection, while the selection of weight vectors, either random or evenly distributed, has practically negligible influence if the number of evenly distributed weight vectors is sufficiently large.

It is an interesting and important issue to identify a small set of useful features from a high dimensional data that can be used to design a classification mechanism. Usually, researchers prefer to find the features that have high relevance, in the sense that the correlation of each of those features with class labels is high or the mutual information between each of the features and class labels is high. Such approaches usually end up finding features that may be linearly dependent with each other. For some biological studies, it may be interesting to find a set of genes (features), which have high relevance with the class labels and also the genes are nonlinearly dependent –we explicitly want to exclude relevant genes that are linearly correlated among them. Although, our primary focus in this study is to find such genes from microarray data sets, such features may also be important in other studies. In this study, the Combinations of Relevantly Non-linear Dependency Subsets (CoRNDS) is proposed to tackle such the multi-objective problem. It opens up a good to simultaneously control selection of number of useful features, optimize the relevance between the selected features with class labels, and the non-linear dependency between the selected features. Using innovative ways we design three new objectives and optimize them by using the well-known multi-objective evolutionary algorithm based on decomposition (MOEA/D) method. To the best of our knowledge, this is the first attempt to feature (gene) selection along with identification of non-linear dependency between features via a multi-objective strategy. Experimental results show that the feasibility and effective performance on microarray cancer dataset. As to these selected gene subsets, investigate their auxiliary role of co-regulation in the biological pathways, and the occurrence in the pathogenesis of cancer are interesting future works.

Evolutionary Optimization based Solution approaches for Many Objective Reliability-Redundancy Allocation Problem

In this paper, we propose a method for solving a real‐world timetabling problem at Mandarine Academy. The primary motivation for this work is to provide an automated professional course scheduling tool to replace the time‐consuming task of manually creating timetables that are constantly incorrect. Following a review of both scientific literature and company requirements, a mathematical model of the problem is provided, which includes 18 constraints (hard/soft) and five objectives, two of which are competing. We test a handful of multi‐objective evolutionary algorithms (MOEA's) starting with the non‐dominated sorting genetic algorithm (NSGA II and NSGA III), the multi‐objective evolutionary algorithm based on decomposition (MOEA/D), the indicator‐based evolutionary algorithm and finally the strength Pareto evolutionary algorithm . Two custom genetic operators (mutation and crossover) are proposed and compared to conventional operators (PMX and swap mutation). To obtain elite configurations, a tuning phase involving all of the aforementioned algorithms is carried out. Experiments were divided by problem size, with three to five objectives tested. Experiments include the use of real‐world data from the company's catalog. This dataset was made available to the scientific community to serve as a testing ground for professional course scheduling, an underexploited field of scheduling. We discuss findings, including a comparison of each algorithm's performance using various metrics, as well as convergence graphs and population evolution.

Multi-objective capacity optimization of a hybrid energy system in two-stage stochastic programming framework

Pareto and decomposition based approaches for the multi-objective home health care routing and scheduling problem with lunch breaks