A Fuzzy Decomposition-Based Multi/Many-Objective Evolutionary Algorithm.

Performance of multi/many-objective evolutionary algorithms (MOEAs) based on decomposition is highly impacted by the Pareto front (PF) shapes of multi/many-objective optimization problems (MOPs), as their adopted weight vectors may not properly fit the PF shapes. To avoid this mismatch, some MOEAs treat solutions as weight vectors to guide the evolutionary search, which can adapt to the target MOP's PF automatically. However, their performance is still affected by the similarity metric used to select weight vectors. To address this issue, this article proposes a fuzzy decomposition-based MOEA. First, a fuzzy prediction is designed to estimate the population's shape, which helps to exactly reflect the similarities of solutions. Then, N least similar solutions are extracted as weight vectors to obtain N constrained fuzzy subproblems ( N is the population size), and accordingly, a shared weight vector is calculated for all subproblems to provide a stable search direction. Finally, the corner solution for each of m least similar subproblems ( m is the objective number) is preserved to maintain diversity, while one solution having the best aggregated value on the shared weight vector is selected for each of the remaining subproblems to speed up convergence. When compared to several competitive MOEAs in solving a variety of test MOPs, the proposed algorithm shows some advantages at fitting their different PF shapes.

A Self-Guided Reference Vector Strategy for Many-Objective Optimization.

Generally, decomposition-based evolutionary algorithms in many-objective optimization (MaOEA/Ds) have widely used reference vectors (RVs) to provide search directions and maintain diversity. However, their performance is highly affected by the matching degree on the shapes of the RVs and the Pareto front (PF). To address this problem, this article proposes a self-guided RV (SRV) strategy for MaOEA/Ds, aiming to extract RVs from the population using a modified k -means clustering method. To give a promising clustering result, an angle-based density measurement strategy is used to initialize the centroids, which are then adjusted to obtain the final clusters, aiming to properly reflect the population's distribution. Afterward, these centroids are extracted to obtain adaptive RVs for self-guiding the search process. To verify the effectiveness of this SRV strategy, it is embedded into three well-known MaOEA/Ds that originally use the fixed RVs. Moreover, a new strategy of embedding SRV into MaOEA/Ds is discussed when the RVs are adjusted at each generation. The simulation results validate the superiority of our SRV strategy, when tackling numerous many-objective optimization problems with regular and irregular PFs.

An Elite Gene Guided Reproduction Operator for Many-Objective Optimization.

Traditional reproduction operators in many-objective evolutionary algorithms (MaOEAs) seem to not be so effective to tackle many-objective optimization problems (MaOPs). This is mainly because the population size cannot be set to an arbitrarily large value if the computational efficiency is of concern. In such a case, the distance between the parents becomes remarkably large and, consequently, it is not easy to reproduce a superior offspring in high-dimensional objective space. To alleviate this problem, an elite gene-guided (EGG) reproduction operator is proposed to tackle MaOPs in this article. In this operator, an elite gene pool is built by collecting the knee points from the current population. Then, the offspring is produced by exchanging the genes with this elite gene pool under an exchange rate, aiming to reserve more promising genes into the next generation. In order to provide new genes for the population, other genes will be disturbed under a disturbance rate. The settings and functional analysis of the exchange rate and disturbance rate are studied using several experiments. The proposed EGG operator is easy to implement and can be embedded to any MaOEA. As examples, we show the embedding of the proposed EGG operator into four competitive MaOEAs, that is, MOEA/D, NSGA-III, θ -DEA, and SPEA2-SDE provide some advantages over simulated binary crossover, differential evolution, and an evolutionary path-based reproduction operator on solving a number of benchmark problems with 3 to 15 objectives.

Cost-Aware Robust Control of Signed Networks by Using a Memetic Algorithm.

The robust controllability (RC) of a complex system tries to select a set of dominating entities for the functional control of this entire system without uncertain disturbances, and the research on RC will help to understand the system's underlying functions. In this article, we introduce the control cost in signed networks and present a cost-aware robust control (CRC) problem in this scenario. The aim of CRC is to minimize the cost to control a set of dominating nodes and transform a set of unbalanced links into balanced ones, such that the signed network can be robustly controlled without uncertain unbalanced factors (like nodes and links). To solve this problem, we first model CRC as a constrained combination optimization problem, and then present a memetic algorithm with some problem-specific knowledge (like the neighbors of nodes, the constraints of CRC, and the fast computation of the cost under each optimization) to solve this problem on signed networks. The extensive experiments on both real social and biological networks assess that our algorithm outperforms several state-of-the-art RC algorithms.

Fuzzy Rule-Based Design of Evolutionary Algorithm for Optimization.

During the last two decades, many multioperator- and multimethod-based evolutionary algorithms for solving optimization problems have been proposed. Although, in general terms, they outperform single-operator-based traditional ones, they do not perform consistently for all the problems tested in the literature. The designs of such algorithms usually follow a trial and error approach that can be improved by using a rule-based approach. In this paper, we propose a new way for two algorithms to cooperate as an effective team, in which a heuristic is applied using fuzzy rules of two complementary characteristics, the quality of solutions and diversity in the population. In this process, two subpopulations are used, one for each algorithm, with greater emphasis placed on the better-performing one. Inferior algorithms learn from trusted ones and a fine-tuning procedure is applied in the later stages of the evolutionary process. The proposed algorithm was analyzed on the CEC2014 unconstrained problems and then tested on other three sets (CEC2013, CEC2005, and 12 classical problems), with its results showing a high success rate and that it outperformed both single-operator-based and different state-of-the-art algorithms.

Reliable Link Inference for Network Data With Community Structures.

Complex systems are often characterized by complex networks with links and entities. However, in many complex systems such as protein-protein interaction networks, recommender systems, and online communities, their links are hard to reveal directly, but they can be inaccurately observed by multiple data collection platforms or by a data collection platform at different times. Then, the links of the systems are inferred by the integration of the collected observations. As those data collection platforms are usually distributed over a large area and in different fields, their observations are unreliable and sensitive to the potential structures of the systems. In this paper, we consider the link inference problem in network data with community structures, in which the reliability of data collection platforms is unknown a priori and the link errors and reliability of platforms' observations are heterogeneous to the underlying community structures of the systems. We propose an expectation maximization algorithm for link inference in a network system with community structures (EMLIC). The EMLIC algorithm is also used to infer the link errors and reliability of platforms' observations in different communities. Experimental results on both synthetic data and eight real-world network data demonstrate that our algorithm is able to achieve lower link errors than the existing reliable link inference algorithms when the network data have community structures.

A Diversity-Enhanced Resource Allocation Strategy for Decomposition-Based Multiobjective Evolutionary Algorithm.

The multiobjective evolutionary algorithm (MOEA) based on decomposition transforms a multiobjective optimization problem into a set of aggregated subproblems and then optimizes them collaboratively. Since these subproblems usually have different degrees of difficulty, resource allocation (RA) strategies have been reported to enhance performance, attempting to dynamically assign proper amounts of computational resources for the solution of each of these subproblems. However, existing schemes for decomposition-based MOEAs fully rely on the relative improvement of the aggregated functions to do this. This paper proposes a diversity-enhanced RA strategy for this kind of MOEA, depending on both relative improvement on aggregated function value and solution density around each subproblem to assign computational resources. Thus, one subproblem surrounded with fewer solutions in its neighboring area and more relative improvement on the aggregated function value will be allocated a higher probability for evolution. Our experimental results show the advantages of our proposed strategy over two popular RA strategies available for decomposition-based MOEAs, on tackling a set of complicated benchmark problems.

An External Archive-Guided Multiobjective Particle Swarm Optimization Algorithm.

The selection of swarm leaders (i.e., the personal best and global best), is important in the design of a multiobjective particle swarm optimization (MOPSO) algorithm. Such leaders are expected to effectively guide the swarm to approach the true Pareto optimal front. In this paper, we present a novel external archive-guided MOPSO algorithm (AgMOPSO), where the leaders for velocity update are all selected from the external archive. In our algorithm, multiobjective optimization problems (MOPs) are transformed into a set of subproblems using a decomposition approach, and then each particle is assigned accordingly to optimize each subproblem. A novel archive-guided velocity update method is designed to guide the swarm for exploration, and the external archive is also evolved using an immune-based evolutionary strategy. These proposed approaches speed up the convergence of AgMOPSO. The experimental results fully demonstrate the superiority of our proposed AgMOPSO in solving most of the test problems adopted, in terms of two commonly used performance measures. Moreover, the effectiveness of our proposed archive-guided velocity update method and immune-based evolutionary strategy is also experimentally validated on more than 30 test MOPs.

Sequence-Based Deterministic Initialization for Evolutionary Algorithms.

It is well known that the performances of evolutionary algorithms are influenced by the quality of their initial populations. Over the years, many different techniques for generating an initial population by uniformly covering as much of the search space as possible have been proposed. However, none of these approaches considers any input from the function that must be evolved using that population. In this paper, a new initialization technique, which can be considered a heuristic space-filling approach, based on both function to be optimized and search space, is proposed. It was tested on two well-known unconstrained sets of benchmark problems using several computational intelligence algorithms. The results obtained reflected its benefits as the performances of all these algorithms were significantly improved compared with those of the same algorithms with currently available initialization techniques. The new technique also proved its capability to provide useful information about the function's behavior and, for some test problems, the initial population produced high-quality solutions. This method was also tested on a few multiobjective problems, with the results demonstrating its benefits.

A Novel Diversity-Based Replacement Strategy for Evolutionary Algorithms.

Premature convergence is one of the best-known drawbacks that affects the performance of evolutionary algorithms. An alternative for dealing with this problem is to explicitly try to maintain proper diversity. In this paper, a new replacement strategy that preserves useful diversity is presented. The novelty of our method is that it combines the idea of transforming a single-objective problem into a multiobjective one, by considering diversity as an explicit objective, with the idea of adapting the balance induced between exploration and exploitation to the various optimization stages. Specifically, in the initial phases, larger amounts of diversity are accepted. The diversity measure considered in this paper is based on calculating distances to the closest surviving individual. Analyses with a multimodal function better justify the design decisions and provide greater insight into the working operation of the proposal. Computational results with a packing problem that was proposed in a popular contest illustrate the usefulness of the proposal. The new method significantly improves on the best results known to date for this problem and compares favorably against a large number of state-of-the-art schemes.

Pareto-adaptive epsilon-dominance.

Efficiency has become one of the main concerns in evolutionary multiobjective optimization during recent years. One of the possible alternatives to achieve a faster convergence is to use a relaxed form of Pareto dominance that allows us to regulate the granularity of the approximation of the Pareto front that we wish to achieve. One such relaxed forms of Pareto dominance that has become popular in the last few years is epsilon-dominance, which has been mainly used as an archiving strategy in some multiobjective evolutionary algorithms. Despite its advantages, epsilon-dominance has some limitations. In this paper, we propose a mechanism that can be seen as a variant of epsilon-dominance, which we call Pareto-adaptive epsilon-dominance (paepsilon-dominance). Our proposed approach tries to overcome the main limitation of epsilon-dominance: the loss of several nondominated solutions from the hypergrid adopted in the archive because of the way in which solutions are selected within each box.