LCS & GBML Central

In this paper, we investigate movement patterns of a particle in the particle swarm optimization (PSO) algorithm. We characterize movement patterns of the particle by two factors: 1) the correlation between its consecutive positions and 2) its range of movement. We introduce the base frequency of movement as a measure for the correlation between positions and the variance of movement as a measure for the range of movement. We determine the base frequency and the variance of movement theoretically and we show how they change with the values of coefficients. We extract a system of equations that enables practitioners to find coefficients’ values to guarantee achieving a given base frequency and variance of movement, i.e., control the movement pattern of particles. We also show that if the base frequency of movement for a particle is small, mid range, or large then the particle’s position at each iteration is positively correlated (smooth movement), uncorrelated (chaotic movement), or negatively correlated (jumping at each iteration) with its previous positions, respectively. We test the effects of the base frequency and variance of movement on the search ability of particles and we show that small base frequencies (i.e., smooth movement) are more effective when the maximum number of function evaluations is large. We found that the most frequently-used coefficient values in PSO literature impose mid-range base frequencies that correspond with a chaotic movement. We also provide new sets of coefficients that outperform existing ones on a set of benchmark functions.

This paper aims to study how the population size affects the computation time of evolutionary algorithms (EAs) in a rigorous way. The computation time of EAs can be measured by either the number of generations (hitting time) or the number of fitness evaluations (running time) to find an optimal solution. Population scalability is the ratio of the expected hitting time between a benchmark algorithm and an algorithm using a larger population size. Average drift analysis is introduced to compare the expected hitting time of two algorithms and to estimate lower and upper bounds on the population scalability. Several intuitive beliefs are rigorously analyzed. It is proven that: 1) using a population sometimes increases rather than decreases the expected hitting time; 2) using a population cannot shorten the expected running time of any elitist EA on any unimodal function on the time-fitness landscape, however, this statement is not true in terms of the distance-based fitness landscape; and 3) using a population cannot always reduce the expected running time on deceptive functions, which depends on whether the benchmark algorithm uses elitist selection or random selection.

Detecting community structure has become one important technique for studying complex networks. Although many community detection algorithms have been proposed, most of them focus on separated communities, where each node can belong to only one community. However, in many real-world networks, communities are often overlapped with each other. Developing overlapping community detection algorithms thus becomes necessary. Along this avenue, this paper proposes a maximal clique based multiobjective evolutionary algorithm (MOEA) for overlapping community detection. In this algorithm, a new representation scheme based on the introduced maximal-clique graph is presented. Since the maximal-clique graph is defined by using a set of maximal cliques of original graph as nodes and two maximal cliques are allowed to share the same nodes of the original graph, overlap is an intrinsic property of the maximal-clique graph. Attributing to this property, the new representation scheme allows MOEAs to handle the overlapping community detection problem in a way similar to that of the separated community detection, such that the optimization problems are simplified. As a result, the proposed algorithm could detect overlapping community structure with higher partition accuracy and lower computational cost when compared with the existing ones. The experiments on both synthetic and real-world networks validate the effectiveness and efficiency of the proposed algorithm.

Niching techniques have recently been incorporated into evolutionary algorithms (EAs) for multisolution optimization in multimodal landscape. However, existing niching techniques inevitably increase the time complexity of basic EAs due to the computation of the distance matrix of individuals. In this paper, we propose a fast niching technique. The technique avoids pairwise distance calculations by introducing the locality sensitive hashing, an efficient algorithm for approximately retrieving nearest neighbors. Individuals are projected to a number of buckets by hash functions. The similar individuals possess a higher probability of being hashed into the same bucket than the dissimilar ones. Then, interactions between individuals are limited to the candidates that fall in the same bucket to achieve local evolution. It is proved that the complexity of the proposed fast niching is linear to the population size. In addition, this mechanism induces stable niching behavior and it inherently keeps a balance between the exploration and exploitation of multiple optima. The theoretical analysis conducted in this paper suggests that the proposed technique is able to provide bounds for the exploration and exploitation probabilities. Experimental results show that the fast niching versions of the multimodal algorithms can exhibit similar or even better performance than their original ones. More importantly, the execution time of the algorithms is significantly reduced.

Decomposition is a well-known strategy in traditional multiobjective optimization. However, the decomposition strategy was not widely employed in evolutionary multiobjective optimization until Zhang and Li proposed multiobjective evolutionary algorithm based on decomposition (MOEA/D) in 2007. MOEA/D proposed by Zhang and Li decomposes a multiobjective optimization problem into a number of scalar optimization subproblems and optimizes them in a collaborative manner using an evolutionary algorithm (EA). Each subproblem is optimized by utilizing the information mainly from its several neighboring subproblems. Since the proposition of MOEA/D in 2007, decomposition-based MOEAs have attracted significant attention from the researchers. Investigations have been undertaken in several directions, including development of novel weight vector generation methods, use of new decomposition approaches, efficient allocation of computational resources, modifications in the reproduction operation, mating selection and replacement mechanism, hybridizing decomposition- and dominance-based approaches, etc. Furthermore, several attempts have been made at extending the decomposition-based framework to constrained multiobjective optimization, many-objective optimization, and incorporate the preference of decision makers. Additionally, there have been many attempts at application of decomposition-based MOEAs to solve complex real-world optimization problems. This paper presents a comprehensive survey of the decomposition-based MOEAs proposed in the last decade.

While Pareto-based multiobjective optimization algorithms continue to show effectiveness for a wide range of practical problems that involve mostly two or three objectives, their limited application for many-objective problems, due to the increasing proportion of nondominated solutions and the lack of sufficient selection pressure, has also been gradually recognized. In this paper, we revive an early developed and computationally expensive strength Pareto-based evolutionary algorithm by introducing an efficient reference direction-based density estimator, a new fitness assignment scheme, and a new environmental selection strategy, for handling both multiobjective and many-objective problems. The performance of the proposed algorithm is validated and compared with some state-of-the-art algorithms on a number of test problems. Experimental studies demonstrate that the proposed method shows very competitive performance on both multiobjective and many-objective problems considered in this paper. Besides, our extensive investigations and discussions reveal an interesting finding, that is, diversity-first-and-convergence-second selection strategies may have great potential to deal with many-objective optimization.

Practical optimization problems frequently include uncertainty about the quality measure, for example, due to noisy evaluations. Thus, they do not allow for a straightforward application of traditional optimization techniques. In these settings, randomized search heuristics such as evolutionary algorithms are a popular choice because they are often assumed to exhibit some kind of resistance to noise. Empirical evidence suggests that some algorithms, such as estimation of distribution algorithms (EDAs) are robust against a scaling of the noise intensity, even without resorting to explicit noise-handling techniques such as resampling. In this paper, we want to support such claims with mathematical rigor. We introduce the concept of graceful scaling in which the run time of an algorithm scales polynomially with noise intensity. We study a monotone fitness function over binary strings with additive noise taken from a Gaussian distribution. We show that myopic heuristics cannot efficiently optimize the function under arbitrarily intense noise without any explicit noise-handling. Furthermore, we prove that using a population does not help. Finally, we show that a simple EDA called the compact genetic algorithm can overcome the shortsightedness of mutation-only heuristics to scale gracefully with noise. We conjecture that recombinative genetic algorithms also have this property.