Through introducing the divide-and-conquer strategy, cooperative co-evolution (CC) has been successfully employed by many evolutionary algorithms (EAs) to solve large-scale optimization problems. In ...practice, it is common that different subcomponents of a large-scale problem have imbalanced contributions to the global fitness. Thus, how to utilize such imbalance and concentrate efforts on optimizing important subcomponents becomes an important issue for improving performance of cooperative co-EA, especially in distributed computing environment. In this paper, we propose a two-layer distributed CC (dCC) architecture with adaptive computing resource allocation for large-scale optimization. The first layer is the dCC model which takes charge of calculating the importance of subcomponents and accordingly allocating resources. An effective allocating algorithm is designed which can adaptively allocate computing resources based on a periodic contribution calculating method. The second layer is the pool model which takes charge of making fully utilization of imbalanced resource allocation. Within this layer, two different conformance policies are designed to help optimizers use the assigned computing resources efficiently. Empirical studies show that the two conformance policies and the computing resource allocation algorithm are effective, and the proposed distributed architecture possesses high scalability and efficiency.
In recent years, multiobjective immune algorithms (MOIAs) have shown promising performance in solving multiobjective optimization problems (MOPs). However, basic MOIAs only use a single hypermutation ...operation to evolve individuals, which may induce some difficulties in tackling complicated MOPs. In this paper, we propose a novel hybrid evolutionary framework for MOIAs, in which the cloned individuals are divided into several subpopulations and then evolved using different evolutionary strategies. An example of this hybrid framework is implemented, in which simulated binary crossover and differential evolution with polynomial mutation are adopted. A fine-grained selection mechanism and a novel elitism sharing strategy are also adopted for performance enhancement. Various comparative experiments are conducted on 28 test MOPs and our empirical results validate the effectiveness and competitiveness of our proposed algorithm in solving MOPs of different types.
This paper proposes a novel bi-velocity discrete particle swarm optimization (BVDPSO) approach and extends its application to the nondeterministic polynomial (NP) complete multicast routing problem ...(MRP). The main contribution is the extension of particle swarm optimization (PSO) from the continuous domain to the binary or discrete domain. First, a novel bi-velocity strategy is developed to represent the possibilities of each dimension being 1 and 0. This strategy is suitable to describe the binary characteristic of the MRP, where 1 stands for a node being selected to construct the multicast tree, whereas 0 stands for being otherwise. Second, BVDPSO updates the velocity and position according to the learning mechanism of the original PSO in the continuous domain. This maintains the fast convergence speed and global search ability of the original PSO. Experiments are comprehensively conducted on all of the 58 instances with small, medium, and large scales in the Operation Research Library (OR-library). The results confirm that BVDPSO can obtain optimal or near-optimal solutions rapidly since it only needs to generate a few multicast trees. BVDPSO outperforms not only several state-of-the-art and recent heuristic algorithms for the MRP problems, but also algorithms based on genetic algorithms, ant colony optimization, and PSO.
Large-scale optimization has become a significant yet challenging area in evolutionary computation. To solve this problem, this paper proposes a novel segment-based predominant learning swarm ...optimizer (SPLSO) swarm optimizer through letting several predominant particles guide the learning of a particle. First, a segment-based learning strategy is proposed to randomly divide the whole dimensions into segments. During update, variables in different segments are evolved by learning from different exemplars while the ones in the same segment are evolved by the same exemplar. Second, to accelerate search speed and enhance search diversity, a predominant learning strategy is also proposed, which lets several predominant particles guide the update of a particle with each predominant particle responsible for one segment of dimensions. By combining these two learning strategies together, SPLSO evolves all dimensions simultaneously and possesses competitive exploration and exploitation abilities. Extensive experiments are conducted on two large-scale benchmark function sets to investigate the influence of each algorithmic component and comparisons with several state-of-the-art meta-heuristic algorithms dealing with large-scale problems demonstrate the competitive efficiency and effectiveness of the proposed optimizer. Further the scalability of the optimizer to solve problems with dimensionality up to 2000 is also verified.
Taking the advantage of estimation of distribution algorithms (EDAs) in preserving high diversity, this paper proposes a multimodal EDA. Integrated with clustering strategies for crowding and ...speciation, two versions of this algorithm are developed, which operate at the niche level. Then these two algorithms are equipped with three distinctive techniques: 1) a dynamic cluster sizing strategy; 2) an alternative utilization of Gaussian and Cauchy distributions to generate offspring; and 3) an adaptive local search. The dynamic cluster sizing affords a potential balance between exploration and exploitation and reduces the sensitivity to the cluster size in the niching methods. Taking advantages of Gaussian and Cauchy distributions, we generate the offspring at the niche level through alternatively using these two distributions. Such utilization can also potentially offer a balance between exploration and exploitation. Further, solution accuracy is enhanced through a new local search scheme probabilistically conducted around seeds of niches with probabilities determined self-adaptively according to fitness values of these seeds. Extensive experiments conducted on 20 benchmark multimodal problems confirm that both algorithms can achieve competitive performance compared with several state-of-the-art multimodal algorithms, which is supported by nonparametric tests. Especially, the proposed algorithms are very promising for complex problems with many local optima.
Particle swarm optimization (PSO) is predominately used to find solutions for continuous optimization problems. As the operators of PSO are originally designed in an n -dimensional continuous space, ...the advancement of using PSO to find solutions in a discrete space is at a slow pace. In this paper, a novel set-based PSO (S-PSO) method for the solutions of some combinatorial optimization problems (COPs) in discrete space is presented. The proposed S-PSO features the following characteristics. First, it is based on using a set-based representation scheme that enables S-PSO to characterize the discrete search space of COPs. Second, the candidate solution and velocity are defined as a crisp set, and a set with possibilities, respectively. All arithmetic operators in the velocity and position updating rules used in the original PSO are replaced by the operators and procedures defined on crisp sets, and sets with possibilities in S-PSO. The S-PSO method can thus follow a similar structure to the original PSO for searching in a discrete space. Based on the proposed S-PSO method, most of the existing PSO variants, such as the global version PSO, the local version PSO with different topologies, and the comprehensive learning PSO (CLPSO), can be extended to their corresponding discrete versions. These discrete PSO versions based on S-PSO are tested on two famous COPs: the traveling salesman problem and the multidimensional knapsack problem. Experimental results show that the discrete version of the CLPSO algorithm based on S-PSO is promising.
This paper studies a specific class of multiobjective combinatorial optimization problems (MOCOPs), namely the permutation-based MOCOPs. Many commonly seen MOCOPs, e.g., multiobjective traveling ...salesman problem (MOTSP), multiobjective project scheduling problem (MOPSP), belong to this problem class and they can be very different. However, as the permutation-based MOCOPs share the inherent similarity that the structure of their search space is usually in the shape of a permutation tree, this paper proposes a generic multiobjective set-based particle swarm optimization methodology based on decomposition, termed MS-PSO/D. In order to coordinate with the property of permutation-based MOCOPs, MS-PSO/D utilizes an element-based representation and a constructive approach. Through this, feasible solutions under constraints can be generated step by step following the permutation-tree-shaped structure. And problem-related heuristic information is introduced in the constructive approach for efficiency. In order to address the multiobjective optimization issues, the decomposition strategy is employed, in which the problem is converted into multiple single-objective subproblems according to a set of weight vectors. Besides, a flexible mechanism for diversity control is provided in MS-PSO/D. Extensive experiments have been conducted to study MS-PSO/D on two permutation-based MOCOPs, namely the MOTSP and the MOPSP. Experimental results validate that the proposed methodology is promising.
Traffic Signal Control (TSC) is a fundamental task in modern intelligent transport systems. TSC is often formulated as a bi‐level optimization problem, comprised by the signal timing at the upper ...level and the Dynamic User Equilibrium (DUE) traffic assignment at the lower level. Since DUE is non‐convex, existing methods either formulate approximation models or adopt traffic simulators. However, approximation models may oversimplify the practical situations, while traffic simulators are usually time‐consuming. This paper formulates a vehicle‐based DUE (vDUE) model and proposes an agile method that can simultaneously maintain the computational simplicity and the traffic dynamics for the traffic assignment. Further, an agile TSC system is built by combining the vDUE at the lower level for the traffic assignment with an adaptive differential evolution algorithm at the upper level for the signal timing optimization. To enhance the effectiveness of optimization, the TSC problem formulation is also improved to make it better characterize the practical requirements. In the experiments undertaken, comparisons of different TSC methods are carried out on both real‐world and synthetic transportation networks. The experimental results validate the effectiveness of the proposed agile TSC system in various traffic situations.
The performance of differential evolution (DE) largely depends on its mutation strategy and control parameters. In this paper, we propose an adaptive DE (ADE) algorithm with a new mutation strategy ...DE/lbest/1 and a two-level adaptive parameter control scheme. The DE/lbest/1 strategy is a variant of the greedy DE/best/1 strategy. However, the population is mutated under the guide of multiple locally best individuals in DE/lbest/1 instead of one globally best individual in DE/best/1. This strategy is beneficial to the balance between fast convergence and population diversity. The two-level adaptive parameter control scheme is implemented mainly in two steps. In the first step, the population-level parameters F p and CR p for the whole population are adaptively controlled according to the optimization states, namely, the exploration state and the exploitation state in each generation. These optimization states are estimated by measuring the population distribution. Then, the individual-level parameters F i and CR i for each individual are generated by adjusting the population-level parameters. The adjustment is based on considering the individual's fitness value and its distance from the globally best individual. This way, the parameters can be adapted to not only the overall state of the population but also the characteristics of different individuals. The performance of the proposed ADE is evaluated on a suite of benchmark functions. Experimental results show that ADE generally outperforms four state-of-the-art DE variants on different kinds of optimization problems. The effects of ADE components, parameter properties of ADE, search behavior of ADE, and parameter sensitivity of ADE are also studied. Finally, we investigate the capability of ADE for solving three real-world optimization problems.
The covariance matrix adaptation evolution strategy (CMA-ES) is a powerful evolutionary algorithm for single-objective real-valued optimization. However, the time and space complexity may preclude ...its use in high-dimensional decision space. Recent studies suggest that putting sparse or low-rank constraints on the structure of the covariance matrix can improve the efficiency of CMA-ES in handling large-scale problems. Following this idea, this paper proposes a search direction adaptation evolution strategy (SDA-ES) which achieves linear time and space complexity. SDA-ES models the covariance matrix with an identity matrix and multiple search directions, and uses a heuristic to update the search directions in a way similar to the principal component analysis. We also generalize the traditional 1/5th success rule to adapt the mutation strength which exhibits the derandomization property. Numerical comparisons with nine state-of-the-art algorithms are carried out on 31 test problems. The experimental results have shown that SDA-ES is invariant under search-space rotational transformations, and is scalable with respect to the number of variables. It also achieves competitive performance on generic black-box problems, demonstrating its effectiveness in keeping a good tradeoff between solution quality and computational efficiency.
PDF
