Moving Peak Benchmark Research Articles

Static and Dynamic Multimodal Optimization by Improved Covariance Matrix Self-Adaptation Evolution Strategy With Repelling Subpopulations

The covariance matrix self-adaptation evolution strategy with repelling subpopulations (RS-CMSA-ES) is one of the most successful multimodal optimization (MMO) methods currently available. However, some of its components may become inefficient in certain situations. This study introduces the second variant of this method, called RS-CMSA-ESII. It improves the adaptation schemes for the normalized taboo distances of the archived solutions and the covariance matrix of the subpopulation, the termination criteria for the subpopulations, and the way in which the infeasible solutions are treated. It also improves the time complexity of RS-CMSA-ES by updating the initialization procedure of a subpopulation and developing a more accurate metric for determining critical taboo regions. The effects of these modifications are illustrated by designing controlled numerical simulations. RS-CMSA-ESII is then compared with the most successful and recent niching methods for MMO on a widely adopted test suite. The results obtained reveal the superiority of RS-CMSA-ESII over these methods, including the winners of the competition on niching methods for MMO in previous years. Besides, this study extends RS-CMSA-ESII to dynamic MMO and compares it with a few recently proposed methods on the modified moving peak benchmark functions.

Moving peak drone search problem: An online multi-swarm intelligence approach for UAV search operations

Many practical, real-world applications have dynamic features. This paper introduces a novel dynamic optimization problem applied to Unmanned Aerial Vehicle (UAV) search and rescue scenarios, named the Moving Peak Drone Search Problem (MPDSP). It utilizes the dynamic environment generator of the well-known Moving Peak Benchmark (MPB) and it is formulated as a maximization problem, with additional constraints imposed by the use of UAVs. For solving the MPDSP, a multi-swarm framework is proposed and seven optimization algorithms are tested. Five well known swarm intelligence algorithms and two algorithms effectively used in continuous and dynamic optimization problems. The implemented methods are evaluated and compared on 105 scenarios with 4 different UAV fleet configurations. Among the tested swarm intelligence variants, the Particle Swarm Optimization implementations proved to be the most effective for solving the MPDSP.

An Interleaved Artificial Bee Colony algorithm for dynamic optimisation problems

ABSTRACTDynamic optimisation problems (DOPs) have attracted a lot of research attention in recent years due to their practical applications and complexity. DOPs are more challenging than static optimisation problems because the problem information or data is either revealed or changed during the course of an ongoing optimisation process. This requires an optimisation algorithm that should be able to monitor the movement of the optimal point and the changes in the landscape solutions. In this paper, we proposed an Interleaved Artificial Bee Colony (I-ABC) algorithm for DOPs. Artificial Bee Colony (ABC) is a nature inspired algorithm which has been successfully used in various optimisation problems. The proposed I-ABC algorithm has two populations, called ABC1 and ABC2, which worked in an interleaved manner. While ABC1 focused on exploring the search space though using a probabilistic solution acceptance mechanism, ABC2 worked inside ABC1 and focused on the search around the current best solutions by using a greedy mechanism. The proposed algorithm was tested on the Moving Peak Benchmark. The experimental results indicated that the proposed algorithm achieved better results than the compared methods for 8 out of 11 scenarios.

A novel approach for optimization in dynamic environments based on modified cuckoo search algorithm

Cuckoo search algorithm is one of the famous algorithms in the area of swarm intelligence algorithms. It has been supplied widely for solving static optimization problems. However, it should be considered that a great number of optimization problems in the real world, are in the form of dynamic optimization problems. In fact, the algorithms which have been implemented for static environments are not able to solve problems in dynamic environments. In this paper, a novel multi-swarm algorithm based on modified cuckoo search algorithm (MCSA) has been proposed to find and track the optimum (optima) of the problem space in dynamic environments. Each swarm performs optimization process based on MCSA. Also, a deactivation mechanism has been utilized to improve the efficiency of this approach. Finally the proposed algorithm has been tested on moving peak benchmark, one of the most well-known benchmarks of this domain, and compared with several prominent algorithms in this area. The results indicate the superiority of this approach.

Multi-Thread Memory Particle Swarm Optimization for Dynamic Optimization Problems

This paper proposes a multi-thread-memory particle swarm optimization (MTM-PSO) for dynamic optimization problems (DOPs). It introduces multi-thread memory to multi-swarm approaches to deal with DOPs. External memory and multi-swarm approaches are adopted. The best particles near the peaks in each environment are saved in the memory according to storage strategy of update and implement. Multi-thread memory makes full use of local and global optima found in each environment. It makes the good information in the previous evolution transfer to the current population adequately. Using the multi-thread memory and its storage strategy, the particles in the memory are always the best information of local and global optima found until in the current envionment. The information will benefit the future evolution. Experiments on the moving peak benchmark (MPB) for different numbers of peaks testiy MTM-PSO has better performance than dynamic optimization algorithms only with multi-swarm approach.

MNAFSA: A novel approach for optimization in dynamic environments with global changes

Artificial fish swarm algorithm (AFSA) is one of the state-of-the-art swarm intelligence algorithms that is widely used for optimization purposes in static environments. However, numerous real-world problems are dynamic and uncertain, which could not be solved using static approaches. The contribution of this paper is twofold. First, a novel AFSA algorithm, so called NAFSA, has been proposed in order to eliminate weak points of standard AFSA and increase convergence speed of the algorithm. Second, a multi-swarm algorithm based on NAFSA (mNAFSA) was presented to conquer particular challenges of dynamic environment by proposing several novel mechanisms including particularly modified multi-swarm mechanism for finding and covering potential optimum peaks and diversity increase mechanism which is applied after detecting an environment change. The proposed approaches have been evaluated on moving peak benchmark, which is the most prominent benchmark in this domain. This benchmark involves several parameters in order to simulate different configurations of dynamic environments. Extensive experiments show that the proposed algorithm significantly outperforms previous algorithms in most of the tested dynamic environments modeled by moving peaks benchmark.

A multi-population electromagnetic algorithm for dynamic optimisation problems

This paper is derived from an interest in the development of approaches to tackle dynamic optimisation problems. This is a very challenging research area due to the fact that any approaches utilised should be able to track the changes and simultaneously seek for global optima as the search progresses. In this research work, a multi-population electromagnetic algorithm for dynamic optimisation problems is proposed. An electromagnetic algorithm is a population based meta-heuristic method which imitates the attraction and repulsion of the sample points. In order to track the dynamic changes and to effectively explore the search space, the entire population is divided into several sub-populations (referred as multi-population that acts as diversity mechanisms) where each sub-population takes charge in exploring or exploiting the search space. In addition, further investigation are also conducted on the combination of the electromagnetic algorithm with different diversity mechanisms (i.e. random immigrants, memory mechanism and memory based immigrant schemes) with the aim of identifying the most appropriate diversity mechanism for maintaining the diversity of the population in solving dynamic optimisation problems. The proposed approach has been applied and evaluated against the latest methodologies in reviewed literature of research works with respect to the benchmark problems. This study demonstrates that the electromagnetic algorithm with a multi-population diversity mechanism performs better compared to other population diversity mechanisms investigated in our research and produces some of the best known results when tested on Moving Peak Benchmark (MPB) problems.

A multi-population harmony search algorithm with external archive for dynamic optimization problems

Dynamic optimization problems present great challenges to the research community because their parameters are either revealed or changed during the course of an ongoing optimization process. These problems are more challenging than static problems in real-world applications because the latter are usually dynamic, with the environment constantly subjected to change or the size of a problem increasing sporadically. In solving dynamic optimization problems in the real world, proposed solutions should be able to monitor the movement of the optimal point and the changes in the landscape solutions. In this paper, a multi-population harmony search algorithm with external archive for dynamic optimization problems is proposed. Harmony search algorithm is a population-based meta-heuristic optimization technique that is similar to a musical process when a musician is attempting to find a state of harmony. To tackle the problem of dynamism, the population of solutions is divided into several sub-populations such that each sub-population takes charge exploring or exploiting the search space. To enhance the algorithm performance further, an external archive is used to save the best solutions for later use. These solutions will then be used to replace redundant solutions in the harmony memory. The proposed algorithm is tested on the Moving Peak Benchmark. Empirical results show that the proposed algorithm produces better results than several of the current state-of-the-art algorithms.

A Hybrid Harmony Search Algorithm for Solving Dynamic Optimisation Problems

Many optimisation problems are dynamic in the sense that changes occur during the optimisation process, and therefore are more challenging than the stationary problems. To solve dynamic optimisation problems, the proposed approaches should not only attempt to seek the global optima but be able to also keep track of changes in the track record of landscape solutions. In this research work, one of the most recent new population-based meta-heuristic optimisation technique called a harmony search algorithm for dynamic optimization problems is investigated. This technique mimics the musical process when a musician attempts to find a state of harmony. In order to cope with a dynamic behaviour, the proposed harmony search algorithm was hybridised with a (i) random immigrant, (ii) memory mechanism and (iii) memory based immigrant scheme. The performance of the proposed harmony search is verified by using the well-known dynamic test problem called the Moving Peak Benchmark (MPB) with a variety of peaks. The empirical results demonstrate that the proposed algorithm is able to obtain competitive results, but not the best for most of the cases, when compared to the best known results in the scientific literature published so far.

A novel multi-swarm algorithm for optimization in dynamic environments based on particle swarm optimization

Optimization in dynamic environment is considered among prominent optimization problems. There are particular challenges for optimization in dynamic environments, so that the designed algorithms must conquer the challenges in order to perform an efficient optimization. In this paper, a novel optimization algorithm in dynamic environments was proposed based on particle swarm optimization approach, in which several mechanisms were employed to face the challenges in this domain. In this algorithm, an improved multi-swarm approach has been used for finding peaks in the problem space and tracking them after an environment change in an appropriate time. Moreover, a novel method based on change in velocity vector and particle positions was proposed to increase the diversity of swarms. For improving the efficiency of the algorithm, a local search based on adaptive exploiter particle around the best found position as well as a novel awakening–sleeping mechanism were utilized. The experiments were conducted on Moving Peak Benchmark which is the most well-known benchmark in this domain and results have been compared with those of the state-of-the art methods. The results show the superiority of the proposed method.