Proposal of Adaptive Randomness in Differential Evolution

Differential Evolution (DE) algorithm is a heuristic random search algorithm based on the group difference, and it is also an optimization algorithm which processes random search in the continuous space with actual number vector coding. In uranium ore classification, its impossible to know in advance the number of best features to select. This paper puts forward a new algorithm named Variable-number Differential Evolution (VDE) algorithm, and applies it to selecting the best features of hyperspectral data. Then applies k-nearest neighbor, decision tree, naïve bayes, naïve bayes tree and support vector machine algorithm on the newly obtained data set only containing the selected features, records average accuracy by 10-fold cross-validation. The results show that new algorithm can improve the accuracy of classification compared with genetic algorithm (GA) and original DE algorithm.

Differential evolution (DE), as a class of biologically inspired and meta-heuristic techniques, has attained increasing popularity in solving many real world optimization problems. However, DE is not always successful. It can easily get stuck in a local optimum or an undesired stagnation condition. This paper proposes a new DE algorithm Differential Evolution with Alopex-Based Local Search (DEALS), for enhancing DE performance. Alopex uses local correlations between changes in individual parameters and changes in function values to estimate the gradient of the landscape. It also contains the idea of simulated annealing that uses temperature to control the probability of move directions during the search process. The results from experiments demonstrate that the use of Alopex as local search in DE brings substantial performance improvement over the standard DE algorithm. The proposed DEALS algorithm has also been shown to be strongly competitive (best rank) against several other DE variants with local search.

Population-based algorithms are a well-established category of metaheuristic optimization algorithms in which individuals collaborate with each other to find the optimal solution in a search space. During the search process, each individual provides a partial intelligence which can assist the population movement toward promising regions. In this paper, a dimension-wise strategy is proposed to collect the intelligence of whole population to generate a new trial candidate solution. For new individual, the value of each variable is calculated using the votes of a more-crowded cluster of individuals obtained on each dimension (one-dimensional clustering). Accordingly, a group of candidate solutions in the population collaborate to determine a variable value of new individual. Utilizing this strategy, collective intelligence (CI) aims the algorithm to find better candidate solutions. Since the proposed method keeps untouched all other parts of the algorithm, it can be used with any population-based algorithm. This paper presents the modification of two well-known population-based algorithms based on the proposed strategy in utilizing Collective Intelligence (CI), Differential Evolution (CIDE) and Particle Swarm optimization (CIPSO). In conducted experiments, two proposed algorithms are compared with classical version of DE and PSO on 30 functions of CEC2017 benchmark. The results indicate that the proposed method generates an individual with better objective function value than many of the individuals in the population which leads totally better results in overall.

Particle Swarm Optimization or Differential Evolution—A comparison

The berth allocation problem (BAP) is an important and challenging problem in the maritime transportation industry. BAP can be defined as the problem of assigning a berth position and service time to a given set of vessels while ensuring that all BAP constraints are respected. The goal is to minimize the total waiting time of all vessels. In this paper, we propose a differential evolution (DE) algorithm for the BAP. DE is a nature-inspired meta-heuristic that has been shown to be an effective method to addresses continuous optimization problems. It involves a population of solutions that undergo the process of selection and variation. In DE, the mutation operator is considered the main variation operator responsible for generating new solutions. Several mutation operators have been proposed and they have shown that different operators are more suitable for different problem instances and even different stages in the search process. In this paper, we propose an enhanced DE that utilizes several mutation operators and employs game theory to control the selection of mutation operators during the search process. The BAP benchmark instances that have been used by other researchers are used to assess the performance of the proposed algorithm. Our experimental results reveal that the proposed DE can obtain competitive results with less computational time compared to existing algorithms for all tested problem instances.

In this paper we proposed the circle trajectory assembly algorithm to control the multi-UAVs circular assembly formation. CTFAP solution provides rapid formation of UAVs on a circular orbit and solve the problem of large scattering distance. Proposed Distributed model prediction control framework improves the optimization ability and reduces the computation consumption with the better convergence ability of the UAV formation. Firstly, a circular trajectory following algorithm with an adaptive parameter is proposed to complete the rapid formation of UAVs on a circular orbit and solve the problem of large scattering distance during formation forming. Then, in the stage of formation reconfiguration, with distributed model prediction control framework (DMPC), the proposed method gets the prediction information of DMPC to optimize the population of classical differential evolution (DE) algorithm and improve the iterative optimization ability of DE algorithm. Experiments show that the proposed differential evolution algorithm greatly improves the efficiency of solving the formation reconfiguration problem under the DMPC framework and overcomes the disadvantages of random population of classical DE. For the proposed rapid forming method, assembly range is reduced by 41% compared with direct linearly formation assembly, and the formation forming time is reduced by approximately 21%. Compared with other optimization algorithms such as Particle Swarm Optimization (PSO), Genetic Algorithm (GA) and DE, the proposed differential evolution algorithm reduces instruction response time of single-drones by 16%–30%.

Butterfly optimisation algorithm (BOA) is a newcomer in the family of nature inspired optimisation algorithms. Although it is an effective algorithm, still, like other population-based optimisation algorithms, it encounters two probable problems: 1) entrapment in local optima; 2) slow convergence speed. In order to increase the potential of the algorithm, it is hybridised with an efficient algorithm, differential evolution (DE), which accelerates the global convergence speed to the true global optimum while preserving the main feature of the basic BOA. In this paper, a novel hybrid algorithm based on BOA and DE, namely BOA/DE is proposed to solve numerical optimisation problems. The proposed algorithm has advantages of both BOA and DE which enable the algorithm to balance the tradeoff between exploration and exploitation which produces efficient results. Engineering design problem and standard benchmark functions are employed to validate the proposed algorithm and according to the simulation results, the performance of the hybrid algorithm is superior to or at least highly competitive with the standard BOA and DE.

Social learning differential evolution

Intelligent-PID controller design for speed track in automatic train operation system with heuristic algorithms

Real-world optimization problems in engineering, logistics, and resource allocation are often constrained and multi-modal, posing a challenge for traditional optimization algorithms. Metaheuristic algorithms inspired by natural and artificial phenomena have shown promise, but many fail to balance exploration and exploitation effectively, especially under stringent constraints. Existing algorithms such as Genetic Algorithms (GA), Particle Swarm Optimization (PSO), and Differential Evolution (DE) face issues in convergence speed and constraint handling, particularly in high-dimensional spaces or when constraints are dynamic or complex. We propose an Adaptive Pattern-Driven Optimization (APDO) algorithm, a novel tailor-inspired metaheuristic that mimics the adaptive decision-making process of a tailor designing garments. APDO integrates three primary operators—Pattern Selection, Fabric Adjustment, and Stitch Reinforcement—to handle constraints adaptively. The algorithm combines pattern memory (historical bests), probabilistic pattern mutation, and a constraint-domination principle to ensure feasibility and diversity. The core idea is to iteratively “cut and stitch” solutions to adapt the search process, enabling dynamic constraint satisfaction and global optimization. We benchmarked APDO against five popular methods (GA, PSO, DE, Firefly Algorithm, and Whale Optimization Algorithm) on a suite of 10 real-world constrained problems, including mechanical component design and energy scheduling tasks. APDO outperformed all baselines in terms of convergence speed, constraint satisfaction rate, and solution quality. In particular, APDO achieved an average feasibility rate of 97.6% and an improvement of 4.2–11.8% in best fitness across problems.

Differential evolution (DE) was introduced by Stone and Price in 1995 as a population-based stochastic search technique for solving optimization problems in a continuous space. DE has been successfully applied to various real world numerical optimization problems. In recent years not only continuous real-valued function, the applications of DE on combinatorial optimization problems with discrete decision variables are reported. However, genetic operator in the standard DE can not directly applied to discrete space. In this paper, we propose a method to solve quadratic assignment problems (QAP) by DE. The QAP is a well-known combinatorial optimization problem with a wide variety of practical applications. It is NP-hard and is considered to be one of the most difficult problems. In the QAP, a candidate solution can represented a permutation of integer. The proposed method employs permutation representation for individuals in DE. Therefore, a individual vector is encoded directly as a permutation. In discrete space, to realize efficient solution search like standard DE which have continuous nature, we modify differential operator to handle permutation encoding. Additionally, in order to maintain diversity of population, restart strategy and tabu list are introduced to proposed method instead of crossover operator. Finally, we show the experimental results using instances of QAPLIB and the efficacy of proposed method.

Adaptive parameter control is a proven method to increase efficiency of any optimisation algorithm and have has been universally proven on various benchmark problems. In this research report, a Universal model free method of adaptive control of optimisation parameters was proposed. The goal of the research is to explore the method that can be used for any model of optimisation algorithm (‘Swiss army knife’ approach). The proposed method utilises a score system in which points are rewarded for improvement found on individual agent performance while non-improving will experience a score-decay. The proposed method was tested on two types of common optimisation algorithm, Truncated Lěvy flight and the Differential Evolution (DE). This Adaptive parameter strategy is solely based on search agent's performance and hence is not algorithm specific (model free). As a preliminary study, this report will only focus on Lower Dimensional problems (D=10) using CEC 2014 benchmark test sets. The results showed that it work well on DE but gave mediocre results for Le $\check{v}$ y Flight when compared with their static parameter counterparts. This showed performance varies across algorithms types but verified the adaptive capability of the proposed method.

Guest Editorial: Situational awareness of integrated energy systems

We address adversarial attacks on the actuators at the joints of legged robots trained by deep reinforcement learning. The vulnerability to the joint attacks can significantly impact the safety and robustness of legged robots. In this study, we demonstrate that the adversarial perturbations to the torque control signals of the actuators can significantly reduce the rewards and cause walking instability in robots. To find the adversarial torque perturbations, we develop black-box adversarial attacks, where, the adversary cannot access the neural networks trained by deep reinforcement learning. The black box attack can be applied to legged robots regardless of the architecture and algorithms of deep reinforcement learning. We employ three search methods for the black-box adversarial attacks: random search, differential evolution, and numerical gradient descent methods. In experiments with the quadruped robot Ant-v2 and the bipedal robot Humanoid-v2, in OpenAI Gym environments, we find that differential evolution can efficiently find the strongest torque perturbations among the three methods. In addition, we realize that the quadruped robot Ant-v2 is vulnerable to the adversarial perturbations, whereas the bipedal robot Humanoid-v2 is robust to the perturbations. Consequently, the joint attacks can be used for proactive diagnosis of robot walking instability.

Enhanced artificial bee colony algorithm through differential evolution