Dynamic Evolutionary Algorithms Research Articles

A federated GAN network-based evolutionary constrained optimization approach to integrated coal mine energy system

The integrated coal mine energy system (ICMES) is a kind of system with multiple scenarios, variables and parameters, which belongs to dynamic constrained multi-objective optimization problem (DCMOP). One of the challenges in solving ICMES lies in searching for feasible solutions when the frequency of changes is quick. To solve the above mentioned issues, this paper proposes a federated GAN network-based evolutionary constrained optimization for ICMES (FGECO). Firstly, multiple GAN networks are utilized in the framework of federated learning (FL) to estimate the distribution of feasible regions that satisfy each constraint. Following that, they are fused to realize the intersection of all feasible regions, and generate one feasible region that can meet all constrained requirements. Subsequently, an initial population with guidance of evolution is generated based on the proposed shared GAN network model. Finally, FGECO is compared with four popular dynamic constrained multi-objective evolutionary algorithms (DCMOEAs) on ICMES. Experimental results indicate its superiority.

A Comparative Study of Single-Constraint Routing in Wireless Mesh Networks Using Different Dynamic Programming Algorithms

Finding the shortest route in wireless mesh networks is an important aspect. Many techniques are used to solve this problem like dynamic programming, evolutionary algorithms, weighted-sum techniques, and others. In this paper, we use dynamic programming techniques to find the shortest path in wireless mesh networks due to their generality, reduction of complexity and facilitation of numerical computation, simplicity in incorporating constraints, and their onformity to the stochastic nature of some problems. The routing problem is a multi-objective optimization problem with some constraints such as path capacity and end-to-end delay. Single-constraint routing problems and solutions using Dijkstra, Bellman-Ford, and Floyd-Warshall algorithms are proposed in this work with a discussion on the difference between them. These algorithms find the shortest route through finding the optimal rate between two nodes in the wireless networks but with bounded end-to-end delay. The Dijkstra-based algorithm is especially favorable in terms of processing time. We also present a comparison between our proposed single-constraint Dijkstra-based routing algorithm and the mesh routing algorithm (MRA) existing in the literature to clarify the merits of the former.

Assessing the Effects of Tradable Green Certificates and Renewable Portfolio Standards through Demand-Side Decision-Making Simulation: A Case of a System Containing Photovoltaic Power

Understanding the effect of a tradable green certificate (TGC) and renewable portfolio standard (RPS) policy mix is of great importance for sustainable renewable-energy development and carbon neutrality, given that the demand side subjects are the responsible subjects under China’s RPSs and studies from the demand-side perspective are relatively limited. To fill this gap, this paper analyzes the coupled relationship between the TGC market and the electricity market as well as the reflexivity of the TGC market. Meanwhile, on the basis of modeling TGC prices and renewable-energy uncertainty, this paper constructs a Markov decision process (MDP) model to simulate the sequential decision-making process of the demand side and further proposes a solution model based on dynamic programming and evolutionary algorithms. The results show that: (1) In addition to policy parameters such as RPS weight, TGC price caps and penalties, a preference for short-term benefits and renewable-energy uncertainty also affect transaction behaviors on the demand side. (2) Increasing RPS weight within an appropriate range can stimulate demand for renewable power and TGC, while excessively low RPS weight will result in accumulation of unsold TGC. In addition, the preference for short-term benefits can stimulate demand for renewable power and curb demand for TGC. (3) An increase in the TGC price cap can stimulate demand for renewable power and restrain demand for TGC, but this phenomenon may not exist when RPS weight is too low or responsible subjects prefer short-term benefits. (4) Setting a penalty of no less than the TGC price cap is of great significance to ensure the operation of the TGC market and RPSs.

A new moving peaks benchmark with attractors for dynamic evolutionary algorithms

• A new dynamic benchmark suite with configurable predictability degree of the optima. • Severity, direction and randomness of the optima’s movement, can be chosen. • Introduction of a new performance metric for prediction-driven optimisers. • Seven state-of-the-art evolutionary algorithms for dynamic optimisation are assessed. Prediction in evolutionary dynamic optimization (EDO), such as predicting the movement of optima, or when and how an environment will change, is a topic that is still under investigation and presents unsolved challenges. A few studies approach prediction based on re-initialising a population or requirement satisfaction problems such as Robust Optimization Over Time. The benchmark problems in these studies inherently use randomly changing parameters and therefore such randomness may make it difficult to compare these algorithms with other EDO approaches. In this paper, we introduce a new benchmark, called Moving Peaks Benchmark with Attractors, which incorporates an attractor heuristic that attracts peaks to a certain location in the environment into the moving peaks problem. The proposed benchmark is fully flexible where the dynamics of the attractors and the rate at which a peak is attracted to such attractors can be modified. By adjusting these characteristics, certain styles of movements can be achieved by a peak. We also introduce a new performance measure that focuses on the comparison of algorithms that use prediction. Seven EDO algorithms based on different working logics are chosen to give a wide representation of the state-of-the-art in this area. We argue that having predictable characteristics in the benchmark problem is more adequate for studying the performances and behaviours of those algorithms that embed prediction mechanisms. Experimental results obtained with the proposed benchmark show it’s suitability for the EDO domain as all algorithms featuring prediction capabilities display higher accuracy than their competitors.

Solving Nonlinear Equations System With Dynamic Repulsion-Based Evolutionary Algorithms

Nonlinear equations system (NES) arises commonly in science and engineering. Repulsion techniques are considered to be the effective methods to locate different roots of NES. In general, the repulsive radius needs to be given by the user before the run. However, its optimal parameter setting is difficult and problem-dependent. To alleviate this drawback, in this paper, we first propose a dynamic repulsion technique, and then a general framework based on the dynamic repulsion technique and evolutionary algorithms (EAs) is presented to effectively solve NES. The major advantages of our framework are: 1) the repulsive radius is controlled dynamically during the evolutionary process; 2) multiple roots of NES can be simultaneously located in a single run; 3) the diversity of the population is preserved due to the population reinitialization; and 4) different repulsion techniques and different EAs can be readily integrated into this framework. To extensively evaluate the performance of our framework, we choose 42 problems with diverse features as the test suite. In addition, some representative differential evolution and particle swarm optimization variants are incorporated into the framework. Our method is also compared with other state-of-the-art methods. Experimental results indicate that the dynamic repulsion technique can improve the performance of the original repulsion technique with static repulsive radius. Moreover, the proposed method is able to yield better results compared with other methods.

A Re-Entry Path Planning Method for Service Robots Based on Dynamic Inver-Over Evolutionary Algorithm

A re-entry path planning method in omitting areas for service robots is suggested based on dynamic Inver-Over evolutionary algorithms after the robot automatically avoids obstacles. The complete coverage path planning is researched for cleaning service robots. Combined with features of dynamic travelling salesmen problem (DTSP), a local operator is employed for the path planning to enhance real-time dynamic properties of the Inver-Over algorithm. The method addresses the path planning problem that a number of cells undergo dynamic changes over time under work environment of cleaning robots. With simulations and experiments performed, it is discovered that the average relative error is 2.2% between the re-entry path planning and the best path, which validates the effectiveness and feasibility of the method.

Small Evolution Antenna Design Method Based on Dynamic Hill Climbing Algorithm and Orthogonal Experiment

Small-scale evolution antennas have the advantages of high gain, wide bandwidth and small size, and have broad application prospects in the aerospace field. Aiming at the complex high-dimensional and dynamic problems of aerial antenna modeling, a dynamic hill-climbing algorithm based on orthogonal design is designed and implemented to simulate and optimize the single-span antenna in high-frequency operation mode. In the optimization problem, this paper defines a new individual comparison mechanism, which can reflect the number of violations of constraints and the degree of violation of each constraint, making the comparison of individuals more reasonable. The antenna simulation results demonstrate the effectiveness and feasibility of using dynamic evolutionary algorithms for antenna design.

Evolutionary dynamic constrained optimization: Test suite construction and algorithm comparisons

Many real-world applications can be modelled as dynamic constrained optimization problems (DCOPs). Due to the fact that objective function and/or constraints change over time, solving DCOPs is a challenging task. Although solving DCOPs by evolutionary algorithms has attracted increasing interest in the community of evolutionary computation, the design of benchmark test functions of DCOPs is still insufficient. Therefore, we propose a test suite for DCOPs. A dynamic unconstrained optimization benchmark with good time-varying characteristics, called moving peaks benchmark, is chosen to be the objective function of our test suite. In addition, we design adjustable dynamic constraints, by which the size, number, and change severity of the feasible regions can be flexibly controlled. Furthermore, the performance of three dynamic constrained optimization evolutionary algorithms is tested on the proposed test suite, one of which is presented in this paper, named dynamic constrained optimization differential evolution (DyCODE). DyCODE includes three main phases: 1) the first phase intends to enter the feasible region from different directions promptly via a multi-population search strategy; 2) in the second phase, some excellent individuals chosen from the first phase form a new population to search for the optimal solution of the current environment; and 3) the third phase combines the memory individuals of the first two phases with some randomly generated individuals to re-initialize the population for the next environment. From the experiments, one can understand the strengths and weaknesses of the three compared algorithms for solving DCOPs in depth. Moreover, we also give some suggestions for researchers to apply these three algorithms on different occasions.

A Distributed Multiple Populations Framework for Evolutionary Algorithm in Solving Dynamic Optimization Problems

Aiming to dynamic optimization problems (DOPs), this paper develops a novel general distributed multiple populations (DMP) framework for evolutionary algorithms (EAs). DMP employs six strategies designed in three levels (i.e., population-level, subpopulation-level, and individual-level) to deal with different kinds of DOPs. First, the population-level subpopulation division estimation strategy in initialization phase rationally divides the whole population into several subpopulations to explore distinct subareas of search space sufficiently. Then, during the steady evolutionary process, diversity preservation in individual-level and population-level accelerates the responsiveness of the whole population to a new landscape, while subpopulation-level self-learning of elitist individuals promotes the exploitation of promising areas. Moreover, in subpopulation-level, the archive quality assurance technique avoids repeat exploring the same peaks by storing the locations of different peaks with low redundancy. When landscape variation occurs, in population-level, historical information containing excellent evolutionary pattern is recorded to guide the population evolution better in the new environment. DMP framework is easy to implement in various EAs due to its well generality and independence about operators and parameters of the embedded algorithm. Four DMP-EAs are accomplished in this paper whose basic algorithms are particle swarm optimization (PSO) and differential evolution (DE) with different settings. The performance of the four proposed DMP-EAs is evaluated on all the widely used complex DOP benchmarks from CEC 2009. The testing results indicate that the DMP-EAs generally significantly outperform many state-of-the-art dynamic EAs (DEAs) on most of DOP benchmarks.

A History-Driven Differential Evolution Algorithm for Optimization in Dynamic Environments

This paper presents a novel differential evolution algorithm to solve dynamic optimization problems. In the proposed algorithm, the entire population is composed of several subpopulations, which are evolved independently and excluded each other by a predefined Euclidian-distance. In each subpopulation, the “DE/best/1” mutation operator is employed to generate a mutant individual in this paper. In order to fully exploit the newly generated individual, the selection operator was extended, in which the newly generated trial vector competed with the worst individual if this trial vector was worse than the target vector in terms of the fitness. Meanwhile, this trial vector was stored as the historical information, if it was better than the worst individual. When the environmental change was detected, some of the stored solutions were retrieved and expected to guide the reinitialized solutions to track the new location of the global optimum as soon as possible. The proposed algorithm was compared with several state-of-the-art dynamic evolutionary algorithms over the representative benchmark instances. The experimental results show that the proposed algorithm outperforms the competitors.

Global replacement-based differential evolution with neighbor-based memory for dynamic optimization

Dynamic optimization problems challenge the evolutionary algorithms, owing to the diversity loss or the low search efficiency of the algorithms, especially when the problems change frequently. This paper presents a novel differential evolution algorithm to address the dynamic optimization problems. Unlike the most used “DE/rand/1” mutation operator, in this paper, the “DE/best/1” mutation is employed to generate a mutant individual. In order to enhance the search efficiency of differential evolution, the classical differential evolution algorithm is modified by a novel replacement operator, in which the worst individual in the whole population is replaced by the newly generated trial vector as a “steady-state” manner. During optimizing, some newly generated solutions are stored into a memory set, in which these stored solutions are located around the current best solution. When the environmental change is detected, the stored solutions are expected to guide the reinitialized solutions to track the new location of global optimum as soon as possible. The performance of the proposed algorithm is compared with six state-of-the-art dynamic evolutionary algorithms over some benchmark problems. The experimental results show that the proposed algorithm clearly outperforms the competitors.

Heterogeneous Differential Evolution with Memory Enhanced Brownian and Quantum Individuals for Dynamic Optimization Problems

In order to solve the dynamic optimization problem (DOP), this paper proposes to use a heterogeneous differential evolution (HDE) algorithm framework with memory enhanced Brownian and quantum (MEBQ) individual scheme. The proposed HDE/MEBQ algorithm has the following two advantages when solving DOP. First and foremost, the HDE optimization framework can satisfy the problem requirement of different characteristics. DOP is actually a continuous process to solve different kinds of optimization problems to meet new requirements when the search environmental change occurs. Therefore, HDE/MEBQ is able to fastly respond to the environmental changes of DOP as the HDE framework uses multiple populations with heterogeneous parameters and operators to meet different search requirements in various search environments. Secondly, according to the phenomenon that most of the environmental changes may not be too drastic in real-world applications, historical information in the past may be useful for finding the optimum solution in the new environment. Thus, the MEBQ scheme used in HDE/MEBQ provides helpful historical evolutionary information from the elite ancestors for guiding individuals to evolve in a new environment strongly and to obtain faster convergence and a more precise solution. We evaluated HDE/MEBQ on several DOPs from CEC 2009 and compared with several state-of-the-art dynamic evolutionary algorithms. The results show that HDE/MEBQ performs superior in statistics and gets very competitive results in most of the test conditions, especially in complex DOPs.

Handling time-varying constraints and objectives in dynamic evolutionary multi-objective optimization

Abstract Recently, several researchers within the evolutionary and swarm computing community have been interested in solving dynamic multi-objective problems where the objective functions, the problem's parameters, and/or the constraints may change over time. According to the related literature, most works have focused on the dynamicity of objective functions, which is insufficient since also constraints may change over time along with the objectives. For instance, a feasible solution could become infeasible after a change occurrence, and vice versa. Besides, a non-dominated solution may become dominated, and vice versa. Motivated by these observations, we devote this paper to focus on the dynamicity of both: (1) problem's constraints and (2) objective functions. To achieve our goal, we propose a new self-adaptive penalty function and a new feasibility driven strategy that are embedded within the NSGA-II and that are applied whenever a change is detected. The feasibility driven strategy is able to guide the search towards the new feasible directions according to the environment changes. The empirical results have shown that our proposal is able to handle various challenges raised by the problematic of dynamic constrained multi-objective optimization. Moreover, we have compared our new dynamic constrained NSGA-II version, denoted as DC-MOEA, against two existent dynamic constrained evolutionary algorithms. The obtained results have demonstrated the competitiveness and the superiority of our algorithm on both aspects of convergence and diversity.

A General Framework of Dynamic Constrained Multiobjective Evolutionary Algorithms for Constrained Optimization

A novel multiobjective technique is proposed for solving constrained optimization problems (COPs) in this paper. The method highlights three different perspectives: 1) a COP is converted into an equivalent dynamic constrained multiobjective optimization problem (DCMOP) with three objectives: a) the original objective; b) a constraint-violation objective; and c) a niche-count objective; 2) a method of gradually reducing the constraint boundary aims to handle the constraint difficulty; and 3) a method of gradually reducing the niche size aims to handle the multimodal difficulty. A general framework of the design of dynamic constrained multiobjective evolutionary algorithms is proposed for solving DCMOPs. Three popular types of multiobjective evolutionary algorithms, i.e., Pareto ranking-based, decomposition-based, and hype-volume indicator-based, are employed to instantiate the framework. The three instantiations are tested on two benchmark suites. Experimental results show that they perform better than or competitive to a set of state-of-the-art constraint optimizers, especially on problems with a large number of dimensions.

A dynamic oppositional biogeography-based optimization approach for time-varying electrical impedance tomography

Dynamic electrical impedance tomography-based image reconstruction using conventional algorithms such as the extended Kalman filter often exhibits inferior performance due to the presence of measurement noise, the inherent ill-posed nature of the problem and its critical dependence on the selection of the initial guess as well as the state evolution model. Moreover, many of these conventional algorithms require the calculation of a Jacobian matrix. This paper proposes a dynamic oppositional biogeography-based optimization (OBBO) technique to estimate the shape, size and location of the non-stationary region boundaries, expressed as coefficients of truncated Fourier series, inside an object domain using electrical impedance tomography. The conductivity of the object domain is assumed to be known a priori. Dynamic OBBO is a novel addition to the family of dynamic evolutionary algorithms. Moreover, it is the first such study on the application of dynamic evolutionary algorithms for dynamic electrical impedance tomography-based image reconstruction. The performance of the algorithm is tested through numerical simulations and experimental study and is compared with state-of-the-art gradient-based extended Kalman filter. The dynamic OBBO is shown to be far superior compared to the extended Kalman filter. It is found to be robust to measurement noise as well as the initial guess, and does not rely on a priori knowledge of the state evolution model.

Dynamic evolutionary community detection algorithms based on the modularity matrix

Motivated by the relationship of the dynamic behaviors and network structure, in this paper, we present two efficient dynamic community detection algorithms. The phases of the nodes in the network can evolve according to our proposed differential equations. In each iteration, the phases of the nodes are controlled by several parameters. It is found that the phases of the nodes are ultimately clustered into several communities after a short period of evolution. They can be adopted to detect the communities successfully. The second differential equation can dynamically adjust several parameters, so it can obtain satisfactory detection results. Simulations on some test networks have verified the efficiency of the presented algorithms.

An Effective Dynamic Evolutionary Algorithm for Engineering Problems

A dynamic evolutionary algorithms (DEA) is designed to solve engineering problems in this paper. The DEA algorithm makes two differences. (1) Dynamic technique is used to handle equality constraints. (2) Two unrelated crossovers (linear crossover and uniform crossover) are combined in the algorithm for avoiding duplicate search and then helping global search. In solving engineering problems, three steps are taken: a DEA algorithm is designed first, then after tested by general benchmark problems, it is improved, and the third step is that the improved DEA algorithm is applied to solve engineering problems. The general test suggests our DEA algorithm outperforms the compared state-of-the-art other algorithms. The experimental results in solving 5 engineering problems indicate that our method works much better than the compared state-of-the-art algorithms, especially, in global search.

Dynamics of Network Selection in Heterogeneous Wireless Networks: An Evolutionary Game Approach

Next-generation wireless networks will integrate multiple wireless access technologies to provide seamless mobility to mobile users with high-speed wireless connectivity. This will give rise to a heterogeneous wireless access environment where network selection becomes crucial for load balancing to avoid network congestion and performance degradation. We study the dynamics of network selection in a heterogeneous wireless network using the theory of evolutionary games. The competition among groups of users in different service areas to share the limited amount of bandwidth in the available wireless access networks is formulated as a dynamic evolutionary game, and the evolutionary equilibrium is considered to be the solution to this game. We present two algorithms, namely, population evolution and reinforcement-learning algorithms for network selection. Although the network-selection algorithm based on population evolution can reach the evolutionary equilibrium faster, it requires a centralized controller to gather, process, and broadcast information about the users in the corresponding service area. In contrast, with reinforcement learning, a user can gradually learn (by interacting with the service provider) and adapt the decision on network selection to reach evolutionary equilibrium without any interaction with other users. Performance of the dynamic evolutionary game-based network-selection algorithms is empirically investigated. The accuracy of the numerical results obtained from the game model is evaluated by using simulations.

A memetic algorithm with adaptive hill climbing strategy for dynamic optimization problems

Dynamic optimization problems challenge traditional evolutionary algorithms seriously since they, once converged, cannot adapt quickly to environmental changes. This paper investigates the application of memetic algorithms, a class of hybrid evolutionary algorithms, for dynamic optimization problems. An adaptive hill climbing method is proposed as the local search technique in the framework of memetic algorithms, which combines the features of greedy crossover-based hill climbing and steepest mutation-based hill climbing. In order to address the convergence problem, two diversity maintaining methods, called adaptive dual mapping and triggered random immigrants, respectively, are also introduced into the proposed memetic algorithm for dynamic optimization problems. Based on a series of dynamic problems generated from several stationary benchmark problems, experiments are carried out to investigate the performance of the proposed memetic algorithm in comparison with some peer evolutionary algorithms. The experimental results show the efficiency of the proposed memetic algorithm in dynamic environments.