Continuous Optimization Algorithm Research Articles

Laplacian Salp Swarm Algorithm for continuous optimization

Laplacian Salp Swarm Algorithm for continuous optimization

Approaches Used In Adapting Metaheuristic Optimization Algorithms Developed For Continuous Problems to Discrete Problems

Many real-world problems such as determining the type and number of wind turbines, facility placement problems, job scheduling problems, are in the category of combinatorial optimization problems in terms of the type of decision variables. However, since many of the evolutionary optimization algorithms are developed for solving continuous optimization problems, they cannot be directly applied to optimization problems with discrete decision variables. Therefore, the continuous decision variable values generated by these metaheuristics need to be converted to binary values using some techniques. In other words, to apply such algorithms to discrete optimization problems, it is necessary to adapt the candidate solution vectors of the algorithms to discrete values and make changes in their working structures. In this study, firstly, adaptation methods that are frequently used in previous studies in transforming metaheuristic optimization algorithms designed for the solution of continuous optimization problems into discrete optimization algorithms are explained. Then, the popular location update strategies used in solving discrete optimization problems are explained. The presented work summarizes the process of adapting continuous optimization algorithms to solve combinatorial problems step by step.

Multiobjective Optimization Design of Interpretable Evolutionary Fuzzy Systems With Type Self-Organizing Learning of Fuzzy Sets

This paper proposes a new multiobjective optimization approach for designing a self-generated interpretable fuzzy logic system (FLS). The types of fuzzy sets can be constructed automatically by self-organizing method, so as to form a hybrid fuzzy system. Different from the existing evolutionary type-1 fuzzy system, which is full of type-1 fuzzy sets, and the evolutionary interval type-2 fuzzy system, which is full of interval type-2 fuzzy sets, there are both type-1 fuzzy sets and interval type-2 fuzzy sets in the hybrid fuzzy system. A new transparency-oriented objective function is defined, and the constraint of the footprint of uncertainty (FOU) of the interval type-2 (IT2) fuzzy set (FS) is considered for the first time. A new FS merging criterion focusing on the proximity of the cores of fuzzy sets is proposed, which is easy to calculate and maintains the characteristics of classical similarity measures. Combined with the new merging criterion, the online cluster and fuzzy set updating (OCFU) algorithm is employed to initialize the reference rule base and the type of fuzzy sets, as it is assumed that no training data are collected in advance. Based on the reference rule base, the advanced multiobjective front-guided continuous ant colony optimization (AMO-FCACO) algorithm is introduced to optimize all the free parameters of the FLS. With the operation mentioned above, the self-generated FLSs achieve a good balance between interpretability and performance. The effectiveness of the proposed method is verified by three nonlinear system tracking problems.

Helper objective-based multifactorial evolutionary algorithm for continuous optimization

Helper objective-based multifactorial evolutionary algorithm for continuous optimization

Monte Carlo based continuous aperture optimization for VMAT on conventional and MR-linacs: A proof of concept.

Currently, the commercial treatment planning systems for magnetic-resonance guided linear accelerators (MR-linacs) only support step-and-shoot intensity-modulated radiation therapy (IMRT). However, recent studies have shown the feasibility of delivering arc therapy on MR-linacs, which is expected to improve dose distributions and delivery speed. By accurately accounting for the electron return effect in the presence of a magnetic field, a Monte Carlo (MC) algorithm is ideally suited for the inverse treatment planning of thistechnique. We propose a novel MC-based continuous aperture optimization (MCCAO) algorithm for volumetric modulated arc therapy (VMAT), including applications to VMAT on MR-linacs and trajectory-based VMAT. A unique feature of MCCAO is that the continuous character of gantry rotation and multileaf collimator (MLC) motion is accounted for at every stage of theoptimization. The optimization process uses a multistage simulation of 4D dose distribution. A phase space is scored at the top surface of the MLC and the energy deposition of each particle history is mapped to its position in this phase space. A progressive sampling method is used, where both MLC leaf positions and monitor unit (MU) weights are randomly changed, while respecting the linac mechanical limits. Due to the continuous nature of the leaf motion, such changes affect not only a single control point, but propagate to the adjacent ones as well, and the corresponding dose distribution changes are accounted for. A dose-volume cost function is used, which includes the MC statisticaluncertainty. We applied our optimization technique to various treatment sites, using standard and flattening-filter-free (FFF) 6 MV beam models, with and without a 1.5 T magnetic field. MCCAO generates deliverable plans, whose dose distributions are in good agreement with measurements on ArcCHECK and stereotactic radiosurgery End-To-EndPhantom. We show that the novel MCCAO method generates VMAT plans that meet clinical objectives for both conventional andMR-linacs.

Keenness for characterizing continuous optimization problems and predicting differential evolution algorithm performance

Fitness landscape analysis devotes to characterizing different properties of optimization problems, such as evolvability, sharpness, and neutrality. Although several landscape features have been proposed, only a few of them can be used in practice as predictors of algorithm performance. In this study, the keenness (textrm{KEE}_{s}) is proposed to characterize the sharpness of the fitness landscape for continuous optimization problems and predict the performance of the differential evolution algorithm. Specifically, a mirror simple random walk algorithm is designed to construct the relevance between the front and back search points in the sampling. The fitness value of each point is replaced by the specific integer. The values in the set of integers with the same circumstance are computed as the feature scalar using the cumulative calculation mechanism. The results of experimental studies in various functions demonstrate the superiority of textrm{KEE}_{s} in terms of accuracy, reliability, and coverage of samples. Moreover, textrm{KEE}_{s} has shown excellent practicability in the application of differential evolution algorithm performance prediction for continuous optimization problems. Thus, textrm{KEE}_{s} is a new landscape feature for fitness landscape analysis of continuous optimization problems and algorithm performance prediction within limited prior knowledge of the unknown problem.

An adaptive two-stage evolutionary algorithm for large-scale continuous multi-objective optimization

An adaptive two-stage evolutionary algorithm for large-scale continuous multi-objective optimization

改进蚁群优化算法的最大似然DOA估计方法

In order to alleviate the huge amount of calculation when using the continuous domain ant colony optimization (ACO) algorithm to handle the maximum likelihood (ML) estimation problem, we propose a maximum likelihood direction of arrival (ML-DOA) estimation method based on modified ant colony optimization (MACO) algorithm. Firstly, MACO algorithm adopts the elite reverse learning strategy to obtain a better initial solution group. Secondly, the optimization method of ant colony is conducted by combining global cross-neighborhood search and local search of Gaussian kernel function to expand the algorithm search space and accelerate the convergence speed. Finally, the nonlinear global optimal solution of ML estimation method is obtained. Simulation results show that, compared with ML estimation methods based on particle swarm optimization (PSO) algorithm and ACO algorithm, the convergence speed of the ML-MACO algorithm is 4 times faster than that of the ML-ACO algorithm, the computational load is 1/3 that of the ML-ACO algorithm, the resolution success rate is higher than the ML-PSO algorithm and the ML-ACO algorithm, and the estimation error is less than the ML-PSO algorithm and the ML-ACO algorithm. The ML-MACO algorithm maintains the excellent estimation performance of the ML algorithm with lower computational effort, better convergence performance, and higher estimation accuracy.

A single-solution–compact hybrid algorithm for continuous optimization

A single-solution–compact hybrid algorithm for continuous optimization

Scattering correcting wavefront shaping for three-photon microscopy.

Three-photon (3P) microscopy is getting traction due to its superior performance in deep tissues. Yet, aberrations and light scattering still pose one of the main limitations in the attainable depth ranges for high-resolution imaging. Here, we show scattering correcting wavefront shaping with a simple continuous optimization algorithm, guided by the integrated 3P fluorescence signal. We demonstrate focusing and imaging behind scattering layers and investigate convergence trajectories for different sample geometries and feedback non-linearities. Furthermore, we show imaging through a mouse skull and demonstrate a novel, to the best of our knowledge, fast phase estimation scheme that substantially increases the speed at which the optimal correction can be found.

A scalable, black-box hybrid genetic algorithm for continuous multimodal optimization in moderate dimensions

Optimization problems can be found in many areas of scienceand technology. Not only the global optimum, but also a(large) number of near-optima are often of interest. Thisgives rise to what are referred to as multimodal optimizationproblems. In most cases, the number and quality of the optimaare unknown and assumptions cannot be made about theobjective functions. In this paper, we focus on continuous,unconstrained optimization in moderately high-dimensionalcontinuous spaces (d ≤ 10).We present a scalablealgorithm with virtually no parameters, which performs wellfor general objective functions (non-convex, discontinuous).It is based on two well-established algorithms (CMA-ES,deterministic crowding). Novel elements of the algorithminclude the detection of seed points for local searches andcollision avoidance, both based on nearest neighbors, and astrategy for semi-sequential optimization to realize scalability.The performance of the proposed algorithm is numericallyevaluated using the CEC2013 niching benchmark suite for1 − 20 dimensional functions, and a 9 dimensional real-worldproblem from constraint optimization in climate research.The algorithm performs well in relation to the CEC2013benchmarks and only falls short on higher dimensional andstrongly inisotropic problems. In the case of the climate-related problem, the algorithm is able to find a high number(> 150) of optima of relevance to climate research. Theproposed algorithm does not require special configuration forthe optimization problems considered in this paper, i.e., itshows good black-box behavior.

DV-Hop-based localization algorithm using optimum anchor nodes subsets for wireless sensor network

Node localization has become a crucial technology in wireless sensor network (WSN) research field. Although the widely used DV-Hop localization algorithm is simple and easy to implement, its positioning accuracy still needs to be further enhanced. To improve the DV-Hop algorithm accuracy, a DV-Hop-based scheme using optimum anchor nodes subsets (OANS DV-Hop) is put forward in this article. For OANS DV-Hop algorithm, first of all, each anchor node localizes itself by using other anchor nodes, and employs binary particle swarm optimization (BPSO) algorithm to generate an optimum subset composed of other anchor nodes except itself. Then the anchor node applies OANS to recalculate its average hop size and broadcasts the new hop size and OANS to the nearest unknown nodes. The unknown node localizes itself by using OANS instead of all anchor nodes. Finally, a fitness function is designed based on OANS, and the continuous particle swarm optimization (PSO) algorithm is applied to further increase the localization accuracy. Simulation results demonstrate that OANS DV-Hop algorithm owns higher localization accuracy compared with the primal DV-Hop and other improved DV-Hop algorithms in various network environments.

Integrating Conjugate Gradients Into Evolutionary Algorithms for Large-Scale Continuous Multi-Objective Optimization

Large-scale multi-objective optimization problems (LSMOPs) pose challenges to existing optimizers since a set of well-converged and diverse solutions should be found in huge search spaces. While evolutionary algorithms are good at solving small-scale multi-objective optimization problems, they are criticized for low efficiency in converging to the optimums of LSMOPs. By contrast, mathematical programming methods offer fast convergence speed on large-scale single-objective optimization problems, but they have difficulties in finding diverse solutions for LSMOPs. Currently, how to integrate evolutionary algorithms with mathematical programming methods to solve LSMOPs remains unexplored. In this paper, a hybrid algorithm is tailored for LSMOPs by coupling differential evolution and a conjugate gradient method. On the one hand, conjugate gradients and differential evolution are used to update different decision variables of a set of solutions, where the former drives the solutions to quickly converge towards the Pareto front and the latter promotes the diversity of the solutions to cover the whole Pareto front. On the other hand, objective decomposition strategy of evolutionary multi-objective optimization is used to differentiate the conjugate gradients of solutions, and the line search strategy of mathematical programming is used to ensure the higher quality of each offspring than its parent. In comparison with state-of-the-art evolutionary algorithms, mathematical programming methods, and hybrid algorithms, the proposed algorithm exhibits better convergence and diversity performance on a variety of benchmark and real-world LSMOPs.

Drunkard Adaptive Walking Chaos Wolf Pack Algorithm in Parameter Identification of Photovoltaic Module Model

The rapid and accurate identification of photovoltaic (PV) model parameters is of great significance in solving practical engineering problems such as PV power prediction, maximum power point tracking and battery failure model recognition. Aiming at the shortcomings of low accuracy and poor reliability and being easy to fall into local optimization when standard intelligent optimization algorithms identify PV model parameters, a novel drunken adaptive walking chaotic wolf swarm algorithm is proposed, which is named DCWPA for short. The DCWPA uses the chaotic map sequence to initialize the population, thus to improve the diversity of the initial population. It adopts the walking direction mechanism based on the drunk walking model and the adaptive walking step size to increase the randomness of walking, enhance the individual’s ability to explore and develop and improve the ability of algorithm optimization. It also designs the judgment conditions for half siege in order to accelerate the convergence of the algorithm and improve the speed of the algorithm. In the iterative process, according to the change of the optimal solution, the Hamming Distance is used to judge the similarity of individuals in the population, and the individuals in the population are constantly updated to avoid the algorithm from stopping evolution prematurely due to falling into local optimization. This paper firstly analyzes the time complexity of the algorithm, and then selects eight standard test functions (Benchmark) with different characteristics to verify the performance of the DCWPA algorithm for continuous optimization, and finally the improved algorithm is applied for parameter identification of PV models. The experiments show that the DCWPA has higher identification accuracy than other algorithms, and the results are more consistent with the measured data. Thus, the effectiveness and superiority of the improved algorithm in identifying solar cell parameters are verified, and the identification effect of the improved algorithm on solar cell parameters under different illumination is shown. This research provides a new idea and method for parameter identification of a PV module model.

Energy-efficient resource management for CCFD massive MIMO systems in 6G networks

This paper presents a co-time co-frequency full-duplex (CCFD) massive multiple-input multiple-output (MIMO) system to meet high spectrum efficiency requirements for beyond the fifth-generation (5G) and the forthcoming the sixth-generation (6G) networks. To achieve equilibrium of energy consumption, system resource utilization, and overall transmission capacity, an energy-efficient resource management strategy concerning power allocation and antenna selection is designed. A continuous quantum-inspired termite colony optimization (CQTCO) algorithm is proposed as a solution to the resource management considering the communication reliability while promoting energy conservation for the CCFD massive MIMO system. The effectiveness of CQTCO compared with other algorithms is evaluated through simulations. The results reveal that the proposed resource management scheme under CQTCO can obtain a superior performance in different communication scenarios, which can be considered as an eco-friendly solution for promoting reliable and efficient communication in future wireless networks.

Opposition-based ant colony optimization with all-dimension neighborhood search for engineering design

AbstractThe ant colony optimization algorithm is a classical swarm intelligence algorithm, but it cannot be used for continuous class optimization problems. A continuous ant colony optimization algorithm (ACOR) is proposed to overcome this difficulty. Still, some problems exist, such as quickly falling into local optimum, slow convergence speed, and low convergence accuracy. To solve these problems, this paper proposes a modified version of ACOR called ADNOLACO. There is an opposition-based learning mechanism introduced into ACOR to effectively improve the convergence speed of ACOR. All-dimension neighborhood mechanism is also introduced into ACOR to further enhance the ability of ACOR to avoid getting trapped in the local optimum. To strongly demonstrate these core advantages of ADNOLACO, with the 30 benchmark functions of IEEE CEC2017 as the basis, a detailed analysis of ADNOLACO and ACOR is not only qualitatively performed, but also a comparison experiment is conducted between ADNOLACO and its peers. The results fully proved that ADNOLACO has accelerated the convergence speed and improved the convergence accuracy. The ability to find a balance between local and globally optimal solutions is improved. Also, to show that ADNOLACO has some practical value in real applications, it deals with four engineering problems. The simulation results also illustrate that ADNOLACO can improve the accuracy of the computational results. Therefore, it can be demonstrated that the proposed ADNOLACO is a promising and excellent algorithm based on the results.

Vertical electrical sounding data inversion using continuous ant colony optimization algorithm: A case study from Hassi R'Mel, Algeria

ABSTRACTAmong the existing geophysical methods, the vertical electrical sounding remains a fast and economical way to detect groundwater resources. However, the interpretation of the vertical electrical sounding data often suffers from non‐uniqueness due to the ill‐posed nature of the inverse problem. In recent years, metaheuristic algorithms have been successfully used for solving ill‐conditioned and ill‐posed problems. This work presents a scheme that uses the continuous ant colony optimization (ACOR) technique to invert vertical electrical sounding data. The ACOR is a global search algorithm that explores and finds the globally optimal solution over a search space by mimicking the behaviour of biological ants. The development of this algorithm was due to the requirement to interpret a set of vertical electrical sounding collected at the region of Hassi R'Mel (Algerian Sahara). The area has a particular geological/geoelectrical structure, which renders the interpretation of vertical electrical sounding challenging as standard inversion approaches tend to fail to recover a reliable resistivity model. The ACOR algorithm was initially tested with synthetic data from models simulating the geological/hydrogeological structure of the studied area. The results verified the robustness and stability of the ACOR algorithm even in the presence of a high level of noise. Furthermore, the tests indicated that the ACOR algorithm performed better when compared to other inversion techniques for this particular geoelectrical structure. Five vertical electrical sounding profiles using a Schlumberger array collected in the region of Hassi R'Mel were inverted using the ACOR algorithm. The models confirmed the presence of the two central aquifer systems and showed the geometry of the aquifer with the most favourable conditions for water accumulations.

A Fixed-Time Distributed Optimization Algorithm Based on Event-Triggered Strategy

This paper considers the fixed-time distributed optimization problem with consensus constraint and strongly convex local cost functions, and a distributed optimization algorithm involving two stages is designed. The first stage is to make each agent converge to its own locally optimal state (the minimizer of local cost function) from any initial value in fixed time by designing distributed local optimization controllers. The second one is to realize the goal that all agents achieve the globally optimal state (the minimizer of global cost function) in fixed time under the distributed global optimization protocol. During the second stage of the proposed algorithm, each agent only communicates with its neighbors at event-triggered instants. Hence, comparing to the continuous communication optimization algorithm, our method has the advantage in the terms of saving the communication resources. Furthermore, Zeno behavior is avoided under such control strategy. The proposed algorithm in this paper can ensure that all agents achieve the globally optimal state in fixed time, which is independent of agents’ initial values and decided by some tunable parameters. Finally, the effectiveness of the presented optimization algorithm is demonstrated by a simulation example.

Fast optimization via inertial dynamics with closed-loop damping

In a real Hilbert space \mathcal{H} , in order to develop fast optimization methods, we analyze the asymptotic behavior, as time t tends to infinity, of a large class of autonomous dissipative inertial continuous dynamics. The function f: \mathcal{H} \to \mathbb{R} to be minimized (not necessarily convex) enters the dynamic via its gradient, which is assumed to be Lipschitz continuous on bounded subsets of \mathcal{H} . This results in autonomous dynamical systems with nonlinear damping and nonlinear driving force. We first consider the case where the damping term \partial \phi (\dot{x}(t)) acts as closed-loop control of the velocity. The damping potential \phi : \mathcal{H} \to \mathbb{R}_+ is a convex continuous function which reaches its minimum at the origin. We show the existence and uniqueness of a global solution to the associated Cauchy problem. We analyze the asymptotic convergence and the convergence rates of the trajectories generated by this system. To do this, we use techniques from optimization, control theory, and PDEs: Lyapunov analysis based on the decreasing property of an energy-like function, quasi-gradient and Kurdyka–Łojasiewicz theory, and monotone operator theory for wave-like equations. Convergence rates are obtained based on the geometric properties of the data f and \phi . We put forward minimal hypotheses on the damping potential \phi guaranteeing the convergence of trajectories, thus showing the dividing line between strong and weak damping. When f is strongly convex, we give general conditions on the damping potential \phi which provide exponential convergence rates. Then, we extend the results to the case where additional Hessian-driven damping enters the dynamic, which reduces the oscillations. Finally, we consider a new inertial system where damping jointly involves the velocity \dot{x}(t) and the gradient \nabla f(x(t)) . This study naturally leads to similar results for proximal-gradient algorithms obtained by temporal discretization; some of them are studied in the article. In addition to its original results, this work surveys numerous works devoted to the interaction between damped inertial continuous dynamics and numerical optimization algorithms, with an emphasis on autonomous systems, adaptive procedures, and convergence rates.

Wireless communication system throughput maximization based on UAV path planning

This paper studies the path planning of unmanned aerial vehicle (UAV) in wireless information and energy transmission system of wireless sensor network. UAV transmits radio frequency energy to enable ground sensors, and the ground sensors transmit information to the UAV. In order to solve the non-convex optimization problem in path planning, a new alternate optimization framework is proposed to optimize the fly trajectory of the UAV and maximize the throughput of the entire system. The proposed framework firstly utlizes the lagrangian method to obtain relaxation solution without maximum speed constraint, then implements genetic algorithm and continuous convex optimization algorithm to obtain optimal trajectory and energy allocation strategy. Numerical simulations results show that the UAV-assisted wireless information and energy transmission system can realize self-powered sensor network and data collection in special environments, and improve the throughput of the sensor network system.