Continuous Function Optimization Research Articles

On asymptotic convergence rate of random search

This paper presents general theoretical studies on asymptotic convergence rate (ACR) for finite dimensional optimization. Given the continuous problem function and discrete time stochastic optimization process, the ACR is the optimal constant for control of the asymptotic behaviour of the expected approximation errors. Under general assumptions, condition ACR<1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$<1$$\\end{document} implies the linear behaviour of the expected time of hitting the ε\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\varepsilon $$\\end{document}- optimal sublevel set with ε→0+\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\varepsilon \\rightarrow 0^+ $$\\end{document} and determines the upper bound for the convergence rate of the trajectories of the process. This paper provides general characterization of ACR and, in particular, shows that some algorithms cannot converge linearly fast for any nontrivial continuous optimization problem. The relation between asymptotic convergence rate in the objective space and asymptotic convergence rate in the search space is provided. Examples and numerical simulations with use of a (1+1) self-adaptive evolution strategy and other algorithms are presented.

An Adaptive Cuckoo Algorithm-Based Optimization Method for Tourist Traffic Routes

This paper presents in-depth research and analysis of the optimization method of tourist traffic routes using the adaptive cuckoo algorithm. The traditional cuckoo algorithm has the disadvantages of slow convergence speed and easy falling into local extremes. This paper proposes the iterative adaptive CHSACS algorithm based on iteration. Based on the original CS algorithm, a dynamic adaptive step control amount and a segmented weighted position update formula are introduced to give a class of improved CS algorithms to coordinate the problem of local search and global search of the CS algorithm and speed up the convergence speed at the later stage. To address the problem that the out-of-bounds nests interfere with the convergence of the algorithm, a memory strategy is introduced to relocate the out-of-bounds nests in the search space to improve the stability of the algorithm. Experiments are conducted on the iterative adaptive-based conductive CHSACS algorithm with test function sets. Compared with the original CS algorithm, and ACO algorithm, the CHSACS algorithm has faster convergence, higher search accuracy and a better ability to avoid local optima when dealing with continuous function optimization problems. For the dynamic travel path problem of travel time optimization, the road travel time and sightseeing time of different periods are predicted based on historical data, and the most traveled distance of travel time between two sights is dynamically searched by using the search mechanism based on time windows. The iterative adaptive CHSACS algorithm is used to continuously find the tourist traffic route with the shortest travel time travel path from all combinations of tour sequences. This paper combines the characteristics of bus vehicle scheduling itself, takes into account the interests of both bus companies and tourists, establishes a bus vehicle scheduling model with the departure interval as the independent variable, introduces this hybrid cuckoo algorithm into bus scheduling, verifies the scientific and feasibility of the algorithm through examples, and provides a new idea for solving bus scheduling optimization problems.

Using data mining technology to explore causes of inaccurate reliability data and suggestions for maintenance management

Reliability data reflects equipment safety and provides a reference for setting inspection period, thereby serving as crucial information for the implementation of equipment integrity management policies. The calculation foundation of reliability data is maintenance records of adequate data quality. However, maintenance records of doubtful quality are common. Despite excluding poor quality recodes and using only the remaining maintenance recodes to calculate the reliability data, the calculated results generally lack a sufficient degree of confidence. This study applied data mining technology, including quality metrics, the association rule, and clustering, to explore the cause of low-quality maintenance data. The results revealed that the low data quality of maintenance records was due to ineffective maintenance policies, the low integrity of key system columns, nonadherence to the policy, and misunderstanding of column definitions. The proposed method successfully identified the causes of low-quality maintenance records. By incorporating the method into the function module of a CMMS, operators can equip the system with self-diagnosis, self-supervision, and continuous optimization functions.

Novo rešenje problema višekriterijumskog celobrojnog programiranja pomoću višekriterijumske optimizacije zasnovane na verovatnoći

Introduction/purpose: In this paper, a new solution for solving a multiobjective integer programming problem with probabilistic multi - objective optimization is formulated. Furthermore, discretization by means of the good lattice point and sequential optimization are employed for a successive simplifying treatment and deep optimization. Methods: In probabilistic multi - objective optimization, a new concept of preferable probability has been introduced to describe the preference degree of each performance utility of a candidate; each performance utility of a candidate contributes a partial preferable probability and the product of all partial preferable probabilities deduces the total preferable probability of a candidate; the total preferable probability thus transfers a multi-objective problem into a single-objective one. Discretization by means of the good lattice point is employed to conduct discrete sampling for a continuous objective function and sequential optimization is used to perform deep optimization. At first, the requirements of integers in the treatment could be given up so as to simply conduct above procedures. Finally, the optimal solutions of the input variables must be rounded to the nearest integers. Results: This new scheme is used to deal with two production problems, i.e., maximizing profit while minimizing pollution and determining a purchasing plan for spending as little money as possible while getting as large amount of raw materials as possible. Promising results are obtained for the above two problems from the viewpoint of the probability theory for simultaneous optimization of multiple objectives. Conclusion: This method properly considers simultaneous optimization of multiple objectives in multi-objective integer programming, which naturally reflects the essence of multi-objective programming, and opens a new way of solving multi-objective problems.

An improved pigeon-inspired optimisation for continuous function optimisation problems

An improved pigeon-inspired optimisation for continuous function optimisation problems

An improved pigeon-inspired optimisation for continuous function optimisation problems

An improved pigeon-inspired optimisation for continuous function optimisation problems

Metaheuristic–Boltzmannian optimization model: A new methodology for convergence using the Jensen–Shannon metric in continuous optimization problems

We present a new methodology called J–SIGMA to infer state change information using the minimum Jensen–Shannon distance to describe a continuous optimization problem as a Boltzmannian system, as well as its applications to population-based metaheuristics. In general, a Boltzmannian system describes a macrostate from the statistics of the constituent microstate where the minimum energy is the most probable. If we model an optimization problem as a Boltzmann process, the global optimum would be the most probable state. To achieve this, we propose an analytical derivation of the minimum distance to the Boltzmann distribution using the parameters μ and σ 2 to fit this model. As a case study, we implemented the J–SIGMA methodology on three families of population-based metaheuristics: Swarm, Evolutionary, and Estimation of Distribution, and used a set of continuous optimization functions from CEC’17 to evaluate their performance against other metaheuristics of each family. Finally, from a statistical analysis of the convergence performance, the evidence is shown to affirm that the J–SIGMA methodology can significantly improve the convergence performance of the algorithms, regardless of the metaheuristic family to which it belongs.

Differential evolution with perturbation for continuous function optimization

Differential evolution with perturbation for continuous function optimization

Determining the optimal strategy for aggregate production planning (APP) during the Covid-19 crisis using an algorithm Harmony Search Algorithm

Determining the optimal strategy for aggregate production planning (APP) during the Covid-19 crisis using an algorithm Harmony Search Algorithm

Systematic Review of Enhancement of Artificial Bee Colony Algorithm Using Ant Colony Pheromone

The artificial bee colony (ABC) is a well-studied algorithm developed to solve continuous function optimization problems by Karboga and Akay in 2009. ABC has been proven to be more effective than other biological-inspired algorithms with good exploration. However, ABC suffers from low exploitation and slow convergence in some cases. The ABC algorithm study has risen significantly over the past decade, with many researchers trying to improve ABC performance and apply it to solve problems. One method to enhance ABC is to borrow exploration technique from other algorithms. Researchers use pheromone, which is a technique used by Ant Colony optimization algorithm, to enhance ABC and addressed several aspects of using a pheromone to enhance the ABC. This systematic review aims to review and analysis articles about using pheromone to enhance ABC. Articles on related topics were systematically searched in four major databases namely Scopus, Web of Science, Association for Computing Machinery ACM and Google Scholar. To ensure that all research articles were considered the start date is not restrictions the search carry out till February 2021.Five articles were selected based on our inclusion and exclusion criteria for the systematic review. The results show that the use Pheromone to enhance ABC can increase the ABC exploitation ability and overcoming the late convergence. This paper also illustrates several potential pheromone using for future work.

A Comparative Study of Common Nature-Inspired Algorithms for Continuous Function Optimization.

Over previous decades, many nature-inspired optimization algorithms (NIOAs) have been proposed and applied due to their importance and significance. Some survey studies have also been made to investigate NIOAs and their variants and applications. However, these comparative studies mainly focus on one single NIOA, and there lacks a comprehensive comparative and contrastive study of the existing NIOAs. To fill this gap, we spent a great effort to conduct this comprehensive survey. In this survey, more than 120 meta-heuristic algorithms have been collected and, among them, the most popular and common 11 NIOAs are selected. Their accuracy, stability, efficiency and parameter sensitivity are evaluated based on the 30 black-box optimization benchmarking (BBOB) functions. Furthermore, we apply the Friedman test and Nemenyi test to analyze the performance of the compared NIOAs. In this survey, we provide a unified formal description of the 11 NIOAs in order to compare their similarities and differences in depth and a systematic summarization of the challenging problems and research directions for the whole NIOAs field. This comparative study attempts to provide a broader perspective and meaningful enlightenment to understand NIOAs.

An improved elephant herding optimization using sine–cosine mechanism and opposition based learning for global optimization problems

An improved elephant herding optimization (EHOI) is proposed for continuous function optimization, financial stress prediction problem and two engineering optimization problems in this work. Elephant Herding Optimization (EHO) is a swarm-based algorithm and was inspired by the social behaviour of elephant clans. In the literature, EHO has received great attention from researchers due to its global optimization capability and ease of implementation. However, it has few limitations like random replacing of worst individual and lack of exploitation, which leads to slow convergence. In this work, EHO was enhanced with the help of the position updating mechanism of sine–cosine algorithm (SCA) and opposition-based learning (OBL). The separating operator in original EHO was replaced by the sine–cosine mechanism and followed by opposition-based learning was introduced to increase the performance of EHO. The proposed EHOI was compared with eight well-known meta-heuristic optimization algorithms (MAs) by using 23 classical benchmark functions, 10 modern CEC2019 benchmark test functions and two engineering optimization problems. From the results, it was observed that the proposed EHOI outperformed most of the selected MAs in terms of solution quality. A kernel extreme learning machine (KELM) model was optimized by improved EHO and applied to handle financial stress prediction. The efficiency of the proposed EHOI_KELM model was tested on two popular financial datasets and compared with popular classifiers, EHO_KELM and SCA_KELM models. The results demonstrate that the proposed EHOI_KELM model shows excellent performance than the popular classifiers, EHO_KELM & SCA_KELM models and it can also serve as an effective tool for financial prediction.

A study of hybridization of abc for continuous function optimization- a survey

Swarm intelligence algorithms are meta heuristics that simulates the nature for solving optimization problems, Artificial Bee Colony (ABC) algorithm is one of the most recent nature inspired algorithms which used for problem optimization, numerous research efforts has been concentrated in this particular area. However, the Artificial Bee Colony performance of the local search process and the bee movement or the solution improvement equation still has some weaknesses. The Artificial Bee Colony is good in avoiding trapping at the local optimum but it spends its time searching around unpromising random selected solutions, in order to overcome these limitations as well as to broaden the scope and viability of nature inspired algorithms many variations of this algorithm are being presented and the results being very amazing. This paper presents an overview of some of the hybridized meta heuristics with Artificial Bee Colony algorithm for continuous function optimization; many benchmark functions have been used to show the validity of every approach.

A detailed study about CDW-PSO, BWO and GM-CPSO methods on continuous function optimization

Gauss map based chaotic particle swarm optimization (GM-CPSO) is a state-of-the-art method involving the necessary chaotic map for PSO and has proved itself in global optimization, hybrid classifier design, etc. GM-CPSO can outperform recent techniques such as chaotic dynamic weight PSO (CDW-PSO), outclassing 20 optimization methods. However, the behavior of GM-CPSO on continuous characterized functions is unknown. As the main aim, this paper comprehensively determines the performance of GM-CPSO specifically on continuous function optimization. Black widow optimization (BWO) includes a non-stable population size that cannot be fixed. In BWO, the population can increase without any intervention during iterations, which prevents an objective comparison of the method with other methods. Thus, as the second aim, a new viewpoint on BWO population size selection is suggested for an objective comparison of the method. In various disciplines, stochastic optimization is inevitable to efficiently perform function optimization. Here, the necessary question concerns with which method the best convergence and performance can be achieved. As the third aim, we evaluate three state-of-the-art optimization methods to answer this question. To realize all of these aims, GM-CPSO is compared with CDW-PSO and BWO methods by using 10 continuous benchmark functions to perform a detailed comparison and reveal which one can achieve reliable scores on low-, middle-, and high-dimensional problems. Fitness-based comparisons, computation time analysis, and convergence-based evaluations are presented to determine the robustness of algorithms. As a result, GM-CPSO arises as the most remarkable method, especially for the middle-and high-dimensional continuous functions.

Research on Improved Chaotic Particle Optimization Algorithm Based on Complex Function

In order to improve the performance of Particle Swarm Optimization (PSO) algorithm in solving continuous function optimization problems, a chaotic particle optimization algorithm for complex functions is proposed. Firstly, the algorithm uses qubit Bloch spherical coordinate coding scheme to initialize the initial position of the population. This coding method can expand the ergodicity of the search space, increase the diversity of the population, and further accelerate the convergence speed of the algorithm. Secondly, Logistic chaos is used to search the elite individuals of the population, which effectively prevents the PSO algorithm from falling into local optimization, thus obtaining higher quality optimal solution. Finally, complex functions are used to improve chaotic particles to further improve the convergence speed and optimization accuracy of PSO algorithm. Through the optimization tests of four complex high-dimensional functions, the simulation results show that the improved algorithm is more competitive and its overall performance is better, especially suitable for the optimization of complex high-dimensional functions.

A Velocity-Combined Local Best Particle Swarm Optimization Algorithm for Nonlinear Equations

Many people use traditional methods such as quasi-Newton method and Gauss–Newton-based BFGS to solve nonlinear equations. In this paper, we present an improved particle swarm optimization algorithm to solve nonlinear equations. The novel algorithm introduces the historical and local optimum information of particles to update a particle’s velocity. Five sets of typical nonlinear equations are employed to test the quality and reliability of the novel algorithm search comparing with the PSO algorithm. Numerical results show that the proposed method is effective for the given test problems. The new algorithm can be used as a new tool to solve nonlinear equations, continuous function optimization, etc., and the combinatorial optimization problem. The global convergence of the given method is established.

Data Estimation of Injury-Prone Sports by 3D Image Joint Probability Distribution

The objective of the paper is to study and analyze sports injuries from multiple perspectives. The reduction of damage risk factors of young athletes in sports would reduce or avoid the occurrence of sports injuries. The obtained point cloud data is preprocessed by three-dimensional (3D) image technology for the registration of the cloud data to be registered. The parallel Bayesian network structure was established to realize the parallelization of the probability distribution estimation algorithm. The research results have shown that the parallel probability distribution estimation algorithm would provide a great degree of efficiency improvement in terms of solving continuous function optimization and real-time optimization problems, as well as the problems of improving the efficiency of the algorithm to some extent. It could be inferred that the combination of improved rasterized nearest point search method has shortened the search time of the nearest point, thereby improving the efficiency of the algorithm. The correctness and rationality of the algorithm were verified from both theoretical and practical perspectives.

Hybridizing Bees Algorithm with Firefly Algorithm for Solving Complex Continuous Functions

In this article, two hybrid schemes using the Bees Algorithm (BA) and the Firefly Algorithm (FA) are presented for numerical complex problem resolution. The BA is a recent population-based optimization algorithm, which tries to imitate the natural behaviour of honey bees foraging for food. The FA is a swarm intelligence technique based upon the communication behaviour and the idealized flashing features of tropical fireflies. The first approach, called the Hybrid Bee Firefly Algorithm (HBAFA), centres on improvements to the BA with FA during the local search thus increasing exploitation in each research zone. The second one, namely the Hybrid Firefly Bee Algorithm (HFBA), uses FA in the initialization step for a best exploration and detection of promising areas in research space. The performance of the novel hybrid algorithms was investigated on a set of various benchmarks and compared with standard BA, and other methods found in the literature. The results show that the proposed algorithms perform better than the Standard BA, and confirm their effectiveness in solving continuous optimization functions.

Prediction Optimization of Cervical Hyperextension Injury: Kernel Extreme Learning Machines With Orthogonal Learning Butterfly Optimizer and Broyden- Fletcher-Goldfarb-Shanno Algorithms

In this research, X-ray and MRI images of patients suffering from cervical hyperextension injury are investigated. Also, radiographic images are collected from patients who suffered from trauma but without cervical hyperextension injury. The core engine algorithm of the optimized prediction model is kernel extreme learning machine (KELM), and the input data is 17 factors that may cause cervical hyperextension injury. As the optimization core, we utilized the Butterfly optimization algorithm (BOA). Up to now, few improved variants of BOA have been reported. The original BOA converges slowly and quickly falls into a locally optimal solution. An enhanced BOA based on orthogonal learning, Levy flight, and an exploitation engine is proposed in this paper to relieve these two shortcomings, which is called LBOLBOA. Orthogonal learning is utilized to construct guidance vectors for guiding agents toward the global optimum solution aiming to increase the accuracy of the solutions. Also, Levy flight and Broyden-Fletcher-Goldfarb-Shanno mechanisms are utilized to enrich the intensification propensities of BOA and stagnation avoidance. The proposed LBOLBOA is used to deal with continuous function optimization and machine learning problems, including parameter optimization of KELM. We rigorously verified this variant using a comprehensive set of the benchmark test suite and real-world dataset on cervical hyperextension injury. The results indicate that LBOLBOA can achieve improved performance in dealing with the function optimization and machine learning problems, especially the capability for prediction of cervical hyperextension injury.

Hybridization of ABC for continuous function optimization- A survey

Hybridization of ABC for continuous function optimization- A survey