Algorithms For Dynamic Optimization Problems Research Articles

Orthogonal Design-Based Control Vector Parameterization Combined With Improved Seagull Optimization Algorithm for Dynamic Optimization Problems

Orthogonal Design-Based Control Vector Parameterization Combined With Improved Seagull Optimization Algorithm for Dynamic Optimization Problems

A New Approach to Enhanced Swarm Intelligence Applied to Video Target Tracking.

This work proposes a new approach to improve swarm intelligence algorithms for dynamic optimization problems by promoting a balance between the transfer of knowledge and the diversity of particles. The proposed method was designed to be applied to the problem of video tracking targets in environments with almost constant lighting. This approach also delimits the solution space for a more efficient search. A robust version to outliers of the double exponential smoothing (DES) model is used to predict the target position in the frame delimiting the solution space in a more promising region for target tracking. To assess the quality of the proposed approach, an appropriate tracker for a discrete solution space was implemented using the meta-heuristic Shuffled Frog Leaping Algorithm (SFLA) adapted to dynamic optimization problems, named the Dynamic Shuffled Frog Leaping Algorithm (DSFLA). The DSFLA was compared with other classic and current trackers whose algorithms are based on swarm intelligence. The trackers were compared in terms of the average processing time per frame and the area under curve of the success rate per Pascal metric. For the experiment, we used a random sample of videos obtained from the public Hanyang visual tracker benchmark. The experimental results suggest that the DSFLA has an efficient processing time and higher quality of tracking compared with the other competing trackers analyzed in this work. The success rate of the DSFLA tracker is about 7.2 to 76.6% higher on average when comparing the success rate of its competitors. The average processing time per frame is about at least 10% faster than competing trackers, except one that was about 26% faster than the DSFLA tracker. The results also show that the predictions of the robust DES model are quite accurate.

Polynomial approximation of inequality path constraints in dynamic optimization

We propose an algorithm for dynamic optimization problems with inequality path constraints. It solves a sequence of approximated problems where the path constraint is imposed on a finite number of points. Between adjacent points, an approximating polynomial of the constraint value is calculated and an additional constraint is imposed on the maximum value of this polynomial. We consider Taylor and Hermite polynomials. New points are added based on constraint violations or large approximations errors of the approximating polynomials. We prove finite convergence to a feasible point assuming: (i) the dynamic optimization problem has a Slater point, (ii) pointwise constraints are respected at each iteration. We compare the performance of the algorithm with the algorithm by Fu et at. (Automatica 62, 2015, p. 184–192) for three small case studies and an up-to-date industrial application where we calculate optimal feed rates for a semi-batch emulsion polymerization reactor. The results show that our proposed algorithm needs to solve fewer subproblems, i.e. fewer iterations, at the cost of more constraints, resulting in smaller CPU times.

Flexible Wolf Pack Algorithm for Dynamic Multidimensional Knapsack Problems.

Optimization problems especially in a dynamic environment is a hot research area that has attracted notable attention in the past decades. It is clear from the dynamic optimization literatures that most of the efforts have been devoted to continuous dynamic optimization problems although the majority of the real-life problems are combinatorial. Moreover, many algorithms shown to be successful in stationary combinatorial optimization problems commonly have mediocre performance in a dynamic environment. In this study, based on binary wolf pack algorithm (BWPA), combining with flexible population updating strategy, a flexible binary wolf pack algorithm (FWPA) is proposed. Then, FWPA is used to solve a set of static multidimensional knapsack benchmarks and several dynamic multidimensional knapsack problems, which have numerous practical applications. To the best of our knowledge, this paper constitutes the first study on the performance of WPA on a dynamic combinatorial problem. By comparing two state-of-the-art algorithms with the basic BWPA, the simulation experimental results demonstrate that FWPA can be considered as a feasibility and competitive algorithm for dynamic optimization problems.

Dual-archive-based particle swarm optimization for dynamic optimization

In dynamic optimization problems, although the problem environments keep changing, a new environment is usually related to its previous environments. Based on the relevance, the search experience in the previous environments can be reused to accelerate the optimization of the current new environment. Thus, in this paper, we propose a dual-archive-based particle swarm optimization to utilize the useful information accumulated in past environments as well as to explore the emerging information of each new environment. Specifically, in the proposed algorithm, the good solutions found in past environments are stored in two different archives, i.e., a fine-grained archive and a coarse-grained archive, so as to preserve both detailed information and systemic information, respectively. Once the environment is changed, the solutions in the two archives will be used for guidance to quickly find high-quality solutions in the new environment. The proposed algorithm is evaluated on the famous moving peaks benchmark in terms of two performance measures. The experimental results show that the proposed algorithm is competitive with state-of-the-art algorithms for dynamic optimization problems.

A novel framework for improving multi-population algorithms for dynamic optimization problems: A scheduling approach

This paper presents a novel framework for improving the performance of multi-population algorithms in solving dynamic optimization problems (DOPs). The fundamental idea of the proposed framework is to incorporate the concept of scheduling into multi-population methods with the aim to allocate more function evaluations to the best performing sub-populations. Two methods are developed based on the proposed framework, each of which uses a different approach for scheduling the sub-populations. The first method combines the quality of sub-populations and the degree of diversity among them into a single feedback parameter for detecting the best performing sub-population. The second method uses the learning automata as the central unit for performing the scheduling operation. In order to validate the applicability of the proposed methods, they are incorporated into three well-known algorithms for DOPs. The experimental results show the efficiency of the scheduling approach for improving the multi-population methods on the moving peaks benchmark (MPB) and generalized dynamic benchmark generator.

A dual-population multi operators harmony search algorithm for dynamic optimization problems

Abstract Dynamic optimization problems (DOPs) have been widely researched in recent years. This is due to its numerous practical applications in real-life conditions. To solve DOPs, the optimizer should be able to track the changes and simultaneously seek for global optima in the search space. This paper proposes a dual population multi operators harmony search algorithm for DOPs to deal with changes in the problem landscape. The main difference between the proposed algorithm and other techniques are twofold: dual population for exploring and exploiting the search space, and the use of multi operators at different points of the search. Extensive experiments were conducted on the Moving Peaks Benchmark (MPB) and six dynamic test functions proposed in the IEEE Congress on Evolutionary Computation (CEC 2009) were used to evaluate the performance of the proposed algorithm. Empirical results indicate the superiority of the proposed algorithm when compared to state-of-the-art algorithms from the literature.

Multi-Operator Genetic Algorithm for Dynamic Optimization Problems

Multi-Operator Genetic Algorithm for Dynamic Optimization Problems

Multi-Operator Genetic Algorithm for Dynamic Optimization Problems

<span lang="EN-US">Maintaining population diversity is the most notable challenge in solving dynamic optimization problems (DOPs). Therefore, the objective of an efficient dynamic optimization algorithm is to track the optimum in these uncertain environments, and to locate the best solution. In this work, we propose a framework that is based on multi operators embedded in genetic algorithms (GA) and these operators are heuristic and arithmetic crossovers operators. The rationale behind this is to address the convergence problem and to maintain the diversity. The performance of the proposed framework is tested on the well-known dynamic optimization functions i.e., OneMax, Plateau, Royal Road and Deceptive. Empirical results show the superiority of the proposed algorithm when compared to state-of-the-art algorithms from the literature.</span>

New measures for comparing optimization algorithms on dynamic optimization problems

Dynamic optimization problems have emerged as an important field of research during the last two decades, since many real-world optimization problems are changing over time. These problems need fast and accurate algorithms, not only to locate the optimum in a limited amount of time but also track its trajectories as close as possible. Although lots of research efforts have been given in developing dynamic benchmark generator/problems and proposing algorithms to solve these problems, the role of numerical performance measurements have been barely considered in the literature. Several performance criteria have been already proposed to evaluate the performance of algorithms. However, because they only take confined aspects of the algorithms into consideration, they do not provide enough information about the effectiveness of each algorithm. In this paper, at first we review the existing performance measures and then we present a set of two measures as a framework for comparing algorithms in dynamic environments, named fitness adaptation speed and alpha–accuracy. A comparative study is then conducted among different state-of-the-art algorithms on moving peaks benchmark via proposed metrics, along with several other performance measures, to demonstrate the relative advantages of the introduced measures. We hope that the collected knowledge in this paper opens a door toward a more comprehensive comparison among algorithms for dynamic optimization problems.

Adaptive-mutation compact genetic algorithm for dynamic environments

In recent years, the interest in studying nature-inspired optimization algorithms for dynamic optimization problems (DOPs) has been increasing constantly due to its importance in real-world applications. Several techniques such as hyperselection, change prediction, hypermutation and many more have been developed to address DOPs. Among these techniques, the hypermutation scheme has proved beneficial for addressing DOPs, but requires that the mutation factors be picked a priori and this is one of the limitations of the hypermutation scheme. This paper investigates variants of the recently proposed adaptive-mutation compact genetic algorithm (amcGA). The amcGA is made up of a change detection scheme and mutation schemes, where the degree of change regulates the probability of mutation (i.e. the probability of mutation is directly proportional to the degree of change). This paper also presents a change trend scheme for the amcGA so as to boost its performance whenever a change occurs. Experimental results show that the change trend and mutation schemes have an impact on the performance of the amcGA in dynamic environment and also indicate that the effect of the schemes depends on the dynamics of the environment as well as the dynamic problem being considered.

Memetic Algorithm for Dynamic Optimization Problems

optimization problems has attracted much attention of researchers. However, due to complexity and uncertainty to solve dynamic optimization problems, it very difficult to find out the optimum solution that could be changed over time. Thus, it is necessary to develop efficient or improved an algorithms to solve dynamic optimization problems. A memetic algorithm that based on local search along with an evolutionary algorithm such as genetic algorithm can be used to tackle dynamic optimization problems. This paper investigates the use of multi-crossover operator that is based on heuristic and arithmetic with GA as well as local search for dynamic optimization problems. The proposed approach utilises solution features in terms of diversity and selection to generate better solution. To evaluate the efficiency and feasibility of the proposed operator, a comparison between the results of this study and the results of different works is conducted through a number of evaluations over dynamic optimization problems with various levels of difficulty. The significant findings emerge from this study are the efficiency of the proposed algorithm in solving dynamic environments when compared with other method.

Diploidy in evolutionary algorithms for dynamic optimization problems

Purpose – In this work, the authors show the performance of the proposed diploid scheme (a representation where each individual contains two genotypes) with respect to two dynamic optimization problems, while addressing drawbacks the authors have identified in previous works which compare diploid evolutionary algorithms (EAs) to standard EAs. The paper aims to discuss this issue. Design/methodology/approach – In the proposed diploid representation of EA, each individual possesses two copies of the genotype. In order to convert this pair of genotypes to a single phenotype, each genotype is individually evaluated in relation to the fitness function and the best genotype is presented as the phenotype. In order to provide a fair and objective comparison, the authors make sure to compare populations which contain the same amount of genetic information, where the only difference is the arrangement and interpretation of the information. The two representations are compared using two shifting fitness functions which change at regular intervals to displace the global optimum to a new position. Findings – For small fitness landscapes the haploid (standard) and diploid algorithms perform comparably and are able to find the global optimum very quickly. However, as the search space increases, rediscovering the global optimum becomes more difficult and the diploid algorithm outperforms the haploid algorithm with respect to how fast it relocates the new optimum. Since both algorithms use the same amount of genetic information, it is only fair to conclude it is the unique arrangement of the diploid algorithm that allows it to explore the search space better. Originality/value – The diploid representation presented here is novel in that instead of adopting a dominance scheme for each allele (value) in the vector of values that is the genotype, dominance is adopted across the entire genotype in relation to its homologue. As a result, this representation can be extended across any alphabet, for any optimization function.

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 DE and PSO based hybrid algorithm for dynamic optimization problems

Many real world optimization problems are dynamic in which the fitness landscape is time dependent and the optima change over time. Such problems challenge traditional optimization algorithms. For such problems, optimization algorithms not only have to find the global optimum but also need to closely track its trajectory. In this paper, a new hybrid algorithm integrating a differential evolution (DE) and a particle swarm optimization (PSO) is proposed for dynamic optimization problems. Multi-population strategy is adopted to enhance the diversity and try to keep each subpopulation on a different peak in the fitness landscape. A hybrid operator combining DE and PSO is designed, in which each individual is sequentially carried out DE and PSO operations. An exclusion scheme is proposed that integrates the distance based exclusion scheme with the hill-valley function to track the adjacent peaks. The algorithm is applied to the set of benchmark functions used in CEC 2009 competition for dynamic environment. Experimental results show that it is more effective in terms of overall performance than other comparative algorithms.

A Distributed Subgradient Method for Dynamic Convex Optimization Problems Under Noisy Information Exchange

We consider a convex optimization problem for non-hierarchical agent networks where each agent has access to a local or private time-varying function, and the network-wide objective is to find a time-invariant minimizer of the sum of these functions, provided that such a minimizer exists. Problems of this type are common in dynamic systems where the objective function is time-varying because of, for instance, the dependency on measurements that arrive continuously to each agent. A typical outer-loop optimization iteration for optimization problems of this type consists of a local optimization step based on the information provided by neighboring agents, followed by a consensus step to exchange and fuse local estimates of the agents. A great deal of research effort has been directed towards developing and better understanding such algorithms, which find many applications in distinct areas such as cognitive radio networks, distributed acoustic source localization, coordination of unmanned vehicles, and environmental modeling. Contrasting with existing work, which considers either dynamic systems or noisy links (but not both jointly), in this study we devise and analyze a novel distributed online algorithm for dynamic optimization problems in noisy communication environments. The main result of the study proves sufficient conditions for almost sure convergence of the algorithm as the number of iterations tends to infinity. The algorithm is applicable to a wide range of distributed optimization problems with time-varying cost functions and consensus updates corrupted by additive noise. Our results therefore extend previous work to include recently proposed schemes that merge the processes of computation and data transmission over noisy wireless networks for fast and efficient consensus protocols. To give a concrete example of an application, we show how to apply our general technique to the problem of distributed detection with adaptive filters.

Best practices in measuring algorithm performance for dynamic optimization problems

Dynamic optimization problems (DOPs) have attracted considerable attention due to the wide range of problems they can be applied to. Lots of efforts have been expended in modeling dynamic situations, proposing algorithms, and analyzing the results (too often in a visual way). Numeric performance measurements and their statistical validation have been however barely used in the literature. Most of works in DOPs report only the best-of-generation fitness, due to its simplicity of computation. Although this measure indicates the best algorithm in terms of fitness, it does not provide any details about the actual strength and weakness of each algorithm. In this article, we conduct a comparative study among algorithms of different search modes via several performance measures to demonstrate their relative advantages. We discuss the role of using different performance measures in drawing balanced conclusions about algorithms for DOPs.

Novel Hybrid Evolutionary Algorithm for Dynamic Optimization Problems and Its Application in an Ethylene Oxide Hydration Reactor

A novel hybrid evolutionary algorithm (HEA) that combines the genetic algorithm (GA) and particle swarm optimization (PSO) is proposed to solve the dynamic optimization problems of chemical processes using numerical methods. Based on the characteristics of dynamic optimization problems, the concept of “search region reduction” is integrated into the HEA to improve the convergence rate. A control vector parametrization (CVP) method based on the HEA is also employed to improve the accuracy of the results. The dynamic optimization problem with state variable constraints is an important research area in process system engineering and is difficult to solve. Thus, the present work also proposes a novel method embedding information about infeasible chromosomes into the evaluation function to solve dynamic optimization problems with or without state variable constraints. The results of several case studies demonstrate the feasibility and efficiency of the proposed methods. Finally, the proposed methods are used to solve the temperature distribution problem in an ethylene oxide hydration reactor. Moreover, the proposed algorithm can be regarded as a useful optimization tool, especially when gradient information is unavailable.

Particle Swarm Optimization With Composite Particles in Dynamic Environments

In recent years, there has been a growing interest in the study of particle swarm optimization (PSO) in dynamic environments. This paper presents a new PSO model, called PSO with composite particles (PSO-CP), to address dynamic optimization problems. PSO-CP partitions the swarm into a set of composite particles based on their similarity using a "worst first" principle. Inspired by the composite particle phenomenon in physics, the elementary members in each composite particle interact via a velocity-anisotropic reflection scheme to integrate valuable information for effectively and rapidly finding the promising optima in the search space. Each composite particle maintains the diversity by a scattering operator. In addition, an integral movement strategy is introduced to promote the swarm diversity. Experiments on a typical dynamic test benchmark problem provide a guideline for setting the involved parameters and show that PSO-CP is efficient in comparison with several state-of-the-art PSO algorithms for dynamic optimization problems.

Multi-population Based Univariate Marginal Distribution Algorithm for Dynamic Optimization Problems

Many real-world problems are dynamic optimization problems in which the optimal solutions need to be continuously tracked over time. In this paper a multi-population based univariate marginal distribution algorithm (MUMDA) is proposed to solve dynamic optimization problems. The main idea of the algorithm is to construct several probability models by dividing the population into several parts. The objective is to divide the search space into several regions to maintain the diversity. Concretely, MUMDA uses one probability vector to do the search in the promising areas identified previously, and uses other probability vectors to search for new promising optimal solutions. Moreover the convergence of univariate marginal distribution algorithm (UMDA) is proved, which can be used to analyze the validity of the proposed algorithm. Finally, the experimental study was carried out to compare the performance of several UMDA, and the results show that the MUMDA is effective and can be well adaptive to the dynamic environments rapidly.