Continuous Dynamic Optimization Research Articles

Vulnerability Evolution Mechanism of High-Speed Railway Construction System in the Goaf Site of Qinshui Coalfield

The main reason for serious consequences caused by disasters is “insufficient emergency preparedness and obvious system vulnerability”. To ensure the safe operation and maintenance of the high-speed railway in goaf sites and achieve effective hierarchical management, the vulnerability theory was introduced, based on the system approach, to explore the characteristics of hierarchical evolution. Firstly, based on the analysis of the internal and external disturbances of the high-speed railway construction system with underlying goaf areas, the vulnerability characteristic elements were defined, and a conceptual vulnerability model was proposed. Secondly, based on the literature research, accident cases, and standards and specifications, 25 factors affecting vulnerability were identified and a two-dimensional cross matrix was used to establish a vulnerability evaluation index system. Then, ISM was used to build hierarchical relationships among indicators, analyze the vulnerability characteristics of direct factors, indirect factors and essential factors, and a vulnerability evolution analysis framework was proposed. Finally, the Taiyuan–Jiaozuo high-speed railway project was selected for hierarchical and progressive vulnerability management. The study analyzed the coupling effect and evolution mechanism of various elements of the safety management system under external disturbances, identified the weak links of the high-speed railway system in the goaf site, and provided a decision-making basis for continuous dynamic optimization and emergency response technology, which complied with the strategic policy of sustainable development.

Optimal R&D investment in the management of invasive species

Invasive alien species (IAS) threaten world biodiversity, ecosystem services, and economic welfare. While existing literature has characterized the optimal control of an established IAS, it has not considered how research and development (R&D) into new removal methods or technologies can affect management decisions and costs over time. R&D can lower the costs of control in a management plan and creates an intertemporal trade-off between quick but costly control and gradual but cheaper removal over time. In this paper, we develop and solve a continuous time dynamic optimization model to study how investment in R&D influences the optimal control of an established invasive species. After characterizing the dynamic model solution, we solve the model numerically to study the benefits from R&D in the management of the brown tree snake (Boiga irregularis), and explore how optimal solutions vary across economic and biological conditions. We find that the introduction of R&D significantly reduces overall costs of IAS and management and that the cost reductions substantially outweigh research expenditure. These results imply that policymakers seeking to control IAS should consider R&D as a vital component of cost effective control strategies.

Dynamic Optimization in Fast-Changing Environments via Offline Evolutionary Search

Dynamic optimization, for which the objective functions change over time, has attracted intensive investigations due to the inherent uncertainty associated with many real-world problems. For its robustness with respect to noise, Evolutionary Algorithms (EAs) have been expected to have great potential for dynamic optimization. Many dynamic optimization methods such as diversity-driven methods, memory methods, and prediction methods have been proposed based on EAs to deal with environmental changes. However, they face difficulties in adapting to fast changes in dynamic optimization as EAs normally need quite a few fitness evaluations to find a near-optimum solution. To address this issue, this paper proposes a new framework of applying EAs in the context of dynamic optimization to deal with fast changing environments. We suggest that, instead of online evolving (searching) solutions for the ever-changing objective function, EAs are more suitable for acquiring an archive of solutions in an offline way, which could be adopted to construct a system to provide high-quality solutions efficiently in a dynamic environment. To be specific, we formulate the offline search as a static set-oriented optimization problem. Then, a set of solutions is obtained by an EA for this set-oriented optimization problem. After this, the obtained solution set is adopted to do fast adaptation to the corresponding dynamic optimization problem. The general framework is instantiated for continuous dynamic constrained optimization problems, and the empirical results show the potential of the proposed framework. The superiority of the framework is also verified on a dynamic vehicle routing problem with changing demands.

A Survey of Evolutionary Continuous Dynamic Optimization Over Two Decades—Part B

This article presents the second Part of a two-Part survey that reviews evolutionary dynamic optimization (EDO) for single-objective unconstrained continuous problems over the last two decades. While in the first part, we reviewed the components of dynamic optimization algorithms (DOAs); in this part, we present an in-depth review of the most commonly used benchmark problems, performance analysis methods, static optimization methods used in the framework of DOAs, and real-world applications. Compared to the previous works, this article provides a new taxonomy for the benchmark problems used in the field based on their baseline functions and dynamics. In addition, this survey classifies the commonly used performance indicators into fitness/error-based and efficiency-based ones. Different types of plots used in the literature for analyzing the performance and behavior of algorithms are also reviewed. Furthermore, the static optimization algorithms that are modified and utilized in the framework of DOAs as the optimization components are covered. We then comprehensively review some real-world dynamic problems that are optimized by EDO methods. Finally, some challenges and opportunities are pointed out for future directions.

A Survey of Evolutionary Continuous Dynamic Optimization Over Two Decades—Part A

Many real-world optimization problems are dynamic. The field of dynamic optimization deals with such problems where the search space changes over time. In this two-part article, we present a comprehensive survey of the research in evolutionary dynamic optimization for single-objective unconstrained continuous problems over the last two decades. In Part A of this survey, we propose a new taxonomy for the components of dynamic optimization algorithms (DOAs), namely, convergence detection, change detection, explicit archiving, diversity control, and population division and management. In comparison to the existing taxonomies, the proposed taxonomy covers some additional important components, such as convergence detection and computational resource allocation. Moreover, we significantly expand and improve the classifications of diversity control and multipopulation methods, which are underrepresented in the existing taxonomies. We then provide detailed technical descriptions and analysis of different components according to the suggested taxonomy. Part B of this survey provides an in-depth analysis of the most commonly used benchmark problems, performance analysis methods, static optimization algorithms used as the optimization components in the DOAs, and dynamic real-world applications. Finally, several opportunities for future work are pointed out.

Benchmarking Continuous Dynamic Optimization: Survey and Generalized Test Suite.

Dynamic changes are an important and inescapable aspect of many real-world optimization problems. Designing algorithms to find and track desirable solutions while facing challenges of dynamic optimization problems is an active research topic in the field of swarm and evolutionary computation. To evaluate and compare the performance of algorithms, it is imperative to use a suitable benchmark that generates problem instances with different controllable characteristics. In this article, we give a comprehensive review of existing benchmarks and investigate their shortcomings in capturing different problem features. We then propose a highly configurable benchmark suite, the generalized moving peaks benchmark, capable of generating problem instances whose components have a variety of properties, such as different levels of ill-conditioning, variable interactions, shape, and complexity. Moreover, components generated by the proposed benchmark can be highly dynamic with respect to the gradients, heights, optimum locations, condition numbers, shapes, complexities, and variable interactions. Finally, several well-known optimizers and dynamic optimization algorithms are chosen to solve generated problems by the proposed benchmark. The experimental results show the poor performance of the existing methods in facing new challenges posed by the addition of new properties.

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.

Optimal Scheduling of Active Distribution Networks With Limited Switching Operations Using Mixed-Integer Dynamic Optimization

The optimal scheduling of active distribution networks (ADNs) significantly enhances voltage security and reduces costs, particularly as the numbers of distributed generation sources and energy storage devices increase. Therefore, this paper proposes a mixed-integer dynamic optimization (MIDO) model for the optimal scheduling of ADNs. This model incorporates loads and distributed generation outputs with continuous trajectories and aims to provide optimal continuous-trajectory schemes for ADNs. The optimization is conducted with the objective of minimizing the daily costs of electricity purchased from distribution substations. However, in practice, discrete control devices are required to adopt a limited number of switching operations, which increase the computational complexity of the MIDO model. Hence, a reduced convex relaxation method is utilized to achieve reduced convex transformation and tight relaxation of the MIDO model with respect to integer variables. This converts the MIDO model into a continuous dynamic optimization model, which is then further approximated as a nonlinear programming model using the Radau collocation method. Meanwhile, the absolute-value constraints limiting the number of switching operations are eliminated by an equivalent conversion to a series of linear inequalities. Numerical simulations on IEEE 33-bus, PG&E 69-bus, and real-world 110-bus ADNs demonstrate the effectiveness and efficiency of the proposed methodology.

A Scalable Test Suite for Continuous Dynamic Multiobjective Optimization.

Dynamic multiobjective optimization (DMO) has gained increasing attention in recent years. Test problems are of great importance in order to facilitate the development of advanced algorithms that can handle dynamic environments well. However, many of the existing dynamic multiobjective test problems have not been rigorously constructed and analyzed, which may induce some unexpected bias when they are used for algorithmic analysis. In this paper, some of these biases are identified after a review of widely used test problems. These include poor scalability of objectives and, more important, problematic overemphasis of static properties rather than dynamics making it difficult to draw accurate conclusion about the strengths and weaknesses of the algorithms studied. A diverse set of dynamics and features is then highlighted that a good test suite should have. We further develop a scalable continuous test suite, which includes a number of dynamics or features that have been rarely considered in literature but frequently occur in real life. It is demonstrated with empirical studies that the proposed test suite is more challenging to the DMO algorithms found in the literature. The test suite can also test algorithms in ways that existing test suites cannot.

Field evaluation of performance of HVAC optimization system in commercial buildings

New smart building technologies that offer continuous dynamic optimization of Heating, Ventilation, and Air Conditioning (HVAC) control hold promise to advance building operations for efficiency and grid response. These technologies use data from the control system to determine the analytically optimal setpoints, and then write back the optimal setpoints into the control system to minimize system energy consumption or costs. There are limited studies documenting field validations of these technologies. This paper presents the results from a long-term field evaluation of a model-predictive HVAC optimization system that installed in four commercial buildings.Energy savings analysis was conducted based on pre/post submetered energy use. Across the cohort of evaluation sites, HVAC savings following the implementation of the optimization system were mixed, ranging from 0–9%. Analysis of site operational data showed that occupant comfort was neither positively nor negatively impacted. Key technology adoption considerations and recommendations are summarized in the paper. The technology performs best when HVAC systems are in good working condition, and can be exercised to achieve the full range of its optimized setpoints–however it may not provide extensive additional savings over cases where best practice sequences of operation and reset strategies are already comprehensively implemented.

Evolutionary and population-based methods versus constructive search strategies in dynamic combinatorial optimization

Optimization in dynamic environments is a hot research area that has attracted a notable attention in the past decade. It is clear from the dynamic optimization literature that most of the effort is devoted to continuous dynamic optimization problems although majority of the real-life problems are combinatorial. Additionally, in comparison to evolutionary or population-based approaches, constructive search strategy, which is shown to be successful in stationary combinatorial optimization problems, is commonly ignored by the dynamic optimization community. In the present work, a constructive and multi-start search strategy is proposed to solve dynamic multi-dimensional knapsack problem, which has numerous applications in real world. Making use of constructive and multi-start features, the aim here is to test the performance of such a strategy and to observe its behavior in dynamically changing environments. In this regard, this strategy is compared to the well-known evolutionary and population-based approaches, including a Genetic Algorithm-based memetic algorithm, Differential Evolution algorithm, Firefly Algorithm and a hyper-heuristic, which employs these population-based algorithms as low-level heuristics in accordance with their individual contributions. Furthermore, in order to improve their performances in dynamic environments, the mentioned evolutionary algorithms are enhanced by using triggered random immigrants and adaptive hill climbing strategies. As one can see from the comprehensive experimental analysis, while the proposed approach outperforms most of the evolutionary-based approaches, it is outperformed by firefly and hyper-heuristic algorithms in some of the instances. This points out competiveness of the proposed approaches. Finally, according to the statistical results of non-parametric tests, one can conclude that the proposed approach can be considered as a promising and a competitive algorithm in dynamic environments.

An adaptive bi-flight cuckoo search with variable nests for continuous dynamic optimization problems

This paper presents an adaptive bi-flight cuckoo search algorithm for continuous dynamic optimization problems. Unlike the standard cuckoo search which relies on Levy flight, the proposed method uses two types of flight that are chosen adaptively by a learning automaton to control the global and local search ability of the method during the run. Furthermore, a variable nest scheme and a new cuckoo addition mechanism are introduced. A greedy local search method is also integrated to refine the best found solution. An extensive set of experiments is conducted on a variety of dynamic environments generated by the moving peaks benchmark, to evaluate the performance of the proposed approach. Results are also compared with those of other state-of-the-art algorithms from the literature. The experimental results indicate the effectiveness of the proposed approach.

Continuous Dynamic Constrained Optimization With Ensemble of Locating and Tracking Feasible Regions Strategies

Dynamic constrained optimization problems (DCOPs) are difficult to solve because both objective function and constraints can vary with time. Although DCOPs have drawn attention in recent years, little work has been performed to solve DCOPs with multiple dynamic feasible regions from the perspective of locating and tracking multiple feasible regions in parallel. Moreover, few benchmarks have been proposed to simulate the dynamics of multiple disconnected feasible regions. In this paper, first, the idea of tracking multiple feasible regions, originally proposed by Nguyen and Yao, is enhanced by specifically adopting multiple subpopulations. To this end, the dynamic species-based particle swam optimization (DSPSO), a representative multipopulation algorithm, is adopted. Second, an ensemble of locating and tracking feasible regions strategies is proposed to handle different types of dynamics in constraints. Third, two benchmarks are designed to simulate the DCOPs with dynamic constraints. The first benchmark, including two variants of G24 (called G24v and G24w), could control the size of feasible regions. The second benchmark, named moving feasible regions benchmark (MFRB), is highly configurable. The global optimum of MFRB is calculated mathematically for experimental comparisons. Experimental results on G24, G24v, G24w, and MFRB show that the DSPSO with the ensemble of strategies performs significantly better than the original DSPSO and other typical algorithms.

Multi-population methods in unconstrained continuous dynamic environments: The challenges

The multi-population method has been widely used to solve unconstrained continuous dynamic optimization problems with the aim of maintaining multiple populations on different peaks to locate and track multiple changing peaks simultaneously. However, to make this approach efficient, several crucial challenging issues need to be addressed, e.g., how to determine the moment to react to changes, how to adapt the number of populations to changing environments, and how to determine the search area of each population. In addition, several other issues, e.g., communication between populations, overlapping search, the way to create populations, detection of changes, and local search operators, should be also addressed. The lack of attention on these challenging issues within multi-population methods hinders the development of multi-population based algorithms in dynamic environments. In this paper, these challenging issues are comprehensively analyzed by a set of experimental studies from the algorithm design point of view. Experimental studies based on a set of popular algorithms show that the performance of algorithms is significantly affected by these challenging issues on the moving peaks benchmark.

Optimal interior Earth–Moon Lagrange point transfer trajectories using mixed impulsive and continuous thrust

Optimal interior Earth–Moon Lagrange point transfer trajectories results with fixed flight time using mixed impulsive and continuous thrust propulsion in the framework of the planar Circular Restricted Three-Body Problem are presented. A virtual spacecraft departs geosynchronous or low-Earth orbit and enters a specified Lyapunov orbit around the interior Earth–Moon Lagrange point. For these transfer trajectory designs, a direct transcription and collocation method is employed to reformulate the continuous dynamic optimization problem into a discrete optimization problem, which then is solved using nonlinear programming software. As the design parameters, flight time and relative weighting factor between impulsive and continuous thrust are adjusted in the transfer trajectory design procedure. For practically implementable transfer trajectory designs, the constraints for coast arc and bounded control thrust are applied in the problem formulation as equality and inequality constraints, respectively. In addition, both quadratic performance index and minimum fuel performance index are used to show the relative comparison and analysis in the transfer trajectory design results. According to the relative weighting factor, the transfer trajectories are classified into direct and spiral departure trajectories whose virtual spacecraft directly departs the Earth parking orbit and departs after generating spirals around the Earth, respectively. The convergence of these transfer trajectory design methods are numerically verified by generating varying numbers of nodes and comparing their design results. Especially, the primer vector theory is utilized to analyze the transfer trajectory design results using minimum fuel performance index. Finally, the progressive homotopy continuation method is applied to design low-Earth departure transfer trajectories. These transfer trajectories show that they are numerically and theoretically valid results with the benefit of mixed impulsive and continuous thrust.

A Population Prediction Strategy for Evolutionary Dynamic Multiobjective Optimization

This paper investigates how to use prediction strategies to improve the performance of multiobjective evolutionary optimization algorithms in dealing with dynamic environments. Prediction-based methods have been applied to predict some isolated points in both dynamic single objective optimization and dynamic multiobjective optimization. We extend this idea to predict a whole population by considering the properties of continuous dynamic multiobjective optimization problems. In our approach, called population prediction strategy (PPS), a Pareto set is divided into two parts: a center point and a manifold. A sequence of center points is maintained to predict the next center, and the previous manifolds are used to estimate the next manifold. Thus, PPS could initialize a whole population by combining the predicted center and estimated manifold when a change is detected. We systematically compare PPS with a random initialization strategy and a hybrid initialization strategy on a variety of test instances with linear or nonlinear correlation between design variables. The statistical results show that PPS is promising for dealing with dynamic environments.

A multiple local search algorithm for continuous dynamic optimization

Many real-world optimization problems are dynamic (time dependent) and require an algorithm that is able to track continuously a changing optimum over time. In this paper, we propose a new algorithm for dynamic continuous optimization. The proposed algorithm is based on several coordinated local searches and on the archiving of the optima found by these local searches. This archive is used when the environment changes. The performance of the algorithm is analyzed on the Moving Peaks Benchmark and the Generalized Dynamic Benchmark Generator. Then, a comparison of its performance to the performance of competing dynamic optimization algorithms available in the literature is done. The obtained results show the efficiency of the proposed algorithm.

Continuous Dynamic Constrained Optimization—The Challenges

Many real-world dynamic problems have constraints, and in certain cases not only the objective function changes over time, but also the constraints. However, there is no research in answering the question of whether current algorithms work well on continuous dynamic constrained optimization problems (DCOPs), nor is there any benchmark problem that reflects the common characteristics of continuous DCOPs. This paper contributes to the task of closing this gap. We will present some investigations on the characteristics that might make DCOPs difficult to solve by some existing dynamic optimization (DO) and constraint handling (CH) algorithms. We will then introduce a set of benchmark problems with these characteristics and test several representative DO and CH strategies on these problems. The results confirm that DCOPs do have special characteristics that can significantly affect algorithm performance. The results also reveal some interesting observations where the presence or combination of different types of dynamics and constraints can make the problems easier to solve for certain types of algorithms. Based on the analyses of the results, a list of potential requirements that an algorithm should meet to solve DCOPs effectively will be proposed.

An algorithm comparison for dynamic optimization problems

This work presents a study on the performance of several algorithms on different continuous dynamic optimization problems. Eight algorithms have been used: SORIGA (an Evolutionary Algorithm), an agents-based algorithm, the mQSO (a widely used multi-population PSO) as well as three heuristic-rule-based variations of it, and two trajectory-based cooperative strategies. The algorithms have been tested on the Moving Peaks Benchmark and the dynamic version of the Ackley, Griewank and Rastrigin functions. For each problem, a wide variety of configuration variations have been used, emphasizing the influence of dynamism, and using a full-factorial experimental design. The results give an interesting overview of the properties of the algorithms and their applicability, and provide useful hints to face new problems of this type with the best algorithmic approach. Additionally, a recently introduced methodology for comparing a high number of experimental results in a graphical way is used.

A sustainable fuel strategy for the Iranian passenger cars using a continuous dynamic optimization approach

Using alternative fuels for vehicles is of great importance even in developed countries. The current paper attempts to analyze the possible choices for passenger car fuel and to present an appropriate strategy for choosing an alternative fuel. In this regard, four types of fuels including gasoline as the current prevailing energy content in Iran were selected. The alternatives were LPG, CNG, and hydrogen. Potential strategies have been produced by using a continuous dynamic approach according to political, economical and social objectives. The strategies are statically and dynamically applicable. However, in this study the dynamical continuous approach was selected. The results show that hydrogen as a zero emission fuel is a suitable choice although the cultural and infrastructural obstacles exist against it. The second proposed fuel after gasoline is CNG which is the current choice of the country as an alternative fuel. The methodology presented herein can be extended to more alternatives and wider period in order to gain more comprehensive results.