Infeasible Regions Research Articles

COST OPTIMIZATION METHOD FOR INFORMATIONAL INFRASTRUCTURE DEPLOYMENT IN STATIC MULTI-CLOUD ENVIRONMENT

Context. In recent years, the topic of deploying informational infrastructure in a multi-cloud environment has gained popularity. This is because a multi-cloud environment provides the ability to leverage the unique services of cloud providers without the need to deploy all infrastructure components inside them. Therefore, all available services across different cloud providers could be used to build up information infrastructure. Also, multi-cloud offers versatility in selecting different pricing policies for services across different cloud providers. However, as the number of available cloud service providers increases, the complexity of building a costoptimized deployment plan for informational infrastructure also increases. Objective. The purpose of this paper is to optimize the operating costs of information infrastructure while leveraging the service prices of multiple cloud service providers. Method. This article presents a novel cost optimization method for informational infrastructure deployment in a static multicloud environment whose goal is to minimize the hourly cost of infrastructure utilization. A genetic algorithm was used to solve this problem. Different penalty functions for the genetic algorithm were considered. Also, a novel parameter optimization method is proposed for selecting the parameters of the penalty function. Results. A series of experiments were conducted to compare the results of different penalty functions. The results demonstrated that the penalty function with the proposed parameter selection method, in comparison to other penalty functions, on average found the best solution that was 8.933% better and took 18.6% less time to find such a solution. These results showed that the proposed parameter selection method allows for efficient exploration of both feasible and infeasible regions. Conclusion. A novel cost optimization method for informational infrastructure deployment in a static multi-cloud environment is proposed. However, despite the effectiveness of the proposed method, it can be further improved. In particular, it is necessary to consider the possibility of involving scalable instances for informational infrastructure deployment.

A Multi‐Objective Evolutionary Algorithm Based on Bilayered Decomposition for Constrained Multi‐Objective Optimization

This paper proposes a multi‐objective evolutionary algorithm based on bilayered decomposition (MOEA/BLD) for solving constrained multi‐objective optimization problems. MOEA/D is an effective method for solving unconstrained multi‐objective optimization problems. It decomposes the objective space using weight vectors and simultaneously searches for solutions for the subproblems. However, real‐world applications impose many constraints, and these constraints must be handled appropriately when searching for good feasible solutions. The proposed MOEA/BLD treats such constraints as an additional objective function. Furthermore, in addition to the conventional weight vector, an augmented weight vector is introduced that decomposes the objective space and constraint violation space hierarchically. In the first stage, the objective space is decomposed by conventional weight vectors. In the next stage, the bi‐objective space consisting of the scalarizing function and constraint violation is decomposed by augmented weight vectors. The augmented weights are adjusted so that they decrease linearly in the search process as the search gradually moves from infeasible regions to feasible regions. The proposed algorithm is compared to several state‐of‐the‐art constrained MOEA/Ds using multi‐ and many‐objective problems. The results show that the proposed method outperforms existing methods, in terms of search performance, under various conditions. © 2024 Institute of Electrical Engineers of Japan and Wiley Periodicals LLC.

An adaptive co-evolutionary competitive particle swarm optimizer for constrained multi-objective optimization problems

In constrained multi-objective optimization problems, it is challenging to balance the convergence, diversity and feasibility of the population, especially encountering complex infeasible regions. In order to effectively balance the three indicators, from the aspects of the handling of infeasible solution and the quality of individuals, a multi-population co-evolutionary competitive particle swarm optimization algorithm hybridized with infeasible solution transfer and an adaptive technique (ACCPSO) is proposed. Firstly, the information of feasible and infeasible individuals is fully utilized and the individuals are classified by Hamming distance. Then, a novel constraint handling technique based on learning from the promising feasible direction is designed to make individuals cross large infeasible regions and explore more potential feasible regions. Moreover, aiming to provide robust search capability and consequently further generate high-quality solutions, the genetic operators and the particle swarm optimization operator with the competitive mechanism are introduced as operators with an adaptive mechanism. Finally, compared with the state-of-the-art methods, the performance of the proposed algorithm is verified on LIR-CMOP, MW and DTLZ, as well as two real-world problems. The results indicate that ACCPSO exhibits stronger competitiveness in terms of convergence, the solution quality, and distribution diversity on the feasible Pareto front.

A staged fuzzy evolutionary algorithm for constrained large-scale multiobjective optimization

Constrained multiobjective optimization problems (CMOPs) are prevalent in practical applications, where constraints play a significant role. Building on techniques from constrained single-objective optimization, classical methods such as the constrained dominance principle have been extended to CMOPs. However, these methods struggle with CMOPs characterized by complex infeasible regions. Furthermore, as the number of decision variables increases, the search efficiency of algorithms deteriorates dramatically. To solve those issues, we propose a staged fuzzy evolutionary algorithm (i.e., SFEA) for constrained large-scale problems. To balance exploration and exploitation, a fuzzy stage adjustment strategy based on the sigmoid function is proposed. Furthermore, this article develops an improved fuzzy operator to perform fuzzy operations on various vectors (e.g., solutions or constraint violations). Computational experiments were conducted on CMOP test suites with up to 500 decision variables and a series of real-world applications. The experimental results demonstrate that, compared to existing peer algorithms, our algorithm exhibits superior or competitive performance.

Deep reinforcement learning assisted novelty search in Voronoi regions for constrained multi-objective optimization

Solving constrained multi-objective optimization problems (CMOPs) requires optimizing multiple conflicting objectives while satisfying various constraints. Existing constrained multi-objective evolutionary algorithms (CMOEAs) cross infeasible regions by ignoring constraints. However, these methods might neglect promising search directions, leading to insufficient exploration of the search space. To address this issue, this paper proposes a deep reinforcement learning assisted constrained multi-objective quality-diversity algorithm. The proposed algorithm designs a diversity maintenance mechanism to promote evenly coverage of the final solution set on the constrained Pareto front. Specifically, first, a novelty-oriented archive is created using a centroid Voronoi tessellation, which divides the search space into a desired number of Voronoi regions. Each region acts as a repository of non-dominated solutions with different phenotypic characteristics to provide diversity information and supplementary evolutionary trails. Secondly, to improve resource utilization, a deep Q-network is adopted to learn a policy to select suitable Voronoi regions for offspring generation based on their novelty scores. The exploration of these regions aims to find a set of diverse, high-performing solutions to accelerate convergence and escape local optima. Compared with eight state-of-the-art CMOEAs, experimental studies on four benchmark suites and nine real-world applications demonstrate that the proposed algorithm exhibits superior or at least competitive performance, especially on problems with discrete and narrow feasible regions.

Manifold-assisted coevolutionary algorithm for constrained multi-objective optimization

In constrained multi-objective optimization problems (CMOPs), constraints often fragment the Pareto solution space into multiple feasible and infeasible regions. This fragmentation presents a challenge for evolutionary optimization methods as feasible regions can be discrete and isolated by infeasible areas, making exploration difficult and leading to populations getting trapped in local optima. To address these issues, this paper introduces a manifold assisted coevolutionary algorithm for solving CMOPs. Firstly, a guided feasible search strategy is proposed to explore feasible regions, especially those isolated by infeasible barriers. This is achieved by estimating directions to the Constrained Pareto Set (CPS). Secondly, a manifold learning-based exploration strategy is employed to spread the population along the Pareto Set (PS) manifold by estimating the manifold distribution. Moreover, two populations are exploited, where the first population serves as the primary population, considering both constraints and objectives to explore the feasible region and search along the CPS. The second population, on the other hand, does not consider constraints and serves as an auxiliary population to explore the Unconstrained PS. By cooperating, these two populations effectively approach and cover separated CPS segments. The proposed algorithm is evaluated against seven state-of-the-art algorithms on 37 CMOP test functions and 5 CMOPs with fraudulent constraints. The experimental results clearly demonstrate that our algorithm can reliably locate multiple CPSs and is considered state-of-the-art in handling CMOPs.

Multi-timescale dispatch technology for islanded energy system in the Gobi Desert

The Gobi Desert has vast wilderness to utilize, and its renewable energy capacity experiencing rapid growth. To better allocate regulation resources for maintaining power balance and frequency regulation capacity, an islanded grid optimization model considering multi-timescale dispatch optimization is constructed for integrating chemical parks with thermal power units, energy storage, and green hydrogen production. In the day-ahead optimization stage, to improve the level of renewable energy consumption, the ladder-type regulation performance of thermal power units involved in deep peak load with frequency regulation capacity is derived and established. Moving to the real-time frequency regulation stage, a novel graph neural network-based technique with infeasible region modification is proposed to rapidly acquire the operational power scheme. The input features are the time series of total power command, regulation capacity, past operating power, and past mileage command. And the output features are the mileage commands received by the resources. Training data are generated through offline optimization with the genetic algorithm, which utilizes renewable energy generation and load data with a scale of three months in the Gobi Desert. In the one-month simulation test, the proposed method demonstrated a reduction in power deviation by approximately 32.7 % and an improvement in accuracy by roughly 16 %.

Adaptive multi-stage evolutionary search for constrained multi-objective optimization

In this paper, we propose a multi-stage evolutionary framework with adaptive selection (MSEFAS) for efficiently handling constrained multi-objective optimization problems (CMOPs). MSEFAS has two stages of optimization in its early phase of evolutionary search: one stage that encourages promising infeasible solutions to approach the feasible region and increases diversity, and the other stage that enables the population to span large infeasible regions and accelerates convergence. To adaptively determine the execution order of these two stages in the early process, MSEFAS treats the optimization stage with higher validity of selected solutions as the first stage and the other as the second one. In addition, at the late phase of evolutionary search, MSEFAS introduces a third stage to efficiently handle the various characteristics of CMOPs by considering the relationship between the constrained Pareto fronts (CPF) and unconstrained Pareto fronts. We compare the proposed framework with eleven state-of-the-art constrained multi-objective evolutionary algorithms on 56 benchmark CMOPs. Our results demonstrate the effectiveness of the proposed framework in handling a wide range of CMOPs, showcasing its potential for solving complex optimization problems.

Multi-objective optimization algorithm for multi-workflow computation offloading in resource-limited IIoT

Industrial internet of things (IIoT) connects traditional industrial devices with the network to provide intelligent services, which is regarded as the key technology for achieving Industry 4.0 and enabling the transformation of the manufacturing sector. Multi-access edge computing (MEC) has brought significant opportunities to expedite the development of IIoT. However, the unique task characteristics and dense deployment of IIoT devices, coupled with the resource starvation problem (RSP) arising from the limited resources of edge servers, pose challenges to the direct applicability of existing MEC algorithms in MEC-assisted IIoT scenarios. To this end, a multi-objective evolutionary algorithm is proposed to simultaneously optimize delay and energy consumption for multi-workflow execution in resource-limited IIoT. First, the initialization of execution location based on delay and the initialization of execution order satisfying the priority constraint can generate high-quality initial solutions. Then, the improved crossover and mutation operations guide the population evolution, which can span the large infeasible solution region. Finally, dynamic task scheduling (DTS) dynamically changes the execution location of tasks affected by RSP according to the execution efficiency, so as to avoid the tasks blindly waiting for server resources. The comprehensive simulation results demonstrate the effectiveness of the proposed method in achieving a balance between the execution delay and energy consumption of IIoT devices.

Precision manipulation by an optically induced dielectrophoresis system based on an improved A-star algorithm

Cell manipulation using optically induced dielectrophoresis (ODEP) in a microfluidic system has drawn much attention due to its simplicity and being damage-free at the cellular level. Additionally, to improve its manipulation efficiency and accuracy, automatic manipulation methods have been applied in the ODEP system. However, the current automatic manipulation methods of ODEP rarely consider the impact of non-manipulated targets on cell manipulation, thereby reducing the operating efficiency and accuracy. Here, we propose a new, to our knowledge, automatic manipulation method of ODEP based on a path planning algorithm of the improved A-star. First, the maximum influence range of ODEP force generated by the virtual electrode was investigated by a numerical simulation, and it was also taken as the limit to expand the scope of the infeasible region in path planning to avoid the impact of the non-operational target on manipulation accuracy. Then, an improved A-star algorithm with target range constraints was proposed to optimize the manipulation path and improve the operation efficiency. Finally, experiments on cell separation were also carried out to validate the feasibility of the proposed automatic manipulation method. This work provides an automated method to improve the accuracy of ODEP manipulation, which is of great significance to further promote the application of ODEP in cell manipulation.

A dual-population auxiliary multiobjective coevolutionary algorithm for constrained multiobjective optimization problems

The key to solving constrained multiobjective optimization problems (CMOPs) lies in maintaining the feasibility, convergence, and diversity of the population. In recent years, various constraint handling techniques (CHTs) and strategies have been proposed to enhance the performance of constrained multiobjective evolutionary algorithms (CMOEAs). However, most of these algorithms face difficulties in dealing with problems that have large infeasible regions and discontinuous small feasible regions, as they have trouble crossing large infeasible regions while simultaneously maintaining the convergence and diversity of the population. To tackle this issue, this paper proposes a dual-population auxiliary coevolutionary algorithm with an enhanced operator, denoted as DAEAEO. Auxiliary population 1 employs an improved ϵ-constraint handling technique to provide high-quality feasible solutions for the main population. Auxiliary population 2 adopts the non-dominated sorting method to provide favorable objective information for the main population to help it cross the infeasible region. In addition, to further improve diversity, each population adopts an enhanced operator and a genetic operator to generate offspring, respectively. Finally, knowledge transfer between offspring is realized. Compared to six state-of-the-art CMOEAs on DASCMOPs, LIR-CMOPs, DOC test suites, and two real-world problems, the proposed DAEAEO achieved superior performance, especially for CMOPs with large infeasible regions and discontinuous small feasible regions.

Efficient hybrid strategy for simultaneous design of refinery hydrogen networks and pressure swing adsorption unit

Refineries face increasing hydrogen demand due to the consumption of heavy and sour crude oil. This study presents a novel hybrid method to optimize hydrogen network configurations with a rigorous pressure swing adsorption (PSA) process model. This method utilizes Bayesian optimization to address the upper-level unknown constraints black-box optimization problem while employing deterministic algorithms to manage the lower-level nonlinear programming problem. Furthermore, infeasible regions are transformed into feasible ones by introducing a dummy stream, and the costs incurred during the transformation process are accurately calculated. The proposed method is validated using two literature cases. In Case 1, Bayesian optimization outperformed the Kriging model, resulting in a 7.84% reduction in total annual cost (TAC). In Case 2, a comparison of four search strategies revealed the developed two-phase strategy as the most effective one. This method offers a powerful and practical tool for optimizing real-world hydrogen networks with PSA processes.

Probabilistic graph networks for learning physics simulations

Inductive biases play a critical role in enabling Graph Networks (GN) to learn particle and mesh-based physics simulations. In this paper, we propose two generalizable inductive biases that minimize rollout error and energy accumulation. GNs conditioned on the input states and relying on the Mean Squared Error (MSE) loss function implicitly assume Gaussian-distributed output errors. Consequently, GNs may either assign probability densities to infeasible regions in the state space of the deterministic physics problem or fail to assign densities to feasible regions. Instead, we advocate for maximizing the likelihood of the actual target distribution, challenging the underlying assumptions of MSE-based regression models using our proposed conditional normalizing flows (cNF) decoder. We discover that this inductive bias enables GNs to significantly improve their next state prediction accuracy. Existing sequential GNs encode temporal dependencies by autoregressively processing the latent representations of the input data. In our work, we find that inducing the Arrow-of-Time inductive bias through an auto-regressive encoding step before autoregressively processing the resulting latent vectors enables GNs to better minimize rollout error. We critically analyze the impact of existing inductive biases on rollout error and energy accumulation and discover that the choice of biases encoded in a GN, rather than the number of inductive biases, has a substantial impact on forward simulation prediction.

Constrained Bayesian Optimization with Lower Confidence Bound

In this article, we present a hybrid Bayesian optimization (BO) framework to solve constrained optimization problems by adopting a state-of-the-art acquisition function from the unconstrained BO literature, the well-known lower confidence bound acquisition function and propose a novel variant that analyzes the feasible and infeasible regions which ensure the theoretical convergence guarantee. The proposed variant is compared with the existing state-of-the-art approaches in the constrained BO literature via implementing these approaches on six different problems, including black-box, classical engineering, and hyperparameter tuning problems. Further, we demonstrate the effectiveness of our approach through graphical and statistical testing.

A two-stage bidirectional coevolution algorithm with reverse search for constrained multiobjective optimization

Constrained multiobjective optimization problems (CMOPs) are widespread in reality. The presence of constraints complicates the feasible region of the original problem and increases the difficulty of problem solving. There are not only feasible regions, but also large areas of infeasible regions in the objective space of CMOPs. Inspired by this, this paper proposes a bidirectional coevolution method with reverse search (BCRS) combined with a two-stage approach. In the first stage of evolution, constraints are ignored and the population is pushed toward promising regions. In the second stage, evolution is divided into two parts, i.e., the main population evolves toward the constrained Pareto front (CPF) within the feasible region, while the reverse population approaches the CPF from the infeasible region. Then a solution exchange strategy similar to weak cooperation is used between the two populations. The experimental results on benchmark functions and real-world problems show that the proposed algorithm exhibits superior or at least competitive performance compared to other state-of-the-art algorithms. It demonstrates BCRS is an effective algorithm for addressing CMOPs.Graphical

A novel tri-stage with reward-switching mechanism for constrained multiobjective optimization problems

The effective exploitation of infeasible solutions plays a crucial role in addressing constrained multiobjective optimization problems (CMOPs). However, existing constrained multiobjective optimization evolutionary algorithms (CMOEAs) encounter challenges in effectively balancing objective optimization and constraint satisfaction, particularly when tackling problems with complex infeasible regions. Subsequent to the prior exploration, this paper proposes a novel tri-stage with reward-switching mechanism framework (TSRSM), including the push, pull, and repush stages. Each stage consists of two coevolutionary populations, namely Pop1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\ ext {Pop}}_1$$\\end{document} and Pop2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\ ext {Pop}}_2$$\\end{document}. Throughout the three stages, Pop1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\ ext {Pop}}_1$$\\end{document} is tasked with converging to the constrained Pareto front (CPF). However, Pop2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\ ext {Pop}}_2$$\\end{document} is assigned with distinct tasks: (i) converging to the unconstrained Pareto front (UPF) in the push stage; (ii) utilizing constraint relaxation technique to discover the CPF in the pull stage; and (iii) revisiting the search for the UPF through knowledge transfer in the repush stage. Additionally, a novel reward-switching mechanism (RSM) is employed to transition between different stages, considering the extent of changes in the convergence and diversity of populations. Finally, the experimental results on three benchmark test sets and 30 real-world CMOPs demonstrate that TSRSM achieves competitive performance when compared with nine state-of-the-art CMOEAs. The source code is available at https://github.com/Qu-jq/TSRSM.

Boundary-aware value function generation for safe stochastic motion planning

Navigation safety is critical for many autonomous systems such as self-driving vehicles in an urban environment. It requires an explicit consideration of boundary constraints that describe the borders of any infeasible, non-navigable, or unsafe regions. We propose a principled boundary-aware safe stochastic planning framework with promising results. Our method generates a value function that can strictly distinguish the state values between free (safe) and non-navigable (boundary) spaces in the continuous state, naturally leading to a safe boundary-aware policy. At the core of our solution lies a seamless integration of finite elements and kernel-based functions, where the finite elements allow us to characterize safety-critical states’ borders accurately, and the kernel-based function speeds up computation for the non-safety-critical states. The proposed method was evaluated through extensive simulations and demonstrated safe navigation behaviors in mobile navigation tasks. Additionally, we demonstrate that our approach can maneuver safely and efficiently in cluttered real-world environments using a ground vehicle with strong external disturbances, such as navigating on a slippery floor and against external human intervention.

Constraint subsets-based evolutionary multitasking for constrained multiobjective optimization

Constrained multiobjective optimization problems (CMOPs) are challenging because they need to optimize multiple conflicting objectives and satisfy various constraints simultaneously. To solve CMOPs, various constrained multiobjective evolutionary algorithms have been proposed in recent years. However, most of them tackle constraints by considering all constraints or zero constraint scenarios, these extreme treatment methods may be unable to utilize the information of multiple constraint subsets composed of partial constraints to maintain more promising infeasible solutions. To remedy this issue, a constraint subsets-based evolutionary multitasking method is developed, where a CMOP is transformed into a multitasking optimization problem by creating multiple simple auxiliary CMOPs. Particularly, the original CMOP is the main task, while the newly created CMOPs with different constraint subsets are the auxiliary tasks. Each task will be evolved by one specific population, and the knowledge transfer is conducted among tasks to realize the collaborative search. Meanwhile, the updating of the auxiliary task involves two stages. In the first stage, each auxiliary population will evolve to approach the pareto front of the constraint subset (s-CPF), promoting crossing the infeasible regions. While in the second stage, a feasible region-based search mechanism is proposed to approach the pareto front of the main task from each s-CPF, by utilizing unique and promising infeasible solutions. In addition, systematic experiments are carried out on three benchmark test suites and four real-world CMOPs. The experimental results fully demonstrate that the proposed algorithm is highly competitive with other state-of-the-art constrained multiobjective evolutionary algorithms.

Efficient Task Scheduling Approach in Edge-Cloud Continuum based on Flower Pollination and Improved Shuffled Frog Leaping Algorithm

The rise of edge-cloud continuum computing is a result of the growing significance of edge computing, which has become a complementary or substitute option for traditional cloud services. The convergence of networking and computers presents a notable challenge due to their distinct historical development. Task scheduling is a major challenge in the context of edge-cloud continuum computing. The selection of the execution location of tasks, is crucial in meeting the quality-of-service (QoS) requirements of applications. An efficient scheduling strategy for distributing workloads among virtual machines in the edge-cloud continuum data center is mandatory to ensure the fulfilment of QoS requirements for both customer and service provider. Existing research used metaheuristic algorithm to solve tak scheduling problem, however, must of the existing metaheuristics used suffers from falling into local mina due to their inefficiency to avoid unfeasible region in the solution search space. Therefore, there is a dire need for an efficient metaheuristic algorithm for task scheduling. This study proposed an FPA-ISFLA task scheduling model using hybrid flower pollination and improved shuffled frog leaping algorithms. The simulation results indicate that the FPA-ISFLA algorithm is superior to the PSO algorithm in terms of makespan time, resource utilization, and execution cost reduction, especially with an increasing number of tasks.

A double auxiliary optimization constrained multi-objective evolutionary algorithm

In evolutionary constrained multi-objective optimization, the use of auxiliary optimization is gradually attracting attention. It is noted that different forms of auxiliary optimization have different advantages. Combining these advantages in an appropriate manner can further improve the algorithm’s performance. Motivated by this inspiration, we propose a double auxiliary optimization constrained multi-objective evolutionary algorithm, namely DAO. In DAO, two auxiliary optimizations, i.e., the unconstrained optimization and the (M+1)-objective optimization, are applied in a proposed tri-population co-evolution strategy. In this strategy, three populations are used to optimize the core optimization and the two auxiliary optimizations in an interactive evolution form. Furthermore, DAO develops a (M+1)-objective environmental selection strategy to deeply explore the boundary between the feasible and infeasible regions. In experimental studies, the performance of DAO and four other state-of-the-art algorithms is evaluated on three distinct benchmark test suites and two intricate real-world problem scenarios. The outcome of the comprehensive evaluation shows the competitive of DAO solving constrained multi-objective optimization problems.