Dynamic Multi-objective Optimization Research Articles

A modular neural network-based population prediction strategy for evolutionary dynamic multi-objective optimization

This paper presents a novel population prediction algorithm based on modular neural network (PA-MNN) for handling dynamic multi-objective optimization. The proposed algorithm consists of three mechanisms. First, we set up a modular neural network (MNN) and train it with historical population information. Some of the initial solutions are generated by the MNN when an environmental change is detected. Second, some solutions are predicted based on forward-looking center points. Finally, some solutions are generated randomly to maintain the diversity. With these mechanisms, when the new environment has been encountered before, initial solutions generated by MNN will have the same distribution characteristics as the final solutions that were obtained in the same environment last time. Because the initialization mechanism based on the MNN does not need the solutions in recent time, the proposed algorithm can also solve dynamic multi-objective optimization problems with a dramatically and irregularly changing Pareto set. The proposed algorithm is tested on a variety of test instances with different dynamic characteristics and difficulties. The comparisons of experimental results with other state-of-the-art algorithms demonstrate that the proposed algorithm is promising for dealing with dynamic multi-objective optimization.

A feedback-based prediction strategy for dynamic multi-objective evolutionary optimization

Prediction methods are widely used to solve dynamic multi-objective optimization problems (DMOPs). The key to the success of prediction methods lies in the accurate tracking of the new location of the Pareto set (PS) or Pareto front (PF) in a new environment. To improve the prediction accuracy, this paper proposes a novel feedback-based prediction strategy (FPS), which consists of two feedback mechanisms, namely correction feedback (CF) and effectiveness feedback (EF). CF is used to correct an initial prediction model. When the environment changes, CF constructs a representative individual to reflect the characteristics of the current population. The predicted solution of this individual in the new environment is calculated based on the initial prediction model. Afterward, a step size exploration method based on variable classification is introduced to adaptively correct the prediction model. EF is applied to enhance the effectiveness of re-initialization in two stages. In the first stage, half of the individuals in the population are re-initialized based on the corrected prediction model. In the second stage, EF re-initializes the rest of the individuals in the population using two rounds of roulette method based on the re-initialization effectiveness feedback of the first stage. The proposed FPS is incorporated into a dynamic multi-objective optimization evolutionary algorithm (DMOEA) based on decomposition resulting in a new algorithm denoted as MOEA/D-FPS. MOEA/D-FPS is compared with six state-of-the-art DMOEAs on twenty-two different benchmark problems. The experimental results demonstrate the effectiveness and efficacy of MOEA/D-FPS in solving DMOPs.

Concurrent Design of a 2 Dof Five-Bar Parallel Robot a Hybrid Design of Rigid and Flexible Links

In this article, the concurrent optimal design of a planar five-bar parallel robot for a high-speed pick and place task is considered. A trade-off between trajectory tracking, energy consumption and deformation of the flexible links is sought. Due to the high-speed operation, the minimization of the vibratory effect is considered since the design stage. Thus, the design is stated as a non-linear multi-objective dynamic optimization problem that is solved through the Differential Evolution (DE) algorithm, as well as, feasibility rules for constraints handling. Mechanical structural variables that modify the inertial parameters of the rigid and flexible links, as well as, control variables related to gains of a PID controller are considered as independent variables. This problem is subject to maximum torque that each motor could provide; inherent constraints for link manufacture; dimensional synthesis; Grashof’s criterion and initial and boundary conditions. Results show that it is possible, despite the vibrational phenomenon, to reduce the energy consumption without loss of precision through an appropriate mass balance of the actuated links.

Distance-based immune generalised differential evolution algorithm for dynamic multi-objective optimisation

Distance-based immune generalised differential evolution algorithm for dynamic multi-objective optimisation

Distance-based immune generalised differential evolution algorithm for dynamic multi-objective optimisation

This paper presents distance-based immune generalised differential evolution (DIGDE), an improved algorithmic approach to tackle dynamic multi-objective optimisation problems (DMOPs). Its novelty i...

A heredity-based adaptive variation operator for reinitialization in dynamic multi-objective problems

A reinitialization approach is an effective way of generalizing a static multi-objective optimization method to a dynamic one. It is usually comprised of a prediction operator for predicting the approximate location(s) of the optimal solution(s) and a variation operator for enhancing the diversity of the reinitialized solution(s) after a change. While many recent studies have focused on prediction methods, the importance of the variation operator has usually been overlooked. This study systematically explores the effects of the accuracy of the prediction method employed as well as the frequency and severity of the change on the optimal strength of the variation used for reinitialization. Subsequently, it introduces an adaptive variation operator for dynamic multi-objective optimization which can learn the optimal variation strength on-the-fly. To develop this method, firstly, a heredity measure for evolutionary algorithms is formulated to quantify the contribution of each reinitialized solution to the optimization process by measuring the presence of its traits in the final population. Some carefully designed descriptive simulations are performed to explore the capability of the proposed method to learn the optimal variation strength and its sensitivity to the change severity, initial variation strength, and accuracy of the employed prediction method. Finally, the performance of this variation operator on 42 dynamic multi-objective test problems is compared with those of five other popular ones, with numerical comparisons revealing its superior learning capability.

Design of optimal wine distillation recipes using multi-criteria decision-making techniques

In this work, dynamic multi-objective optimization and multi-criteria decision making (MCDM) techniques were applied to design recipes for optimal alembic wine distillations. The optimization problem considered eight objectives associated with sensorial quality, food safety, productivity, and efficiency. Through correlation analysis of the optimal solutions, it was possible to reduce the original objectives into four conflicting objectives. Seven MCDM methods were tested to select the best recipes considering five scenarios. In the equal priority scenario, each multi-criterion decision-making algorithm selected different solutions. In scenarios with higher priority for a single objective, most multi-criteria decision-making algorithms selected similar or identical solutions. A well balanced performance was achieved when a high priority was assigned to ethanol recovery. This work´s methodology can be easily adapted to define recipes for the optimal operation of any fruit batch distillation process.

A Mixture-of-Experts Prediction Framework for Evolutionary Dynamic Multiobjective Optimization.

Dynamic multiobjective optimization requires the robust tracking of varying Pareto-optimal solutions (POS) in a changing environment. When a change is detected in the environment, prediction mechanisms estimate the POS by utilizing information from previous populations to accelerate search toward the true POS. To achieve a robust prediction of POS, a mixture-of-experts-based ensemble framework is proposed. Unlike existing approaches, the framework utilizes multiple prediction mechanisms to improve the overall prediction. A gating network is applied to manage switching among the various predictors based on performance of the predictors at different time intervals of the optimization process. The efficacy of the proposed framework is validated through experimental studies based on 13 dynamic multiobjective benchmark optimization problems. The simulation results show that the proposed framework improves the dynamic optimization performance significantly, particularly for: 1) problems with distinct dynamic POS in decision space over time and 2) problems with highly nonlinear decision variable linkages.

Dynamic Multiobjective Optimization with Multiple Response Strategies Based on Linear Environment Detection

Dynamic multiobjective optimization problems (DMOPs) bring more challenges for multiobjective evolutionary algorithm (MOEA) due to its time-varying characteristic. To handle this kind of DMOPs, this paper presents a dynamic MOEA with multiple response strategies based on linear environment detection, called DMOEA-LEM. In this approach, different types of environmental changes are estimated and then the corresponding response strategies are activated to generate an efficient initial population for the new environment. DMOEA-LEM not only detects whether the environmental changes but also estimates the types of linear changes so that different prediction models can be selected to initialize the population when the environmental changes. To study the performance of DMOEA-LEM, a large number of test DMOPs are adopted and the experiments validate the advantages of our algorithm when compared to three state-of-the-art dynamic MOEAs.

Vine copula-based EDA for dynamic multiobjective optimization

Dynamic Multiobjective Problems cover a set of real-world problems that have many conflicting objectives. These problems are challenging and well known by the dynamic nature of their objective functions, constraint functions, and problem parameters which often change over time. In fact, dealing with these problems has not been investigated in detail using the Estimation of Distribution Algorithms (EDAs). Thus, we propose in this paper an EDA-based on Vine Copulas algorithm to deal with Dynamic Multiobjective Problems (DMOPs). Vines Copulas are graphical models that represent multivariate dependence using bivariate copulas. The proposed Copula-based Estimation of Distribution Algorithm, labeled Dynamic Vine-Copula Estimation of Distribution Algorithm (DynVC-EDA), is used to implement two search strategies. The first strategy is an algorithm that uses the model as a memory to save the status of the best solutions obtained during the current generation. The second strategy is a prediction-based algorithm that uses the history of the best solutions to predict a new population when a change occurs. The proposed algorithms are tested using a set of benchmarks provided with CEC2015 and the Gee-Tan-Abbass. Statistical findings show that the DynVC-EDA is competitive to the state-of-the-art methods in dealing with dynamic multiobjective optimization.

Climatic Impact Toward Regional Water Allocation and Transfer Strategies from Economic, Social and Environmental Perspectives

Aiming to store water in wet seasons and outflow water in dry seasons, and improve reservoirs’ performance, are of great importance. Given the developmental disparities across regions and uneven precipitation within one year, water transfer could be an efficient solution. Here, we formulated a three-stage decision-making framework to simulate possible hydrological, meteorological, economic, and demographic parameters in future scenarios and proposed a market-based dynamic multi-objective optimization model, which optimized the adjusted water allocation and water transfers strategies among regions. A case study was conducted in the Yiluo river basin to evaluate the optimal proportion of local water use and water transfers to verify the application and its effects. Results indicated that water use stress and environmental stress could be relieved from four simulated future scenarios, which further accelerated region- and basin-scale sustainability. The results also gave valuable insights into optimal water use options and transferred to maximize the economic, social, and environmental benefits and climate mitigation.

Dynamic multiobjective optimization for thrust allocation in ship application

Thrust allocation is a key procedure in the dynamic position system (DPS) of marine vessels. The present work aims to study the characteristics of dynamic optimization in thrust allocation. A two-phase analysis process is proposed. In phase-I, the model for thrust allocation is generated from the viewpoint of multiobjective optimization. Fuel consumption and tear-and-wear on the thrusters are chosen as objectives. Multiobjective feasibility enhanced particle swarm optimization algorithm (MOFEPSO) is applied to find the Pareto set of this problem. An additional decision-making procedure, the technique of order preference by similarity to ideal solution (TOPSIS) is utilized to choose the final compromise solution in phase-II. The self-organizing map (SOM) technique is undertaken to mine the Pareto data set. A Remote Operated Vehicle (ROV) example is provided for illustrating the above analysis process. The effects of relative importance between objectives upon characteristics of thrust allocation are studied. The trajectories of decision variables and objectives are examined through the SOM method. Results from numerical examples demonstrate that the multiobjective optimization method together with decision-making skills can extend the application of optimization in the thrust allocation field. The findings in this work add to the understanding of relationships among several aspects of DPS.

Reducing Offloading Latency for Digital Twin Edge Networks in 6G

6G is envisioned to empower wireless communication and computation through the digitalization and connectivity of everything, by establishing a digital representation of the real network environment. Mobile edge computing (MEC), as one of the key enabling factors, meets unprecedented challenges during mobile offloading due to the extremely complicated and unpredictable network environment in 6G. The existing works on offloading in MEC mainly ignore the effects of user mobility and the unpredictable MEC environment. In this paper, we present a new vision of Digital Twin Edge Networks (DITEN) where digital twins (DTs) of edge servers estimate edge servers’ states and DT of the entire MEC system provides training data for offloading decision. A mobile offloading scheme is proposed in DITEN to minimize the offloading latency under the constraints of accumulated consumed service migration cost during user mobility. The Lyapunov optimization method is leveraged to simplify the long-term migration cost constraint to a multi-objective dynamic optimization problem, which is then solved by $Actor$ - $Critic$ deep reinforcement learning. Simulations results show that our proposed scheme effectively diminishes the average offloading latency, the offloading failure rate, and the service migration rate, as compared with benchmark schemes, while saving the system cost with DT assistance.

A prediction strategy based on decision variable analysis for dynamic Multi-objective Optimization

Abstract Many multi-objective optimization problems in reality are dynamic, requiring the optimization algorithm to quickly track the moving optima after the environment changes. Therefore, response strategies are often used in dynamic multi-objective algorithms to find Pareto optimal. In this paper, we propose a hybrid prediction strategy based on the classification of decision variables, which consists of three steps. After detecting the environment change, the first step is to analyze the influence of each decision variable on individual convergence and distribution in the new environment. The second step is to adopt different prediction methods for different decision variables. Finally, adaptive selection is applied to the solution set generated in the first and second steps, and solutions with good convergence and diversity are selected to make the initial population more adaptable to the new environment. The prediction strategy can help the solution set converge while maintaining its diversity. The experimental results and performance show that the proposed algorithm is capable of significantly improving the dynamic optimization performance compared with five state-of-the-art evolutionary algorithms.

Solving Dynamic Multiobjective Problem via Autoencoding Evolutionary Search.

Dynamic multiobjective optimization problem (DMOP) denotes the multiobjective optimization problem, which contains objectives that may vary over time. Due to the widespread applications of DMOP existed in reality, DMOP has attracted much research attention in the last decade. In this article, we propose to solve DMOPs via an autoencoding evolutionary search. In particular, for tracking the dynamic changes of a given DMOP, an autoencoder is derived to predict the moving of the Pareto-optimal solutions based on the nondominated solutions obtained before the dynamic occurs. This autoencoder can be easily integrated into the existing multiobjective evolutionary algorithms (EAs), for example, NSGA-II, MOEA/D, etc., for solving DMOP. In contrast to the existing approaches, the proposed prediction method holds a closed-form solution, which thus will not bring much computational burden in the iterative evolutionary search process. Furthermore, the proposed prediction of dynamic change is automatically learned from the nondominated solutions found along the dynamic optimization process, which could provide more accurate Pareto-optimal solution prediction. To investigate the performance of the proposed autoencoding evolutionary search for solving DMOP, comprehensive empirical studies have been conducted by comparing three state-of-the-art prediction-based dynamic multiobjective EAs. The results obtained on the commonly used DMOP benchmarks confirmed the efficacy of the proposed method.

Individual-Based Transfer Learning for Dynamic Multiobjective Optimization.

Dynamic multiobjective optimization problems (DMOPs) are characterized by optimization functions that change over time in varying environments. The DMOP is challenging because it requires the varying Pareto-optimal sets (POSs) to be tracked quickly and accurately during the optimization process. In recent years, transfer learning has been proven to be one of the effective means to solve dynamic multiobjective optimization. However, the negative transfer will lead the search of finding the POS to a wrong direction, which greatly reduces the efficiency of solving optimization problems. Minimizing the occurrence of negative transfer is thus critical for the use of transfer learning in solving DMOPs. In this article, we propose a new individual-based transfer learning method, called an individual transfer-based dynamic multiobjective evolutionary algorithm (IT-DMOEA), for solving DMOPs. Unlike existing approaches, it uses a presearch strategy to filter out some high-quality individuals with better diversity so that it can avoid negative transfer caused by individual aggregation. On this basis, an individual-based transfer learning technique is applied to accelerate the construction of an initial population. The merit of the IT-DMOEA method is that it combines different strategies in maintaining the advantages of transfer learning methods as well as avoiding the occurrence of negative transfer; thereby greatly improving the quality of solutions and convergence speed. The experimental results show that the proposed IT-DMOEA approach can considerably improve the quality of solutions and convergence speed compared to several state-of-the-art algorithms based on different benchmark problems.

Dynamic multi-objective evolutionary algorithm for IoT services

The primary goal of the Internet of things(IoT) is to provide people with anywhere services in real life. But intelligent IoT shouldn’t only provide services, but also consider how to allocate heterogeneous resources reasonably, which has become a very challenging problem. To obtain the best resource allocation scheme, it is crucial to minimize the service cost and service time. Since the two objectives are contradictory, we have modelled IoT services as a dynamic multi-objective optimization problem. Then a dynamic multi-objective evolutionary algorithm for dynamic IoT services(dMOEA/DI) is proposed. In dMOEA/DI, we have designed operators such as the appropriate encoding method, dynamic detection operator, filtering strategy, differential evolution, and polynomial mutation. Based on the single service strategy and collaborative service strategy, experimental research is performed on the agricultural IoT services with dynamic requests under different distributions. The simulation experimental results prove that dMOEA/DI performs better than the contrasted algorithms on the IoT service optimization problems.

Performance Assessment of a set of Multi-Objective Optimization Algorithms for Solution of Economic Emission Dispatch Problem

This paper addresses the realistic economic emission dispatch (EED) problem by considering the operating fuel cost and environmental emission as two conflicting objectives, and power balance and generator limits as two constraints. A novel dynamic multi-objective optimization algorithm, namely the multi-objective differential evolution with recursive distributed constraint handling (RDC-MODE) has been proposed and successfully employed to address this challenging EED problem. It has been thoroughly investigated in two different test cases at three different load demands. The efficiency of the RDC-MODE is also compared with two other multi-objective evolutionary algorithms (MOEAs), namely, the non-dominated sorting genetic algorithm (NSGA-II) and multi-objective particle swam optimization (MOPSO). Performance evaluation is carried out by comparing the Pareto fronts, computational time and three non-parametric performance metrics. The statistical analysis is also performed, to demonstrate the ascendancy of the proposed RDC-MODE algorithm. Investigation of the performance metrics revealed that the proposed RDC-MODE approach was capable of providing good Pareto solutions while retaining sufficient diversity. It renders a wide opportunity to make a trade-off between operating cost and emission under different challenging constraints.

A reinforcement learning approach for dynamic multi-objective optimization

Dynamic Multi-objective Optimization Problem (DMOP) is emerging in recent years as a major real-world optimization problem receiving considerable attention. Tracking the movement of Pareto front efficiently and effectively over time has been a central issue in solving DMOPs. In this paper, a reinforcement learning-based dynamic multi-objective evolutionary algorithm, called RL-DMOEA, which seamlessly integrates reinforcement learning framework and three change response mechanisms, is proposed for solving DMOPs. The proposed algorithm relocates the individuals based on the severity degree of environmental changes, which is estimated through the corresponding changes in the objective space of their decision variables. When identifying different severity degree of environmental changes, the proposed RL-DMOEA approach can learn better evolutionary behaviors from environment information, based on which apply the appropriate response mechanisms. Specifically, these change response mechanisms including the knee-based prediction, center-based prediction and indicator-based local search, are devised to promote both convergence and diversity of the algorithm under different severity of environmental changes. To verify this idea, the proposed RL-DMOEA is evaluated on CEC 2015 test problems involving various problem characteristics. Empirical studies on chosen state-of-the-art designs validate that the proposed RL-DMOEA is effective in addressing the DMOPs.

Weighted pointwise prediction method for dynamic multiobjective optimization

Prediction methods are useful tools for dynamic multiobjective optimization (DMO), especially if the changes roughly follow some patterns. Multi-model prediction methods, in particular, may capture different types of change patterns; however, they should address two issues. First, they should define a similarity measure that can correctly find the corresponding Pareto-optimal solutions in two successive time steps. Second, they should be reasonably robust to input errors. This study introduces a new information-sharing strategy to improve the robustness of multi-model prediction methods in which each prediction model utilizes some information from the individual models of adjacent solutions. An adaptive scheme based on the relative distribution of population members is also proposed to utilize this information properly. The efficacy of this strategy in improving the robustness of the multi-model prediction method is demonstrated. Furthermore, this study introduces a similarity metric and thoroughly analyzes it alongside some of the commonly used similarity metrics for DMO. A weighted pointwise prediction method (WPPM) for DMO is then developed using the formulated information-sharing strategy and the proposed variable-based similarity metric. WPPM is compared with other well-known prediction methods on the CEC2018 test suite for DMO, with the numerical results revealing the superiority of WPPM.