Dynamic Multi-objective Algorithm Research Articles

Learning to Guide Particle Search for Dynamic Multiobjective Optimization.

Dynamic multiobjective optimization problems (DMOPs) are characterized by multiple objectives that change over time in varying environments. More specifically, environmental changes can be described as various dynamics. However, it is difficult for existing dynamic multiobjective algorithms (DMOAs) to handle DMOPs due to their inability to learn in different environments to guide the search. Besides, solving DMOPs is typically an online task, requiring low computational cost of a DMOA. To address the above challenges, we propose a particle search guidance network (PSGN), capable of directing individuals' search actions, including learning target selection and acceleration coefficient control. PSGN can learn the actions that should be taken in each environment through rewarding or punishing the network by reinforcement learning. Thus, PSGN is capable of tackling DMOPs of various dynamics. Additionally, we efficiently adjust PSGN hidden nodes and update the output weights in an incremental learning way, enabling PSGN to direct particle search at a low computational cost. We compare the proposed PSGN with seven state-of-the-art algorithms, and the excellent performance of PSGN verifies that it can handle DMOPs of various dynamics in a computationally very efficient way.

A Correlation-Guided Layered Prediction Approach for Evolutionary Dynamic Multiobjective Optimization

When solving dynamic multiobjective optimization problems by evolutionary algorithms, the historical moving directions of some special points along the Pareto front, such as the center and knee points, are widely employed to predict the Pareto-optimal solutions (POS). However, special points may be impacted by certain individuals with a large direction deviation, and thus mislead the tracking of dynamic POS. To solve this issue, a correlation-guided layered prediction approach for solving dynamic multiobjective optimization problems is proposed in this paper, where multiple prediction models are integrated by considering the correlation of individuals’ moving directions. To be specific, the population is clustered into three subpopulations (i.e., high, mid, and low correlation) by correlation analysis to perform different prediction behaviors. The high correlation subpopulation aims to predict the moving direction via a linear prediction model. The mid correlation subpopulation is devoted to predicting the manifold change of POS by self-adaptively using the direction and length correction models. The diversity preservation is considered by the low correlation subpopulation. While the three subpopulations focus on different optimization tasks, they also cooperate to track the dynamic POS. The comprehensive experimental results on a variety of benchmark test problems demonstrate the superiority of the proposed approach, as compared with some state-of-the-art prediction-based dynamic multiobjective algorithms.

A dynamic multi-objective optimization method based on classification strategies

The dynamic multi-objective optimization problem is a common problem in real life, which is characterized by conflicting objectives, the Pareto frontier (PF) and Pareto solution set (PS) will follow the changing environment. There are various dynamic multi-objective algorithms have been suggested to solve such problems, but most of the methods suffer from the inability to balance the diversity of populations with convergence. Prediction based method is a common approach to solve dynamic multi-objective optimization problems, but such methods only search for probabilistic models of optimal values of decision variables and do not consider whether the decision variables are related to diversity and convergence. Consequently, we present a prediction method based on the classification of decision variables for dynamic multi-objective optimization (DVC), where the decision variables are first pre-classified in the static phase, and then new variables are adjusted and predicted to adapt to the environmental changes. Compared with other advanced prediction strategies, dynamic multi-objective prediction methods based on classification of decision variables are more capable of balancing population diversity and convergence. The experimental results show that the proposed algorithm DVC can effectively handle DMOPs.

A Self-Learning Based Dynamic Multi-Objective Evolutionary Algorithm for Resilient Scheduling Problems in Steelmaking Plants

Scheduling is one of the most important missions for plant-wide optimization in steelmaking manufacturing systems. In the context of dynamic scheduling, the decision-maker should simultaneously minimize economic objectives within the decision space and violation penalty out of the decision space. In this study, we introduce a resilient scheduling model in steelmaking plants, which provides flexible decisions, including buffering times in between stages and controllable processing speeds in the casting stage, to enable the solution to absorb random disturbances and recover quickly. We formulate the dynamic steelmaking scheduling problem with resilient responding strategies, which is a variant of dynamic multi-objective optimization problems (DMOP), and propose a resilient scheduling optimization framework to solve it over time. First, we employ a vector with problem-specific knowledge to map the whole decision space to sub-schedules in the casting stage, which contains casting priority, casting speed and scaling ratio. Next, we form a multi-objective linear programming model to evaluate these problem-specific vectors. Last but not least, we develop a self-learning based dynamic multi-objective differential evolutionary algorithm to solve the variant DMOP, in which a hypothesis-testing technique is used to detect and identify environmental changes. The sensitivity analysis and algorithm comparisons are performed on a wide range of problem instances under dynamic environments. Experimental evidence validates that the proposed resilient model and the optimization framework is effective to solve the dynamic scheduling problem in steelmaking plants. Note to Practitioners—This paper investigates a dynamic scheduling problem that comes from steelmaking manufacturing systems and is extensively studied in existing works. Because a decision-maker only has incomplete knowledge about the realistic environments, this paper simultaneously considers that both the decision and objective space of a scheduling problem dynamically changed over time. We develop a resilient scheduling model which can absorb the different types or scales of disturbances caused by unforeseen events, and recover rapidly to the original state. We formulate the resilience scheduling model and propose a dynamic multi-objective algorithm based on the self-learning differential evolutionary algorithm to solve it. The effectiveness of the proposed model and algorithm is validated via sensitivity analysis and comparison to other well-known algorithms. Furthermore, the resilient scheduling model and its optimization framework can also be applied to dynamic scheduling problems in other industries.

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.

Cooperative particle swarm optimization with reference-point-based prediction strategy for dynamic multiobjective optimization

Dynamic multiobjective optimization problems (DMOPs) have received increasing attention in the evolutionary community in recent years. The problem environment of a DMOP dynamically changes over time, causing the movement of the Pareto front (PF). It is critical but challenging to find the new PF in a new environment by reusing historical information of past environments since the successive environments are often relevant. Thus, we propose a new cooperative particle swarm optimization with a reference-point-based prediction strategy to solve DMOPs. In the proposed method, multiple swarms cooperate to approximate the whole PF with a new learning strategy in dynamic environments. Specially, when the environment is changed, the outdated particles are relocated based on the PF subparts they belong to using the novel reference-point-based prediction strategy. The proposed algorithm has been evaluated on the very recent scalable dynamic problem test suite with different numbers of objectives and different change severity. Experimental results show that the proposed algorithm is competitive to other typical state-of-the-art dynamic multiobjective algorithms and can find well-diversified and well-converged solution sets in dynamic environments.

A suite of swarm dynamic multi-objective algorithms for rebalancing extremely imbalanced datasets

Imbalanced datasets can be found in a number of fields; they are commonly regarded as big data because of their sheer volume and high attribute dimensions. As the name suggests, imbalanced big datasets come with an extremely imbalanced ratio between the amount of major class and minority class samples. Traditionalmethods: have been attempted but still cannot fully, effectively, and reliably solve the imbalanced class classification problem, especially when the distribution of the classes is exceedingly imbalanced. In this paper, we propose a collection of algorithms to solve the problem of imbalanced datasets in binary data classification. Most traditional methods: rebalance the imbalanced dataset merely by matching the data quantities of the two classes. Our proposed algorithms, which take the form of a suite of variants, focus on guaranteeing the credibility of the classification model and reaching the greatest possible accuracy by dynamically rebalancing the training dataset with multi-objective swarm intelligence optimisation. The new algorithms are extended from those we proposed earlier, which had a single objective – first find a set of solutions that satisfy the Kappa criterion, then search for the solution in the set that offers the highest accuracy. Two main modifications are made in the new algorithms. Multi-objective optimisation is aimed at finding a solution that satisfies several criteria at the same time, such as accuracy and identifying a list of credibility indicators. The other enhancement is the incremental operation of the multi-objective optimisation. Incremental optimisation is imperative for processing data feeds that may arrive in a streaming manner. Instead of waiting for the full data archive to be available before optimisation, incremental optimisation rebalances the data feed segment by segment on the fly. The experimental results from the suite of proposed algorithms show that they can effectively attain better and more stable performances from the classification model and are accompanied by much greater credibility than the other five traditional methods when imbalanced datasets are used as training datasets for inducing a classifier.

A Micro-cloning dynamic multiobjective algorithm with an adaptive change reaction strategy

A Micro-cloning local exploitation and an adaptive change reaction strategy are developed to address complex dynamic multiobjective optimization problems. The former is applied to exploit the uncrowded regions in decision space through cloning a few nondominated individuals, enhancing the exploitation and exploration capability of the proposed algorithm, while the latter accelerates the ability of tracking the changing Pareto front using a specific mechanism. The adaptive change reaction scheme is used to reinitialize the population in terms of a change rate checked and ensure that the proposed algorithm can quickly track each moving Pareto front over time. In addition, a lower computational cost update approach of nondominated set is proposed to obtain a well-distributed and well-spread set of nondominated solutions. We systematically compare the proposed algorithm with several state-of-art algorithms on fourteen dynamic multiobjective test instances with different challenging difficulties, and meanwhile, the performance of these algorithms is compared with each other in terms of several performance measure indicators and nonparametric statistical approaches. Experimental results indicate that the proposed algorithm can obtain a promising tracking ability and well-distributed Pareto front on most of the test instances in each environment.