Solving Dynamic Multiobjective Problem via Autoencoding Evolutionary Search.

Dynamic multi-objective optimization problem (DMOP) denotes the multi-objective optimization problem which varies over time. As changes in DMOP may exist some patterns which are predictable, to solve DMOP, a number of research efforts have been made to develop evolutionary search with prediction approaches to estimate the changes of the problem. A common practice of existing prediction approaches is to predict the change of Pareto-optimal solutions (POS) based on the historical solutions obtained in the decision space. However, the change of a DMOP may occur in both decision and objective spaces. Prediction only in the decision space thus may not be able to give the proper estimation of the problem change. Taking this cue, in this paper, we propose an evolutionary search with multi-view prediction for solving DMOP. In contrast to existing prediction methods, the proposed approach conducts prediction from the views of both decision and objective spaces. To estimate dynamic changes in DMOP, a kernelized autoencoding model is derived to perform the multi-view prediction in a Reproducing Kernel Hilbert Space (RKHS), which holds a closed-form solution. To examine the performance of the proposed method, comprehensive empirical studies on the commonly used DMOP benchmarks, as well as a real-world case study on the movie recommendation problem, are presented. The obtained experimental results verified the efficacy of the proposed method for solving both benchmark and real-world DMOPs.

Adaptive genetic algorithms applied to dynamic multiobjective problems

A pareto-based evolutionary algorithm using decomposition and truncation for dynamic multi-objective optimization

Dynamic multiobjective optimization problem (DMOP) is a class of complex dynamic optimization problem (DOP), its widely exists in many real-world problems. Firstly, an core estimation of distribution model which used to approximately estimate the Pareto solution in the next environment is given, when a change in the environment is detected, the algorithm uses the collected information from the previous searching environments to predict the location of the Pareto solution in the next environment. Furthermore, a dynamic multiobjective optimization evolutionary algorithm with core estimation of distribution is proposed. The computer simulations are made on two dynamic multiobjective optimization problems, and the results indicate the proposed algorithm is effective.

The importance of dynamic multi-objective optimization problems (DMOPs) is on the rise, in complex systems. DMOPs have several objective functions and constraints that vary over time to be considered simultaneously. As a result, the Pareto optimal solutions (POS) and Pareto front (PF) will also vary with time. The desired algorithm should not only locate the optima but also track the moving optima efficiently. In this paper, we propose a new Cultural Algorithm (CA) based on decomposition (CA/D). The primary objective of the CA/D algorithm is to decompose DMOP into several scalar optimization subproblems and solve simultaneously. The subproblems are optimized utilizing the information shared only by its neighboring problems. The proposed CA/D is evaluated using CEC 2015 optimization benchmark functions. The results show that CA/D outperforms CA, Multi-population CA (MPCA), and MPCA incorporating game strategies (MPCA-GS), particularly in hybrid and composite benchmark problems.

Disaster logistics presents a highly complex decision-making challenge under conditions of uncertainty, where the timely and efficient allocation of scarce resources is essential to minimize human suffering. In this context, we propose a novel Quantum-Inspired Hyperheuristic Framework (QHHF) designed to solve Dynamic Multi-Objective Combinatorial Optimization Problems (DMOCOPs) arising in disaster relief operations. The proposed framework integrates Quantum-Inspired Evolutionary Algorithms (QIEAs), which facilitate diverse and explorative solution generation, with a Reinforcement Learning (RL)-based hyperheuristic capable of dynamically selecting the most suitable low-level heuristic in response to evolving disaster conditions. A dynamic multi-objective mathematical model is formulated to simultaneously minimize total travel cost and risk exposure, while maximizing priority-weighted demand satisfaction. The model captures real-world complexity through time-dependent variables, stochastic demand variations, and fluctuating transportation risks. Extensive simulations using real-world disaster scenarios demonstrate the effectiveness of the proposed approach in generating high-quality solutions within stringent response time constraints. Comparative evaluations reveal that QHHF consistently outperforms traditional heuristics and metaheuristics in terms of adaptability, scalability, and solution quality across multiple objective trade-offs. Notably, our method achieves a 9.6% reduction in total travel cost, a 6.5% decrease in cumulative risk exposure, and a 4.7% increase in priority-weighted demand satisfaction when benchmarked against existing techniques. This work contributes both to the advancement of hyperheuristic theory and to the development of practical, AI-enabled decision-support tools for emergency logistics management.

Knowledge guided Bayesian classification for dynamic multi-objective optimization

Dynamic multiobjective optimization problems (DMOPs) aim to optimize multiple (often conflicting) objectives that are changing over time. Recently, there are a number of promising algorithms proposed based on transfer learning methods to solve DMOPs. However, it is very challenging to reduce the negative effect in transfer learning and find more effective transferred solutions. To fill this research gap, this article proposes a clustering-based transfer (CBT) learning method to solve DMOPs. When the environment changes, two novel operations (clustering-based selection (CBS) and CBT) are used to guide knowledge transfer. Specifically, CBS aims to find a population with nondominated solutions and dominated solutions as the training data for the new environment. Then, CBT further collects the previous Pareto-optimal solutions and some noise solutions as the training data for the previous environment. Two training data sets from different environments are, respectively, divided into multiple clusters and transfer learning is conducted on two similar clusters with high probability to reduce the negative effect, which can train an accurate prediction model to identify the promising solutions for the new environment. Empirical studies have been conducted on 14 benchmark DMOPs and one real-life path planning problem of unmanned air/ground vehicles, which validate the effectiveness of our proposed method. Especially, our method can significantly reduce negative transfer on 12 out of 14 cases when compared with direct transfer learning.

Various real-world multiobjective optimization problems are dynamic, requiring evolutionary algorithms (EAs) to be able to rapidly track the moving Pareto front of an optimization problem once an environmental change occurs. To this end, several methods have been developed to predict the new location of the moving Pareto set (PS) so that the population can be reinitialized around the predicted location. In this paper, we present a multidirectional prediction strategy to enhance the performance of EAs in solving a dynamic multiobjective optimization problem (DMOP). To more accurately predict the moving location of the PS, the population is clustered into a number of representative groups by a proposed classification strategy, where the number of clusters is adapted according to the intensity of the environmental change. To examine the performance of the developed algorithm, the proposed prediction strategy is compared with four state-of-the-art prediction methods under the framework of particle swarm optimization as well as five popular EAs for dynamic multiobjective optimization. Our experimental results demonstrate that the proposed algorithm can effectively tackle DMOPs.

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.

Combining a hybrid prediction strategy and a mutation strategy for dynamic multiobjective optimization

Dynamic multi-objective evolutionary algorithms (Dynamic MOEAs) use the evolutionary algorithms to solve the dynamic multi-objective optimization problems (DMOPs). It has become one of the hot areas of research. The challenge of DMOPs is that the objective functions, the constraints or the parameters may change over time. This paper tries to provide a comprehensive overview of the related work, which is organized by the common process of Dynamic MOEAs, such as, the detection of change, the maintenance of diversity, the prediction of change, the test problems and the performance metrics. Finally, topics for further research are suggested.

Many problems in the real-world have more than one objective, with at least two objectives in conflict with one another. In addition, at least one objective changes over time. These kinds of problems are called dynamic multi-objective optimisation problems (DMOOPs). Studies have shown that both the quantum particle swarm optimisation (QPSO) and charged particle swarm optimisation (CPSO) algorithms perform well in dynamic environments, since they maintain swarm diversity. Therefore, this paper investigates the effect of using either QPSOs or CPSOs in the sub-swarms of the dynamic vector-evaluated particle swarm optimisation (DVEPSO) algorithm. These DVEPSO variations are then compared against the default DVEPSO algorithm that uses gbest PSOs and DVEPSO using heterogeneous PSOs that contain both charged and quantum particles. Furthermore, all of the aforementioned DVEPSO configurations are compared against the dynamic multi-objective optimisation (DMOPSO) algorithm that was the winning algorithm of a comprehensive comparative study of dynamic multi-objective optimisation algorithms. The results indicate that charged and quantum particles improve the performance of DVEPSO, especially for DMOOPs with a deceptive POF and DMOOPs with a non-linear POS.

The concept of a K-gradient, introduced in Ref. 1 in order to generalize the concept of a derived convex cone defined by Hestenes, is extended to weak multiobjective optimization problems including not only a state variable, but also a control variable. The new concept is employed to state multiplier rules for the local solutions of such dynamic multiobjective optimization problems. An application of these multiplier rules to the local solutions of an abstract multiobjective optimal control problem yields general necessary optimality conditions that can be used to derive concrete maximum principles for multiobjective optimal control problems, e.g., problems described by integral equations with additional functional constraints.

A new prediction strategy for dynamic multi-objective optimization using Gaussian Mixture Model