Evolutionary Multiobjective Optimization Algorithms Research Articles

Approximating robust Pareto fronts by the MEOF-based multiobjective evolutionary algorithm with two-level surrogate models

The multiobjective optimization problems (MOPs) under uncertain environments are very challenging to be solved due to the sensitivities of some robust decision variables. To find the robust Pareto fronts (PFs) of these MOPs, the mean effective objective function (MEOF) is often used for evaluating the qualities of solutions in the existing evolutionary multiobjective optimization (EMO) algorithms. In the MEOF evaluation, the objective function values of multiple solutions in the neighborhood of a certain solution should be averaged. As a result, the MEOF-based EMO algorithms consume a large number of function evaluations to find robust PFs with high qualities. To overcome this weakness, we propose a new MEOF-based EMO framework with two-level surrogate models, denoted by EMO-MEOF/TS, which utilizes radial basis function and Gaussian process model to predict high-quality robust solutions at the levels of global search and local search. Some experiments are conducted to evaluate the performance of the proposed framework on some modified MOPs with robust decision variables. Our experimental results demonstrate that EMO-MEOF/TS is advantageous against several robust MOEAs in approximating the PFs of MOPs with robust characteristics.

Multilevel thresholding image segmentation algorithm based on Mumford–Shah model

Abstract Image segmentation is one of the important tasks of computer vision and computer image processing, and the purpose of image segmentation is to achieve the extraction and recognition of the target image region. The classical Mumford–Shah (MSh) image segmentation model is used to achieve the segmentation of images. With the goal to get the best segmentation effect on images by minimizing the MSh energy generalization function, a level set strategy is developed, and a model with global information infinite curve evolution is utilized. However, considering the low efficiency of this model for processing level set curves and the general quality of image segmentation. A multi-layer threshold search scheme is proposed to achieve rapid convergence of the target image level set curve. The experimental results showed that the multi-level thresholding image segmentation algorithm based on the MSh model can significantly improve the segmentation effect of images and reduce the segmentation time. The suggested MSK method outperforms the MPO algorithm, SSA algorithm, and EMO algorithm in the picture segmentation convergence time test, respectively, in terms of runtime efficiency by 356, 289, and 71%. Additionally, it performs superbly in both threshold searches and picture quality tests. The research topic has significant reference value for the study of contemporary computer vision imaging technologies.

A problem transformation-based and decomposition-based evolutionary algorithm for large-scale multiobjective optimization

For large-scale multi-objective optimization problems, the search space becomes exceptionally vast, resulting in increased complexity in the search process. The search space usually contains several local optimal individuals, and the difficulty of finding the global optimal individuals increases greatly. A problem transformation-based and decomposition-based large-scale multi-objective evolutionary algorithm is proposed to solve the problem of reducing the dimensionality of the search space and the optimization of populations. Reducing the number of optimization problems in the decision space through problem transformation has lowered the complexity of multi-objective optimization problems and enhanced computational efficiency. In the decision space, employing two direction vectors adaptively guides the generation of promising individuals, thereby preventing the population from falling into local optima. Due to the dimensionality reduction of the decision space and the optimization of the individuals in the objective space, a set of optimal solutions are effectively obtained and uniformly distributed on the approximate Pareto optimal front. Experimental results show that the algorithm is highly competitive with five large-scale multi-objective evolutionary algorithms for large-scale multi-objective optimization test problems with up to 2000 decision variables.

Improving building resilience in the face of future climate uncertainty: A comprehensive framework for enhancing building life cycle performance

This research introduces an innovative resilient design framework, addressing gaps in building performance optimization by considering a holistic life cycle perspective and factoring in climate projection uncertainties from the 2020s to 2090s. The study concludes that in the case study, future climate scenarios in different Shared Socio-Economic Paths significantly impact building life cycle performance, with wall U-value, windows U-value, and wall density identified as major factors affecting building performance under future climate uncertainty. The ensemble learning model achieves high fidelity in predicting life cycle carbon emissions (LCCE), life cycle cost (LCC), and indoor discomfort hours (IDH) through input feature screening and hyperparameter optimization. Comparing optimization algorithms, Two-Archive Evolutionary Algorithm for Constrained multi-objective optimization (C-TAEA) demonstrates better convergence degree and optimization effect. Among the tested multi-criteria decision making methods, the VIKOR method selects the best building resilient design scheme from the Pareto data set, effectively reducing LCCE, LCC, and IDH, and leading to an overall improvement in building life cycle performance. Applying this framework, the finalized scheme for an office building in cold region optimizes 44.0% of LCCE, 8.2% of LCC, and 4.3% of IDH. This framework develops a new approach to improve building life cycle performance under future climate uncertainty and supports informed decision-making for resilient building design. To promote carbon neutrality in construction, it is urged that future studies incorporate additional sources of uncertainty, such as occupant behavior, into the proposed framework.

Multi-objective reinforcement learning for bi-objective time-dependent pickup and delivery problem with late penalties

This study addresses the bi-objective time-dependent pickup and delivery problem with late penalties (TDPDPLP). Incorporating time-dependent travel time into the problem formulation to model traffic congestion is critical, especially for problems with time-related costs, to decrease the difference in the projected quality of solutions when applying optimization methods in the real world. This study proposes a multi-objective reinforcement learning (MORL)-based method with hypernetwork and heterogeneous attention mechanism (HAM) with a two-stage training scheme to solve the bi-objective TDPDPLP. The proposed method can instantly generate an approximation of the Pareto optimal front (POF) after offline training. The conducted ablation study also showed that discarding coordinates from the features simplifies the model and saves several hours of training while improving the quality of the solutions. The performance of the trained model is evaluated on various instances, including real-world-based instances from Barcelona, Berlin, and Porto-Alegre. The performance of the proposed method is evaluated based on the hypervolume (HV) and additive epsilon (ϵ+) of the generated POF. We compare the performance of the proposed method to another MORL method, namely the preference-conditioned multi-objective combinatorial optimization (PMOCO) and several well-known multi-objective evolutionary algorithms (MOEAs). Experiments showed that the proposed method performs better than PMOCO and the employed MOEAs on various problem instances. The trained method only needs minutes to generate a POF approximation, while the MOEAs require hours. Furthermore, it also generalizes well on different characteristics of problem instances and performs well on instances from cities other than the city in the training instances.

Identifying vulnerabilities of industrial control systems using evolutionary multiobjective optimisation

In this paper, we propose a novel methodology to assist in identifying vulnerabilities in real-world complex heterogeneous industrial control systems (ICS) using two Evolutionary Multiobjective Optimisation (EMO) algorithms, NSGA-II and SPEA2. Our approach is evaluated on a well-known benchmark chemical plant simulator, the Tennessee Eastman (TE) process model. We identified vulnerabilities in individual components of the TE model and then made use of these vulnerabilities to generate combinatorial attacks. The generated attacks were aimed at compromising the safety of the system and inflicting economic loss. Results were compared against random attacks, and the performance of the EMO algorithms was evaluated using hypervolume, spread, and inverted generational distance (IGD) metrics. A defence against these attacks in the form of a novel intrusion detection system was developed, using machine learning algorithms. The designed approach was further tested against the developed detection methods. The obtained results demonstrate that the developed EMO approach is a promising tool in the identification of the vulnerable components of ICS, and weaknesses of any existing detection systems in place to protect the system. The proposed approach can serve as a proactive defense tool for control and security engineers to identify and prioritise vulnerabilities in the system. The approach can be employed to design resilient control strategies and test the effectiveness of security mechanisms, both in the design stage and during the operational phase of the system.

Uniformity-Comprehensive Multiobjective Optimization Evolutionary Algorithm Based on Machine Learning

When solving real-world optimization problems, the uniformity of Pareto fronts is an essential strategy in multiobjective optimization problems (MOPs). However, it is a common challenge for many existing multiobjective optimization algorithms due to the skewed distribution of solutions and biases towards specific objective functions. This paper proposes a uniformity-comprehensive multiobjective optimization evolutionary algorithm based on machine learning to address this limitation. Our algorithm utilizes uniform initialization and self-organizing map (SOM) to enhance population diversity and uniformity. We track the IGD value and use K-means and CNN refinement with crossover and mutation techniques during evolutionary stages. Our algorithm’s uniformity and objective function balance superiority were verified through comparative analysis with 13 other algorithms, including eight traditional multiobjective optimization algorithms, three machine learning-based enhanced multiobjective optimization algorithms, and two algorithms with objective initialization improvements. Based on these comprehensive experiments, it has been proven that our algorithm outperforms other existing algorithms in these areas.

Iterated-local-search-based chaotic differential evolution algorithm for hybrid-load part feeding scheduling optimization in mixed-model assembly lines

PurposeDriven by sustainable production, mobile robots are introduced as a new clean-energy material handling tool for mixed-model assembly lines (MMALs), which reduces energy consumption and lineside inventory of workstations (LSI). Nevertheless, the previous part feeding scheduling method was designed for conventional material handling tools without considering the flexible spatial layout of the robotic mobile fulfillment system (RMFS). To fill this gap, this paper focuses on a greening mobile robot part feeding scheduling problem with Just-In-Time (JIT) considerations, where the layout and number of pods can be adjusted.Design/methodology/approachA novel hybrid-load pod (HL-pod) and mobile robot are proposed to carry out part feeding tasks between material supermarkets and assembly lines. A bi-objective mixed-integer programming model is formulated to minimize both total energy consumption and LSI, aligning with environmental and sustainable JIT goals. Due to the NP-hard nature of the proposed problem, a chaotic differential evolution algorithm for multi-objective optimization based on iterated local search (CDEMIL) algorithm is presented. The effectiveness of the proposed algorithm is verified by dealing with the HL-pod-based greening part feeding scheduling problem in different problem scales and compared to two benchmark algorithms. Managerial insights analyses are conducted to implement the HL-pod strategy.FindingsThe CDEMIL algorithm's ability to produce Pareto fronts for different problem scales confirms its effectiveness and feasibility. Computational results show that the proposed algorithm outperforms the other two compared algorithms regarding solution quality and convergence speed. Additionally, the results indicate that the HL-pod performs better than adopting a single type of pod.Originality/valueThis study proposes an innovative solution to the scheduling problem for efficient JIT part feeding using RMFS and HL-pods in automobile MMALs. It considers both the layout and number of pods, ensuring a sustainable and environmental-friendly approach to production.

A decomposition and dynamic niching distance-based dual elite subpopulation evolutionary algorithm for multimodal multiobjective optimization

Solving multimodal multiobjective optimization problems(MMOPs) require obtaining multiple Pareto optimal solution sets (PSs). In recent years, researchers have proposed some multimodal multiobjective evolutionary algorithms (MMEAs), however, many existing MMEAs perform unsatisfactorily in dealing with complicated MMOPs, and even fail to find all Pareto solution sets in a stable manner. Many existing algorithms rely on globally optimal individuals to guide population evolution, which leads to the population rapidly converging to a few easy-to-find Pareto solution sets (PSs) and losing hard-to-find PSs. MMEAs that cannot consistently find all PSs are difficult to handle the increasing complexity of MMOPs. In order to address these problems, this research proposes a decomposition and dynamic niching distance-based dual elite subpopulation evolutionary algorithm, named MMEA-DES. In the proposed algorithm, decomposition-based methods are employed to maintain the diversity of the objective space of MMOPs, and a dynamic niching distance (DND) is proposed to calculate the crowding of the decision space. In addition, the dual elite subpopulations (DES) based on decomposition and DND are implemented to support the algorithm in obtaining well-distributed solutions in both decision space and objective space. To validate the performance of the proposed algorithm, a comparison with state-of-the-art algorithms on 23 test problems shows that the algorithm proposed in this research can stably solve various types of complicated MMOPs.

Software Reliability Prediction using Correlation Constrained Multi-Objective Evolutionary Optimization Algorithm

Software reliability frameworks are extremely effective for estimating the probability of software failure over time. Numerous approaches for predicting software dependability were presented, but neither of those has shown to be effective. Predicting the number of software faults throughout the research and testing phases is a serious problem. As there are several software metrics such as object-oriented design metrics, public and private attributes, methods, previous bug metrics, and software change metrics. Many researchers have identified and performed predictions of software reliability on these metrics. But none of them contributed to identifying relations among these metrics and exploring the most optimal metrics. Therefore, this paper proposed a correlation- constrained multi-objective evolutionary optimization algorithm (CCMOEO) for software reliability prediction. CCMOEO is an effective optimization approach for estimating the variables of popular growth models which consists of reliability. To obtain the highest classification effectiveness, the suggested CCMOEO approach overcomes modeling uncertainties by integrating various metrics with multiple objective functions. The hypothesized models were formulated using evaluation results on five distinct datasets in this research. The prediction was evaluated on seven different machine learning algorithms i.e., linear support vector machine (LSVM), radial support vector machine (RSVM), decision tree, random forest, gradient boosting, k-nearest neighbor, and linear regression. The result analysis shows that random forest achieved better performance.

A novel competitive constrained dual-archive dual-stage evolutionary algorithm for constrained multiobjective optimization

In constrained multi-objective optimization problems (CMOPs), the key problem is how to balance convergence and diversity simultaneously and find as many feasible solutions as possible in the reduced search space. To address this issue, a novel competitive constrained dual-archive dual-stage evolutionary algorithm, named c-DADSEA, is proposed with a convergence-driven archive (CA) and a diversity-driven archive (DA). To improve the algorithm’s convergence, instead of simply excluding infeasible solutions, an adaptive penalty function is novelly proposed to maintain competitively infeasible solutions in CA. To overcome the difficulty in finding the true Pareto front for the dual-population framework in some problems, a dual-stage framework is introduced to make DA search in different directions at different stages (i.e., Forward and Backward), enhancing the diversity of the algorithm. DA evolves without considering the constraints to explore all regions as much as possible in the Forward stage. While in the Backward stage, DA degenerates with increasing constraints to search the regions around the true Pareto front by using ϵ-constrained method. Moreover, to balance convergence and diversity, different benchmark rankings are designed for the individuals in different archives. The experiments on three benchmark CMOPs test suites demonstrate that c-DADSEA is better than seven other state-of-the-art constrained evolutionary algorithms, especially for the CMOPs with a constrained Pareto front away from the unconstrained Pareto front.

An adaptive dynamic community detection algorithm based on multi-objective evolutionary clustering

PurposeCommunity detection of dynamic networks provides more effective information than static network community detection in the real world. The mainstream method for community detection in dynamic networks is evolutionary clustering, which uses temporal smoothness of community structures to connect snapshots of networks in adjacent time intervals. However, the error accumulation issues limit the effectiveness of evolutionary clustering. While the multi-objective evolutionary approach can solve the issue of fixed settings of the two objective function weight parameters in the evolutionary clustering framework, the traditional multi-objective evolutionary approach lacks self-adaptability.Design/methodology/approachThis paper proposes a community detection algorithm that integrates evolutionary clustering and decomposition-based multi-objective optimization methods. In this approach, a benchmark correction procedure is added to the evolutionary clustering framework to prevent the division results from drifting.FindingsExperimental results demonstrate the superior accuracy of this method compared to similar algorithms in both real and synthetic dynamic datasets.Originality/valueTo enhance the clustering results, adaptive variances and crossover probabilities are designed based on the relative change amounts of the subproblems decomposed by MOEA/D (A Multiobjective Optimization Evolutionary Algorithm based on Decomposition) to dynamically adjust the focus of different evolutionary stages.

Topology structure optimization of evolutionary hierarchical fuzzy systems

In this paper, a new method of hierarchical fuzzy system modeling for high-dimensional regression problems is proposed, which is called multi-objective evolutionary hierarchical fuzzy regression system (MOEHFRS). Different from the existing hierarchical fuzzy systems with fixed topology, the proposed MOEHFRS improves the accuracy of the model, reduces the total number of rules, and eliminates unnecessary features by flexibly constructing topology. In the process of topology evolution, MOEHFRS can exchange and combine different sub-fuzzy systems to achieve the selection and reuse of important features, as well as the elimination of unnecessary features, which improves the diversity of topology and enables the model to be well applied to high-dimensional regression problems. Different combinations of sub-fuzzy systems will result in different performance and number of rules. A new multi-objective evolutionary optimization algorithm is proposed to simultaneously optimize the number of rules and the accuracy of the model, which achieves the balance between complexity and accuracy of MOEHFRS. The proposed method is validated on 13 real world regression datasets and compared with other 5 methods. The results show that MOEHFRS is effective and advanced in terms of accuracy, number of rules, retention of important features and universality in different regression problems.

A Competitive and Cooperative Swarm Optimizer for Constrained Multiobjective Optimization Problems

Solving multi-objective optimization problems through meta-heuristic methods gets considerable attention. Based on the classical variation operators, several enhanced operators, as well as multi-objective optimization evolutionary algorithms, have been developed. Among these operators, the competitive swarm optimizer exhibits promising performance. However, it encounters difficulties when tackling constrained multi-objective optimization problems with large objective spaces or complex infeasible regions. In this paper, a competitive and cooperative swarm optimizer is proposed, which contains two particle update strategies: i) the competitive swarm optimizer provides faster convergence speed to accelerate the approximation of the Pareto front; and ii) the cooperative swarm optimizer suggests a mutual-learning strategy to enhance the ability to jump out of local feasible regions or local optima. We also present a new algorithm for constrained multi-objective optimization problems. The results on four benchmark suites with 47 instances demonstrate the superiority of our approach compared with other state-of-the-art methods. Additionally, its effectiveness on large scale constrained multi-objective optimization problems has also been verified.

Cooperative tri-population based evolutionary algorithm for large-scale multi-objective optimization

Cooperative tri-population based evolutionary algorithm for large-scale multi-objective optimization

A two-space-decomposition-based evolutionary algorithm for large-scale multiobjective optimization

Large-scale multiobjective optimization problems (LSMOPs) pose a great challenge to maintaining the diversity of solutions. However, existing large-scale multiobjective optimization algorithms (MOEAs) prefer to directly use environmental selection methods designed for small-scale optimization problems. These methods are not effective in solving complex LSMOPs. To address this issue, this paper proposes a two-space (decision space and objective space) decomposition (TSD)-based diversity maintenance mechanism. Its main idea is to explicitly decompose the decision space and objective space into a number of subspaces, each of which may contain some Pareto-optimal solutions. Searching for Pareto-optimal solutions in these subspaces may help maintain the diversity of solutions. To this end, a diversity design subspace (DDS) is constructed to decompose the decision space. Then, a large-scale MOEA (MOEA/TSD) is designed by using the proposed TSD-based diversity maintenance mechanism. Experimental studies validate the effectiveness of the proposed TSD mechanism. Compared with nine state-of-the-art large-scale MOEAs on 112 benchmark LSMOPs, our proposed algorithm offers considerable advantages in overall optimization performance. The source code of MOEA/TSD is available at https://github.com/yizhizhede/MOEATSD.

Multi-dimensional management framework on fresh groundwater lens of Kish Island in the Persian Gulf, Iran

Groundwater in arid and semi-arid coastal aquifers is vulnerable to seawater intrusion and quality deterioration despite being one of the most reliable sources of water supply due to the increasing number of development plans and competition between water consumers. A multi-dimensional groundwater management framework is developed to trade-off between groundwater abstraction, allocation equity, groundwater quality, and energy considerations in the reverse osmosis (RO) filtration process in the fresh groundwater lens of Kish Island, Iran. An arid island confined in the Persian Gulf is modeled using 3D simulation and three well-occupied multi-objective evolutionary optimization algorithms. Four objectives include: maximizing the groundwater abstraction, minimizing the Gini coefficient (allocation inequity), minimizing the total energy required to pass saline water through the RO membrane to reach the standard total dissolved solids (TDS), and minimizing the average TDS concentration of water abstraction positions from 11 management zones have been considered over a 50-year management horizon. Solutions obtained in the simulation-based constrained multi-objective optimization framework allow managers to choose from 587 Pareto optimal solutions. They provide an abstraction scheme with a range of 1.44 to 4.53 MCM/yr, a Gini coefficient of 0 to 0.98, filtration energy of 988,562 to 1,935,760 kWh/yr, and an average TDS of 19,663 to 21,351 mg/L. The Pareto optimal solutions can help decision-makers decide on the multi-dimensional problems of sustainable coastal groundwater management and show patterns among different objectives.

Interactive niching-based two-stage evolutionary algorithm for constrained multiobjective optimization

When solving constrained multiobjective optimization problems (CMOPs), how to maintain diversity without losing convergence is a major challenge, because some small discrete feasible regions make the population hard to find a complete feasible Pareto Front. To this end, an interactive niching-based two-stage evolutionary algorithm for constrained multiobjective optimization, named INCMO, is proposed in this study. At each stage of INCMO, both two populations are employed to focus on different evolution purposes. Specifically, the main population optimizes the original CMOP, while the auxiliary population only considers the objectives by ignoring all constraints. INCMO uses two different niching mechanisms in two stages. In the early stage, each population independently uses the niching technique to generate offspring, to maintain diversity. In addition, two offspring populations are shared to realize migration between two populations. In the later stage, two populations cooperate to generate offspring based on an interactive niching technique. To be specific, two populations are merged and then divided into different niches. In this case, individuals from two populations will be assigned to the same niche. After that, individuals in the niche produce offspring through crossover and mutation. The process of generating offspring also promotes more effective migration between the two populations on the basis of increasing the diversity of population. Compared with other well-established methods, the proposed method in this study shows better performance on four test suites including 47 benchmark problems.

Dynamic multi-objective workflow scheduling for combined resources in cloud

Cloud resource providers offer idle resources to users as spot instances. The price of the instances changes with market supply and demand, and the dynamic price can have a significant impact on workflow scheduling. In this work, we use a combination of spot and on-demand instances as the foundation cloud resource and characterize the dynamic workflow scheduling problem as a dynamic multi-objective optimization problem (DMOP), where the dynamics originate from the dynamic price of spot instances. The scheduling solution is found by considering three objectives: maximizing the reliability of the instances while minimizing the makespan and cost. In addition, we provide an enhanced MOEAD algorithm called MOEA/D-URDI that combines diversity introduction and uniform random sampling, where the uniform random sampling paradigm is used to generate the initial weight vector. The dynamic multi-objective optimization evolutionary algorithm DMOEA/D-URDI is then created by combining the method with a dynamic optimization framework. Our technique beats existing algorithms, according to experimental data based on dynamic benchmark sets and three well-known scientific procedures in terms of metrics on dynamic benchmark sets and better ensures reliability in scheduling scientific workflows while reducing makespan and cost.

A learning and potential area-mining evolutionary algorithm for large-scale multi-objective optimization

For large-scale multi-objective optimization problems, it is not easy for existing multi-objective evolutionary algorithms to search the entire decision variable space with limited computation resources. To alleviate this problem, we propose a learning and potential area-mining evolutionary algorithm to explore and exploit key regions for accelerating optimization. First, we mine promising areas by clustering the population-gathered regions. Then, potential directions are determined by a multi-guiding point scheme in these promising areas. Subsequently, we design a local search and global search scheme to enhance population convergence while ensuring diversity. Finally, a mutation strategy is used to improve diversity. We execute numerical experiments on two widely-used LSMOP benchmarks and compare the proposed algorithm with three state-of-the-art algorithms. The statistical results indicate that the proposed algorithm has significant performance.