Set Of Non-dominated Solutions Research Articles

A Multiobjective Genetic Algorithm to Evolving Local Interpretable Model-Agnostic Explanations for Deep Neural Networks in Image Classification

Deep convolutional neural networks have become a dominant solution for numerous image classification tasks. However, a main criticism is the poor explainability due to the black-box characteristic, which hurdles the extensive usage of deep convolutional neural networks. To address this issue, this paper proposes a new evolutionary multi-objective based method, which aims to explain the behaviours of deep convolutional neural networks by evolving local explanations on specific images. To the best of our knowledge, this is the first evolutionary multi-objective method to evolve local explanations. The proposed method is model-agnostic, i.e. it is applicable to explain any deep convolutional neural networks. ImageNet is used to examine the effectiveness of the proposed method. Three well-known deep convolutional neural networks -VGGNet, ResNet, and MobileNet, are chosen to demonstrate the modelagnostic characteristic. Based on the experimental results, it can be observed that the local explanations are understandable to end-users, who need to check the sensibility of the evolved explanations to decide whether to trust the predictions made by the deep convolutional neural networks. Furthermore, the local explanations evolved by the proposed method improves the confidence of deep convolutional neural networks making the predictions. Lastly, the pareto front and convergence analyses indicate that the proposed method can form a good set of nondominated solutions.

DpEA: A dual-population evolutionary algorithm for dynamic constrained multiobjective optimization

Dynamic Constrained Multiobjective Optimization Problems (DCMOPs) are very difficult to solve because both of the objectives and constraints may change over time. The existing approaches for solving DCMOPs mainly develop dynamic response techniques and constraint handling techniques. But they do not focus on the search capability of the static optimizer in each environment, which ignores the intrinsic requirement of quickly locating Pareto-optimal Front (PF) in each environment when solving DCMOPs. To this end, this paper proposes a dual-population evolutionary algorithm for solving DCMOPs, called as DpEA, which maintains a population without considering constraints (called UP) for exploration and a population with considering constraints (called CP) for exploitation in each environment. In each iteration of a new environment, UP firstly adopts a stratified mutation strategy (SMS) and a dominated solution repairment strategy (DSR) to enhance the exploration ability of finding promising regions where the PF may reside. SMS uses solutions from different nondominated fronts to generate offspring, while DSR repairs the single-optimal variables of the dominated solutions by sampling from the distribution of those variables of nondominated solutions. Secondly, this paper uses an adaptive offspring ratio adjustment strategy to control the offspring number generated by UP and CP according to the normalized Hausdorff distance between nondominated solution sets from the two latest generations of UP. This strategy is helpful to balance the intensity between exploration and exploitation and thereby ensures efficient search. Experimental results on CEC 2023 DCF test suite show that DpEA has a superior performance over six state-of-the-art algorithms.

An integrated model of supply chain resilience considering supply and demand uncertainties

AbstractThe complexity of the global supply chain has increased dramatically over the past few decades as a result of uncertainty caused by various factors. This paper studies the optimal strategy for supply chain resilience models considering supply disruptions and demand fluctuations. We present two‐stage stochastic programming models based on different scenarios, including a risk‐neutral model that considers the expected total cost, a risk‐averse model that considers the conditional value‐at‐risk measure, and a responsiveness model that considers the service level. We also propose multiobjective mathematical programming that considers all three models simultaneously and suggests the solution approach. Finally, we present the results of computational experiments and demonstrate how to cope with uncertainty through flexibility and redundancy. We offer a set of nondominated solutions from the multiobjective model and derive managerial insights, which suggest a decision‐making strategy between the disruption risk, expected total cost, and service level.

Bi-objective carbon-efficient distributed flow-shop scheduling with multistep electricity pricing

A bi-objective distributed flow-shop scheduling problem with multistep electricity pricing and carbon emissions is studied. One objective is to minimise the completion time of production, and the other is to minimise the total cost of multistep electricity pricing and carbon emissions. A mixed integer programming model and a two-stage knowledge based cooperative algorithm with a local reinforcement strategy are proposed for the problem. The extensive numerical experiments show that the two-stage algorithm was effective statistical significantly in generating non-dominated solution sets and Pareto frontiers. Simulations on Electricity Prices are applied to examine different multistep electricity pricing schemes, and management implications were drawn for both government and companies.

Trajectory planning of tire laser engraving orthogonal robot based on an improved multi-objective grasshopper optimization algorithm

The traditional tire laser engraving robots have the low and stable running capability and discontinuous motion trajectory during operation, leading to long running time, high energy consumption, and uneven operation. In order to solve these problems, this paper proposes an orthogonal robot trajectory planning method based on an improved multi-objective grasshopper optimization algorithm (IMOGOA) with the orthogonal robot as the research object. Firstly, this paper used the quintic non-uniform rational b-splines (NURBS) curves to construct the trajectory. Secondly, the optimization objectives of the orthogonal robot’s running time, energy consumption, and smoothness were used to obtain the Pareto optimal solution by using the IMOGOA to establish the objective function. Then, the optimization method was simulated and analyzed, and the optimal solution was selected to compare with the rest of the non-dominated solution sets. The simulation results showed that the proposed method reduced the running time by 33.68%, improved the energy consumption and smoothness performance by 34.48% and 56.58%, and achieved multi-objective comprehensive optimization of the orthogonal robot. Thus, the effectiveness and feasibility of the proposed method were verified. Finally, a tire laser engraving orthogonal robot experimental platform was built for physical verification experiments. The experimental results showed that the experimental trajectory deviated from the simulated trajectory by only 5.63%, further proving the proposed method’s practicality.

A multi-objective cooperation search algorithm for cascade reservoirs operation optimization considering power generation and ecological flows

With growing attention focused on energy generation and environmental conservation, the operation of cascade reservoirs that considers power generation benefits and ecological flow requirements plays an increasingly important role in water resource and power systems. However, the traditional optimization methods may fail to solve complex cascade reservoirs operation models with strong spatial-temporal coupling physical constraints. To effectively address this problem, this study proposes an efficient multi-objective cooperation search algorithm (MOCSA) that utilizes the modified team communication, reflective learning operator and internal competition operators to enhance global exploration and local exploitation. MOCSA is tested on a group of multi-objective benchmark functions and real-world constrained engineering problems. The results demonstrate that MOCSA can provide better results for most benchmark test functions in comparison with the competitive algorithms. Besides, MOCSA exhibits excellent search ability to find feasible solutions of constrained engineering problems. The proposed method is then applied to resolve a real-world reservoir system under different operation scenarios. Simulations indicate that MOCSA provides diversified decision options for the operation of cascade reservoir system and find a more diverse set of non-dominated solutions within the feasible solution space. Overall, this research presents MOCSA as an effective multi-objective optimization tool for complex cascade reservoir operation problems.

Greenhouse environmental control target constrained by discrete surface curvature and multi-objective optimization algorithm

Protected greenhouse provides a suitable micro-environment for crop growth, which enhances the quality and yield of agricultural products. How to optimize the greenhouse environment is currently a pressing issue in protected agriculture. In this research, we propose a new environmental control method from the perspectives of crop photosynthesis rate and environmental control cost. The photosynthesis rate data are collected from a nested experiment of tomatoes, and these data are combined with the support vector regression algorithm to establish a photosynthesis rate model. The cost function of greenhouse environmental control is established by theoretical calculation. The non-dominated solution sets of photosynthesis rate and control cost are obtained through an improved non-dominated sorting genetic algorithm Ⅱ. To determine the optimal solution among the numerous Pareto solutions, the geometric characteristics of the photosynthetic response surface are considered to constrain the control target. Then, a discrete surface curvature method is proposed to computer the constraint region. The intersection between the Pareto solutions and the constraint region is regarded as the environmental control target. The validation experiment demonstrates that the proposed method can effectively enhance photosynthetic accumulation and reduce control cost. Compared to the traditional saturation method, this method achieves a 53% cost reduction while still obtaining 89% photosynthetic accumulation. Compared to the U-chord method, this method increases photosynthetic accumulation by 12% with only a 3% increase in cost. The research has important implications for protected agriculture production.

Enhanced Genetic Method for Optimizing Multiple Sequence Alignment

In the realm of bioinformatics, Multiple Sequence Alignment (MSA) is a pivotal technique used to optimize the alignment of multiple biological sequences, guided by specific scoring criteria. Existing approaches addressing the MSA challenge tend to specialize in distinct biological features, leading to variability in alignment outcomes for the same set of sequences. Consequently, this paper proposes an enhanced evolutionary-based approach that simplifies the sequence alignment problem without considering the sequences in the non-dominated solution. Our method employs a multi-objective optimization technique that uniquely excludes non-dominated solution sets, effectively mitigating computational complexities. Utilizing the Sum of Pairs and the Total Conserved Column as primary objective functions, our approach offers a novel perspective. We adopt an integer coding approach to enhance the computational efficiency, representing chromosomes with sets of integers during the alignment process. Using the SABmark and BAliBASE datasets, extensive experimentation is conducted to compare our method with existing ones. The results affirm the superior solution quality achieved by our approach compared to its predecessors. Furthermore, via the Wilcoxon signed-rank test, a statistical analysis underscores the statistical significance of our model’s improvement (p < 0.05). This comprehensive approach holds promise for advancing Multiple Sequence Alignment in bioinformatics.

Development of an assessment-based planting structure optimization model for mitigating agricultural greenhouse gas emissions

Optimization of crop structure is an efficient way to reduce greenhouse gas (GHGs) from agriculture production. However, carbon footprint have rarely been incorporated into previous planting structure optimization models due to the challenges of assessing the spatial and temporal distribution of agricultural carbon footprint for multiple crops in irrigated districts. In addition, previous planting structure models suffered from strong subjectivity in objective function determination, and the obtained non-dominated solution set offered difficulties to decision-makers in selecting specific implementation options. To fill such gaps, an integrated accounting-assessment-optimization-decision making (AAODM) approach was proposed, which remedies the shortcomings of previous crop planting structure optimization models in carbon footprint mitigation, and overcomes the subjectivity of objective function determination and the difficulty in selecting specific implementation options. Firstly, life cycle assessment (LCA) method was used to account for the multi-year agricultural carbon footprints of multiple crops in the irrigation district. The optimization objective functions of planting structure optimization models can then be determined based on the assessment method of carbon footprint influencing factors. Next, the Non-dominated Sorting Genetic Algorithm-II (NSGA-II) was used to generate a non-dominated solution set of the optimization model. The optimal planting structure can be finally obtained based on decision making methods by determining the maximum harmonic mean (HM) and knee points (KPs) of the non-dominated solution set. The developed AAODM approach was then applied to a case study of agricultural crop management in Bayan Nur City, China. The results showed that the level of economic development was a key factor influencing the increase in carbon footprint in Bayan Nur City over the past 20 years. The regulation of the level of economic development would significantly influence the agricultural carbon footprint in Bayan Nur City. Moreover, two optimal crop cultivation patterns were provided for decision-makers by selecting solutions from the Pareto front with decision making methods. The comparison results with other methods showed that the solutions obtained by NSGA-II were superior to MOPSO in terms of carbon reduction. The developed AAODM approach for agricultural GHG mitigation could help agricultural production systems in achieving low carbon emissions and high efficiency.

MULTI-RESOURCE ALLOCATION AND LEVELING IN MULTI-PROJECT SCHEDULING PROBLEM WITH HYBRID-CHROMOSOME NON-DOMINATED SORTING GENETIC ALGORITHM II

Multi-resource allocation and leveling in multi-project (MR-AL-MP) scheduling refers to the attempt of producing a project schedule with minimum project duration and maximum resource utilization while complying with all precedence and resource availability constraints in a multi-project environment involving multiple resources. This study proposes a model that integrates both resource allocation and leveling models into a unified framework. This study develops a modified version of the Non-Dominated Sorting Genetic Algorithm II (NSGA-II), called Hybrid-Chromosome NSGA-II, as the optimization algorithm. For validation purposes, the performance of Hybrid-Chromosome NSGA-II is compared with two benchmark metaheuristic algorithms which are Multi-Objective Particle Swarm Optimization (MOPSO) and Multi-Objective Symbiotic Organisms Search (MOSOS) in optimizing a case study. It is shown that the proposed model and algorithm are able to produce a set of non-dominated solutions that represent the feasible trade-off relationships between the objectives. Furthermore, the Hybrid-Chromosome NSGA-II is superior to MOPSO and MOSOS in terms of the quality, spread, and diversity of the solutions.

Explanation of clustering result based on multi-objective optimization.

Clustering is an unsupervised machine learning technique whose goal is to cluster unlabeled data. But traditional clustering methods only output a set of results and do not provide any explanations of the results. Although in the literature a number of methods based on decision tree have been proposed to explain the clustering results, most of them have some disadvantages, such as too many branches and too deep leaves, which lead to complex explanations and make it difficult for users to understand. In this paper, a hypercube overlay model based on multi-objective optimization is proposed to achieve succinct explanations of clustering results. The model designs two objective functions based on the number of hypercubes and the compactness of instances and then uses multi-objective optimization to find a set of nondominated solutions. Finally, an Utopia point is defined to determine the most suitable solution, in which each cluster can be covered by as few hypercubes as possible. Based on these hypercubes, an explanations of each cluster is provided. Upon verification on synthetic and real datasets respectively, it shows that the model can provide a concise and understandable explanations to users.

Performance prediction of the centrifugal air compressor for fuel cells considering degradation characteristics based on the hierarchical evolutionary model

The performance of the centrifugal air compressor is closely related to the efficiency and energy density of the fuel cell system, and extensive work has been done in this study to achieve precise performance predictions of the compressor considering degradation characteristics. The durability test of the compressor was carried out for 5000 h, and degradation characteristics with break-in time were discussed in detail. On this basis, the hierarchical evolutionary model was constructed to perform the performance predictions based on the Light Gradient Boosting Machine (LightGBM) and Multi-objective Whale Optimization Algorithm (MOWOA). The results demonstrate that the outlet pressure of the compressor decreases by 9.4 kPa and the power consumption increases by 0.71 kW at rated volume flow rate after the break-in of 5000 h, with attenuation ratios of 4.7 % and 12.2 %, respectively. The final non-dominated solution sets have excellent uniformity, diversity and convergence, proving that the developed MOWOA has high adaptability and strong optimization capability. The hierarchical evolutionary model achieves exact predictions for the outlet temperature, flow rate and pressure of the compressor, with absolute relative errors (AREs) below 1 % in outlet temperature and pressure while 5 % in outlet flow rate. All of these provide an efficient multi-objective optimization algorithm and an auto-calibrated hierarchical evolutionary model for further performance optimization of the air compressor.

Optimization method of PMU placements base on costs and risk assessments of state estimation

In the context of vigorous development of new energy sources, optimizing the arrangement of phase measurement units (PMUs) is crucial to realize real-time data monitoring for distribution network (DN) condition assessment. Firstly, we propose a multi-objective model for optimal PMU placements. Secondly, we classified the buses based on the Jacobi matrix and the grid structure, and calculated the unobservable risk probability of the system by estimating the state of the PMUs installed on the buses, so as to obtain the observability of the system. Finally, two simulations of PMU placements in the DN implementing the IEEE39 bus are designed and the placement schemes are determined through solving the non-dominated Pareto solution sets by NSGA-II. The verifications show that the model reduces the placement number of PMUs, resulting in a cost reduction of 35.4% and an unobservable risk indicator δ reduction of 13.8%, and achieves an optimal placement of PMUs.

A scenario-based robust possibilistic-flexible programming model for responsive supply chain network design with a performance-oriented solution methodology

This study addresses an integrated multi-objective responsive supply chain network optimization problem under hybrid uncertain business environment and optimal scheme selection. In addition to economic performance, delivery time and delivery reliability, as responsiveness indicators, are introduced into the multi-objective mixed-integer linear programming model. To deal with hybrid uncertainties caused by various scenarios, parameters, and flexible constraints, a scenario-based robust possibilistic flexible programming approach is extended. Moreover, a performance-oriented solution method is developed to solve the multi-objective optimization problem. The method integrates meta-heuristic and entropy-weighted TOPSIS to perform performance evaluation together with iteration optimization. The set of non-dominant solutions obtained by evaluation guide the iteration process. The numerical case verifies the effectiveness and efficiency of the proposed model, uncertainty technical and solution method. Interestingly, Pareto optimal solution set and its sort obtained by evaluation provide the optimal network scheme with the best supply chain performance.

A bi-objective time-dependent vehicle routing problem with delivery failure probabilities

This work presents a bi-objective time-dependent vehicle routing problem with delivery failure probabilities (TDVRPDFP). Two objectives are jointly minimized: operational costs and delivery failure rates. Both travel times and costs, as well as the probabilities of delivery failure and service times and costs, are considered time-dependent. A mixed-integer linear programming model is proposed to obtain sets of non-dominated solutions for small-size instances, while a multi-objective genetic algorithm, NSGA-II, is implemented to obtain approximate sets of non-dominated for large-size instances. Five sets of instances are proposed and used to evaluate the solution approaches. Our results indicate that the implemented NSGA-II algorithm can optimally solve small and large instances and find large Pareto fronts for instances with more than 25 nodes and 40-time intervals.

Multi-objective optimization for the daylighting and thermal comfort performance of elevated subway station buildings in cold climate zone of China

The rapid development of urban rail transit brings about the rapid growth of elevated subway station buildings, while the demand for comfortable waiting environments on the passenger platforms is also increasing. Due to the fact that elevated stations generally have a transparent envelope, there is a contradiction between daylighting, heating, and air conditioning. Therefore, multi-objective optimization design is essential. This article selects the cold regions of northern China as the research object. A field investigation was carried out, and Tianjin University Town Station was found to be a typical station in cold climate zone of China. A prototypical model was built based on it using Grasshopper in Rhino. Sensitivity analysis was used to screen key independent variables, and strength Pareto evolutionary algorithm II was used to optimize the daylighting and thermal comfort performance for the elevated subway station buildings. Two optimization processes, step-by-step and one-step, were used to obtain the non-dominated solution set, and the optimal solution was obtained by technique for order preference by similarity to an ideal solution analysis. The suggested values for the design variables of the prototypical model are also displayed. Reducing the skylight's window-to-wall ratio helps improve daylighting and thermal comfort. Besides, the one-step optimization method has higher efficiency and can obtain better results. The findings proposed here can guide the development of elevated subway station buildings in north China and other areas with similar conditions.

Space division and adaptive selection strategy based differential evolution algorithm for multi-objective satellite range scheduling problem

Satellite range scheduling always plays a crucial role in tracking, telemetry, and control of the spacecraft. With the significant increase in the number and type of satellites in orbit, the demands of users for satellite range scheduling are becoming more and more diverse. However, existing studies for the satellite range scheduling problem (SRSP) rarely consider multiple optimization objectives, which is quite significant in practice. Hence, this paper investigates a multi-objective satellite range scheduling problem (MO-SRSP) that optimizes three objectives simultaneously: the overall profits of tasks, load-balance of antennas, and completion timeliness of tasks. To address MO-SRSP, this paper establishes a mathematical model on the basis of analysis of MO-SRSP and proposes a multi-objective evolutionary algorithm, which is called multi-objective differential evolution algorithm based on space division and adaptive selection strategy (MODE-SDAS). The space division strategy will uniformly divide the objective space into a set of subspaces and preserve a set of non-dominated solutions in each subspace during the environmental selection even if some of these solutions are dominated by other solutions in other subspaces, so as to maintain the diversity of the algorithm. The adaptive selection strategy will adaptively allocate computational resources to different subspaces to improve the convergence of the population. Besides, problem-specific designs such as coding and encoding methods, the discrete differential evolution operator, as well as objective-specific individual variation operators are incorporated into the algorithm to enhance the search capability. Finally, extensive experiments based on simulation test cases are carried out to verify the effectiveness and efficiency of MODE-SDAS. The comparison results show that MODE-SDAS significantly outperforms its competitors in terms of three metrics. Meanwhile, knee point analysis, sensitivity analysis, and application insights are presented.

Multi-objective optimization of energy-efficient retrofitting strategies for single-family residential homes: Minimizing energy consumption, CO2 emissions and retrofit costs

The retrofitting of buildings for improved energy efficiency has been recognized as crucial for achieving climate mitigation goals in Bosnia and Herzegovina (B&H). However, performing multi-objective optimizations for retrofitting existing buildings poses challenges, as it requires balancing conflicting objectives such as retrofit costs, energy savings, and CO2 reduction. To tackle this challenge, we employed a multi-objective analysis approach that aims to identify Pareto-optimal solutions for retrofitting, striking a balance between energy consumption, CO2 emissions, and retrofit costs. In this study, we utilized a combination of Full Factorial Design (FFD) and the state-of-the-art NSGA-III framework to evaluate energy-efficient (EE) retrofit strategies for residential buildings in B&H. The analysis was based on the existing building database from the national TABULA study, serving as a fundamental reference. By analyzing this data, we aimed to determine the optimal approach for EE retrofitting in single-family homes (SFH). Key results indicate that upgrading external walls and improving heating system efficiency are the most effective measures for reducing energy consumption and CO2 emissions. However, these measures come with higher retrofit costs. A multi-objective optimization approach identifies a set of non-dominated solutions representing energy efficiency retrofit measures with the lowest specific final energy for heating, specific CO2 emissions, and overall retrofit costs. The top-ranked set of measures achieves a Simple Payback Period (SPP) of 19.9 years. The insights gained from this study are intended to provide valuable guidance to decision-makers in formulating cost-effective and energy-efficient retrofitting strategies that simultaneously minimize annual energy consumption, CO2 emissions, and retrofit costs.

Optimal Design of the Austenitic Stainless-Steel Composition Based on Machine Learning and Genetic Algorithm.

As the fourth paradigm of materials research and development, the materials genome paradigm can significantly improve the efficiency of research and development for austenitic stainless steel. In this study, by collecting experimental data of austenitic stainless steel, the chemical composition of austenitic stainless steel is optimized by machine learning and a genetic algorithm, so that the production cost is reduced, and the research and development of new steel grades is accelerated without reducing the mechanical properties. Specifically, four machine learning prediction models were established for different mechanical properties, with the gradient boosting regression (gbr) algorithm demonstrating superior prediction accuracy compared to other commonly used machine learning algorithms. Bayesian optimization was then employed to optimize the hyperparameters in the gbr algorithm, resulting in the identification of the optimal combination of hyperparameters. The mechanical properties prediction model established at this stage had good prediction accuracy on the test set (yield strength: R2 = 0.88, MAE = 4.89 MPa; ultimate tensile strength: R2 = 0.99, MAE = 2.65 MPa; elongation: R2 = 0.84, MAE = 1.42%; reduction in area: R2 = 0.88, MAE = 1.39%). Moreover, feature importance and Shapley Additive Explanation (SHAP) values were utilized to analyze the interpretability of the performance prediction models and to assess how the features influence the overall performance. Finally, the NSGA-III algorithm was used to simultaneously maximize the mechanical property prediction models within the search space, thereby obtaining the corresponding non-dominated solution set of chemical composition and achieving the optimization of austenitic stainless-steel compositions.

A multiobjective dynamic rebalancing evolutionary algorithm for free-floating bike sharing

The big challenge of free-floating bike sharing system is to rebalance the supply and demand in different places. Most studies are static rebalancing that moves bikes at night. Dynamic rebalancing considers the scheduling of transport vehicles during the day. It is more effective and difficult to solve. In this paper, a multiobjective dynamic rebalancing problem is solved. The two optimization objectives are considered: minimizing the total distance of rebalancing vehicle and minimizing the total demand unmet. A mathematic model is built to formulate the problem. A new algorithm SFMEA-AP (Sequence Flow Multiobjective Evolutionary Algorithm with Area Protected) that uses the sequence flow encoding is proposed. An novel area protected strategy that includes a non-dominated sorting with similarity comparison is proposed. It simultaneously considers the fairness and competitiveness in solution space. Six neighborhood search operators are designed. They are used as variable neighborhood search strategy. Computational experiments show that SFMEA-AP can obtain better solution quality than SFMEA-VNS, QMOEA, NSGA-II, ILS and LSMOVRPTW. The IGD values of non-dominated solutions of SFMEA-AP are better than those of SFMEA-VNS, QMOEA, NSGA-II, ILS and LSMOVRPTW. In addition, the non-dominated solution set of SFMEA-AP have good diversity.