Bi-objective Optimization Problem Research Articles

Accelerated Driving-Training-Based Optimization for Solving Constrained Bi-Objective Stochastic Optimization Problems

The constrained bi-objective stochastic optimization problem (CBSOP) considers the optimization problem with stochastic bi-objective functions subject to deterministic constraints. The CBSOP is part of a set of hard combinatorial optimization problems regarding time complexity. Ordinal optimization (OO) theory provides a commonly recognized structure to handle hard combinatorial optimization problems. Although OO theory may solve hard combinatorial optimization problems quickly, the deterministic constraints will critically influence computing performance. This work presents a metaheuristic approach that combines driving-training-based optimization (DTBO) with ordinal optimization (OO), abbreviated as DTOO, to solve the CBSOP with a large design space. The DTOO approach comprises three major components: the surrogate model, diversification, and intensification. In the surrogate model, the regularized minimal-energy tensor product with cubic Hermite splines is utilized as a fitness estimation of design. In diversification, an accelerated driving-training-based optimization is presented to determine N remarkable designs from the design space. In intensification, a reinforced optimal computing budget allocation is used to find an extraordinary design from the N remarkable designs. The DTOO approach is applied to a medical resource allocation problem in the emergency department. Simulation results obtained by the DTOO approach are compared with three heuristic approaches to examine the performance of the DTOO approach. Test results show that the DTOO approach obtains an extraordinary design with higher solution quality and computational efficiency than the three heuristic approaches.

Decision-making strategies implemented in SolFinder 1.0 to identify eco-efficient aircraft trajectories: application study in AirTraf 3.0

Abstract. The optimization of aircraft trajectories involves balancing operating costs and climate impact, which are often conflicting objectives. To achieve compromised optimal solutions, higher-level information such as preferences of decision-makers must be taken into account. This paper introduces the SolFinder 1.0 module, a decision-making tool designed to identify eco-efficient aircraft trajectories, which allow for the reduction of the flight's climate impact with limited cost penalties compared to cost-optimal solutions. SolFinder 1.0 offers flexible decision-making options that allow users to select trade-offs between different objective functions, including fuel use, flight time, NOx emissions, contrail distance, and climate impact. The module is included in the AirTraf 3.0 submodel, which optimizes trajectories under atmospheric conditions simulated by the ECHAM/MESSy Atmospheric Chemistry model. This paper focuses on the ability of the module to identify eco-efficient trajectories while solving a bi-objective optimization problem that minimizes climate impact and operating costs. SolFinder 1.0 enables users to explore trajectory properties at varying locations of the Pareto fronts without prior knowledge of the problem results and to identify solutions that limit the cost of reducing the climate impact of a single flight.

State estimators for discrete‐time descriptor linear systems with mixed uncertainties and state constraints

AbstractThis article presents two novel mixed‐uncertainty state estimators for discrete‐time descriptor linear systems, namely linear time‐varying mixed‐uncertainty filter (LTVMF) and linear time‐invariant mixed‐uncertainty filter (LTIMF). The former is based on the minimum‐variance approach, from which quadratic and explicit (special case of quadratic) formulations are derived and addressed to LTV systems. Both formulations incorporate the knowledge of state linear constraints, such as equality (in the descriptor form) and inequality, to mitigate precision and accuracy issues related to initialization and evolution of the state estimates. The LTIMF algorithm is based on the mixed criterion and addressed to LTI systems, with the low‐cost computation being its motivation. Both LTVMF and LTIMF algorithms solve state‐estimation problems in which the uncertainties are combined to yield the so‐called mixed‐uncertainty vector, which is composed by set‐bounded uncertainties, characterized by constrained zonotopes, and stochastic uncertainties, characterized by Gaussian random vectors. As mixed‐uncertainty vectors imply biobjective optimization problems, we innovatively present multiobjective arguments to justify the choice of the solution on the Pareto‐optimal front. In order to discuss the advantages and drawbacks, the state estimators are tested in two numerical examples.

A Multi-Task Decomposition-Based Evolutionary Algorithm for Tackling High-Dimensional Bi-Objective Feature Selection

Evolutionary algorithms have been widely applied for solving multi-objective optimization problems, while the feature selection in classification can also be treated as a discrete bi-objective optimization problem if attempting to minimize both the classification error and the ratio of selected features. However, traditional multi-objective evolutionary algorithms (MOEAs) may have drawbacks for tackling large-scale feature selection, due to the curse of dimensionality in the decision space. Therefore, in this paper, we concentrated on designing an multi-task decomposition-based evolutionary algorithm (abbreviated as MTDEA), especially for handling high-dimensional bi-objective feature selection in classification. To be more specific, multiple subpopulations related to different evolutionary tasks are separately initialized and then adaptively merged into a single integrated population during the evolution. Moreover, the ideal points for these multi-task subpopulations are dynamically adjusted every generation, in order to achieve different search preferences and evolutionary directions. In the experiments, the proposed MTDEA was compared with seven state-of-the-art MOEAs on 20 high-dimensional classification datasets in terms of three performance indicators, along with using comprehensive Wilcoxon and Friedman tests. It was found that the MTDEA performed the best on most datasets, with a significantly better search ability and promising efficiency.

A Bi-Objective Home Health Care Routing and Scheduling Problem under Uncertainty.

Home health care companies provide health care services to patients in their homes. Due to increasing demand, the provision of home health care services requires effective management of operational costs while satisfying both patients and caregivers. In practice, uncertain service times might lead to considerable delays that adversely affect service quality. To this end, this paper proposes a new bi-objective optimization problem to model the routing and scheduling problems under uncertainty in home health care, considering the qualification and workload of caregivers. A mixed-integer linear programming formulation is developed. Motivated by the challenge of computational time, we propose the Adaptive Large Neighborhood Search embedded in an Enhanced Multi-Directional Local Search framework (ALNS-EMDLS). A stochastic ALNS-EMDLS is introduced to handle uncertain service times for patients. Three kinds of metrics for evaluating the Pareto fronts highlight the efficiency of our proposed method. The sensitivity analysis validates the robustness of the proposed model and method. Finally, we apply the method to a real-life case and provide managerial recommendations.

A Population Initialization Method Based on Similarity and Mutual Information in Evolutionary Algorithm for Bi-objective Feature Selection

Feature selection (FS) is an important data pre-processing technique in classification. It aims to remove redundant and irrelevant features from the data, which reduces the dimensionality of data and improves the performance of the classifier. Thus, FS is a bi-objective optimization problem, and evolutionary algorithms (EAs) have been proven to be effective in solving bi-objective FS problems. EA is a population-based metaheuristic algorithm, and the quality of the initial population is an important factor affecting the performance of EA. An improper initial population may negatively affect the convergence speed of the EA and even make the algorithm fall into the local optimum. In this paper, we propose a similarity and mutual information-based initialization method, named SMII, to improve the quality of the initial population. This method determines the distribution of initial solutions based on similarity, and shields features with high correlation to the selected features according to mutual information. In the experiment, we embed SMII, the latest four initialization methods, and a traditional random initialization method into NSGA-II, and compared their performance on 15 public datasets. The experimental results show that SMII performs best on most datasets, and can effectively improve the performance of the algorithm. Moreover, we compare the performance of two other EA before and after embedding SMII on 15 datasets, the results further prove that the proposed method can effectively improve the search capability of the EA for FS.

A Lagrangian bounding and heuristic principle for bi-objective discrete optimization

Lagrangian relaxation is a common and often successful way to approach computationally challenging single-objective discrete optimization problems with complicating side constraints. Its aim is often twofold; first, it provides bounds for the optimal value, and, second, it can be used to heuristically find near-optimal feasible solutions, the quality of which can be assessed by the bounds. We consider bi-objective discrete optimization problems with complicating side constraints and extend this Lagrangian bounding and heuristic principle to such problems. The Lagrangian heuristic here produces non-dominated candidates for points on the Pareto frontier, while the bounding forms a polyhedral outer approximation of the Pareto frontier, which can be used to assess the quality of the candidate points. As an illustration example we consider a facility location problem in which both CO2 emission and cost should be minimized. The computational results are very encouraging, both with respect to bounding and the heuristically found non-dominated solutions. In particular, the Lagrangian bounding is much stronger than the outer approximation given by the Pareto frontier of the problem’s linear programming relaxation.

A novel cost-palatability bi-objective approach to the menu planning problem with an innovative similarity metric using a path relinking algorithm

Bad eating habits are considered with low exercise, tobacco, and alcohol use, among the greatest health risk factors in high-income countries. Here, the spread of non-communicable diseases related to diet contrasts with the increasing availability of diet guidelines and health information. We are all left wondering, why are we not eating healthier? Palatability and cost appear as the two most important barriers to adherence to any prescribed diet. This work aims to generate high-adherence healthy menus attending to Mediterranean standards, modelling and solving a cost palatability bi-objective optimisation problem. Although the latter is implicitly considered in most current models, its use as a quantifiable objective is novel. For this, a novel Similarity Function is introduced, which evaluates the proximity of two different menus and returns a similarity metric between 0 and 1. A multi-criteria optimisation method is used to design nutritious menu plans and analyse the trade-off between the cost and palatability of menus. A Path Relinking algorithm is later applied to improve the objective values, with specific considerations to palatability, designing healthy menus that can beat those adherence barriers.

Integrated System Design for Post-Disaster Management: Multi-Facility, Multi-Period, and Bi-Objective Optimization Approach

Disaster management requires efficient allocation of essential facilities with consideration of various objectives. During the response and recovery phase of disaster management (RRDM), various types of missions occur in multiple periods, and each of them needs different support from facilities. In this study, a bi-objective mathematical model was derived to support multi-period RRDM by optimal allocation of required facilities such as drone stations, shelters, emergency medical facilities, and warehouses according to the mission life cycle. Connectivity between facilities was considered to ensure inter-facility complementarity. For efficient derivation of Pareto solutions, a modified epsilon-constraint algorithm for bi-objective optimization was developed. The algorithm was tested with a realistic disaster simulation scenario using HAZUS 4.0 as a demonstration of the benefits of the proposed approach. With the simulation experiments, the proposed approach was expected to provide efficient operational plans and guidelines to decision makers for the bi-objective optimization problem in RRDM systems. In addition, the consideration of inter-facility connectivity can play an important role in the RRDM, especially for robustness and readiness.

Investigation on distributed scheduling with lot-streaming considering setup time based on NSGA-II in a furniture intelligent manufacturing

Distributed flexible flowshop scheduling is getting more important in the large-scale panel furniture industry. It is vital for a higher manufacturing efficiency and economic profit. The distributed scheduling problem with lot-streaming in a flexible flow shop environment is investigated in this work. Furthermore, the actual constraints of packaging collaborative and machine setup times are considered in the proposed approach. The average order waiting time for packaging and average order delay rate is used as objectives. Non-dominated sorting method is used to handle this bi-objective optimization problem. An improved encoding method was proposed to address the large-scale orders that need to be divided into sub-lots based on genetic algorithm. The proposed approach is firstly validated by benchmark with other multi-objectives evolutionary algorithms. The results found that the proposed approach had a good convergence and diversity. Besides, the influence of the proportion of large-scale orders priority level and sub-lot size was investigated in a panel furniture manufacturing scenario. The results can be concluded that the enterprise could obtain shorter order average waiting time and delay rate when the sub-lot sizes were set as two and the order priority level was allocated in the proportion of 1:2:3:4:5.

A Hybrid Initialization and Effective Reproduction-Based Evolutionary Algorithm for Tackling Bi-Objective Large-Scale Feature Selection in Classification

Evolutionary algorithms have been widely used for tackling multi-objective optimization problems, while feature selection in classification can also be seen as a discrete bi-objective optimization problem that pursues minimizing both the classification error and the number of selected features. However, traditional multi-objective evolutionary algorithms (MOEAs) can encounter setbacks when the dimensionality of features explodes to a large scale, i.e., the curse of dimensionality. Thus, in this paper, we focus on designing an adaptive MOEA framework for solving bi-objective feature selection, especially on large-scale datasets, by adopting hybrid initialization and effective reproduction (called HIER). The former attempts to improve the starting state of evolution by composing a hybrid initial population, while the latter tries to generate more effective offspring by modifying the whole reproduction process. Moreover, the statistical experiment results suggest that HIER generally performs the best on most of the 20 test datasets, compared with six state-of-the-art MOEAs, in terms of multiple metrics covering both optimization and classification performances. Then, the component contribution of HIER is also studied, suggesting that each of its essential components has a positive effect. Finally, the computational time complexity of HIER is also analyzed, suggesting that HIER is not time-consuming at all and shows promising computational efficiency.

A Tri-objective Method for Bi-objective Feature Selection in Classification.

Minimizing the number of selected features and maximizing the classification performance are two main objectives in feature selection, which can be formulated as a biobjective optimization problem. Due to the complex interactions between features, a solution (i.e., feature subset) with poor objective values does not mean that all the features it selects are useless, as some of them combined with other complementary features can greatly improve the classification performance. Thus, it is necessary to consider not only the performance of feature subsets in the objective space, but also their differences in the search space, to explore more promising feature combinations. To this end, this paper proposes a tri-objective method for bi-objective feature selection in classification, which solves a bi-objective feature selection problem as a triobjective problem by considering the diversity (differences) between feature subsets in the search space as the third objective. The selection based on the converted triobjective method can maintain a balance between minimizing the number of selected features, maximizing the classification performance, and exploring more promising feature subsets. Furthermore, a novel initialization strategy and an offspring reproduction operator are proposed to promote the diversity of feature subsets in the objective space and improve the search ability, respectively. The proposed algorithm is compared with five multi-objective-based feature selection methods, six typical feature selection methods, and two peer methods with diversity as a helper objective. Experimental results on 20 real-world classification datasets suggest that the proposed method outperforms the compared methods in most scenarios.

Time–jerk optimal trajectory planning for industrial robots with coupled interpolation function selection

AbstractIn the contemporary field of optimal trajectory planning for industrial robots, it is customary to construct trajectories through the manual predefinition of interpolation functions. Unfortunately, this method frequently overlooks the influence of the interpolation function itself on the optimization objectives, resulting in suboptimal outcomes. To remedy this limitation, an optimal trajectory planning method with coupled interpolation function selection is proposed, in which the total task time and the integral squared jerk are defined as optimization objectives. This method minimizes the optimization objectives while also factoring in the optimal interpolation function, and avoiding subjective interference. To address the aforementioned biobjective optimization problem better, an Improved MultiObjective Golden Eagle Optimizer is introduced. Population diversity and the ability to escape local optima are enhanced through the incorporation of Chaotic Mapping, Opposition‐Based Learning, Differential Evolution, and adaptive inertia weight strategy into the algorithm. The superiority of the algorithm is validated through a series of simulations on 17 benchmark functions. In the context of the robotic stirring operation within the automated block cast charging process, the proposed method is utilized to derive the time–jerk optimal trajectory. The results demonstrate the effectiveness of the proposed method.

Toward Reliable DNN-Based Task Partitioning and Offloading in Vehicular Edge Computing

Modern vehicles have become typical consumer electronics with the development of sensing, transmission, and computation technologies. The emerging intelligent transportation systems (ITSs) yield lots of deep neural network (DNN) based tasks, requiring intensive computation. In view of this, this paper makes the first exploration of accelerating the processing of DNN-based tasks while maintaining decent system reliability in vehicular edge computing (VEC) via task partitioning and offloading. Specifically, we present a specific scenario, where vehicles partition and offload their tasks to nearby vehicles and roadside infrastructures, while they may fail to receive results due to unstable vehicular communications. Then, we model the task delay by considering task properties and node capacities. On this basis, the Partitioning and Offloading Problem (POP) is formulated as a bi-objective optimization problem, to maximize both the acceleration ratio and service ratio of DNN-based tasks in VEC. Further, we propose a Distributed Partitioning and Offloading Solution (DPOS), where a delay-priority-oriented offloading strategy is designed to help edge nodes make offloading decisions, and a stacking-based partitioning strategy is designed to assist client vehicles to make partitioning decisions. Finally, we give a comprehensive performance evaluation, which demonstrates the superiority of the proposed solution.

A Bi-Objective Evolutionary Algorithm for Multimodal Multiobjective Optimization

Multimodal multi-objective optimization problems (MMOPs) possess multiple Pareto optimal sets corresponding to the identical Pareto optimal front (PF). To handle MMOPs, we propose a bi-objective evolutionary algorithm (BOEA), which transforms an MMOP into a bi-objective optimization problem. This problem is constructed by the penalty boundary intersection technique and a diversity indicator to obtain multiple Pareto optimal sets. The first objective reflects the population convergence and factors in the population diversity in the objective space, while the other objective concentrates more on the population diversity in the decision space. Furthermore, an environmental selection strategy is designed to choose the offspring solutions, which consists of non-dominated sorting based on the transformed optimization problem and hierarchical clustering for selecting promising solutions. Experiments on 34 MMOPs demonstrate that BOEA performs better than selected state-of-the-art representatives, including 22 MMOPs from CEC2019 and 12 imbalanced MMOPs. In addition, the effectiveness of BOEA is further validated by six feature selection problemsin real-world applications.

Lightweight Imitation Learning for Real-Time Cooperative Service Migration

Due to the revolution of communication technology, the rapidly increasing number of mobile devices in edge networks generates various real-time service requests, requiring a considerable volume of heterogeneous resources all the time. However, edge devices with limited resources cannot afford substantial learning cost, while migrating services requires heterogeneous resources, especially for dynamic networks. To address these issues, we first establish a cooperative service migration framework and formulate a bi-objective optimization problem to optimize service performance and cost. By analyzing the optimal migration ratio of service cooperative migration, we propose an offline expert policy based on global states to provide optimal expert demonstrations. To realize real-time service migration based on observable states, we design a lightweight online agent policy to imitate expert demonstrations and leverage meta update to accelerate the model transfer. Experimental results show that our algorithm is exceptional in training cost and accuracy, and has significant superiors in multiple metrics such as the service latency and payment under different workloads, compared to other representative algorithms.

A Distributed Scheme for the Taxi Cruising Route Recommendation Problem Using a Graph Neural Network

Despite considerable research efforts being devoted to the taxi cruising route recommendation (TCRR) problem, existing studies still have some shortcomings. To begin with, the competition and collaboration between taxis are not sufficiently taken into account. Furthermore, the TCRR is heavily reliant on potential taxi demand, which is time-variant and difficult to accurately predict due to the underlying spatiotemporal correlation and dynamic traffic patterns. Moreover, the consideration of competition and cooperation among taxis increases the complexity of the TCRR problem, making conventional centralized algorithms computationally expensive. In this paper, we first formulate TCRR as a biobjective optimization problem to balance the collaboration and competition between taxis. Subsequently, we forecast short-term taxi demand using the proposed long-short-term-memory-based graph convolutional network (LSTM-GCN), which considers diverse factors such as road topology, points of interest (POIs), and multiple time-scale features. Lastly, we propose a distributed algorithm based on a Lagrange dual decomposition. The experimental and simulation results demonstrate that our TCRR scheme performs better than any other counterpart, (i) resulting in a 3% reduction in idle taxis per hour, (ii) performing four times faster than the centralized algorithms to obtain the optimal solution, and (iii) resulting in a 7% increase in average profit.

Portfolio optimization based on bi-objective linear programming

In this study, we deal with a portfolio optimization problem including both risky and risk-free assets. We use the infinity norm criterion to measure portfolio risk and formulate the problem as a bi-objective linear optimization problem. Then, a single objective linear program is considered related to the bi-objective optimization problem. Using the well-known Karush-Kuhn-Tucker optimality conditions, we obtain analytic formula for an optimal solution. Moreover, we determine the whole efficient frontier by multi-criteria optimization techniques. Based on the theoretical results, two algorithms are proposed for finding the portfolio weights and the efficient frontier. Numerical examples are given for illustrating the new models and algorithms. Additionally, a simulation study has been conducted to assess the performance of the proposed method.

Bi-Objective Incentive Mechanism for Mobile Crowdsensing With Budget/Cost Constraint

In recent years, mobile crowdsensing (MCS) has been widely adopted as an efficient method for large-scale data collection. In MCS systems, insufficient participation and unstable data quality have become two crucial issues that prevent crowdsensing from further development. Thus designing a valid incentive mechanism is essentially significant. Most of the existing works on incentive mechanism design focus on single-objective optimization with various constraints. However, in the real-world crowdsensing, it is common that several objectives to be optimized exist. Furthermore, constraints on budget or cost are often seen in MCS systems as the feasibility of implementing incentive mechanism is indispensable. This paper studies a bi-objective optimization scenario of MCS to simultaneously optimize total value function and coverage function with budget/cost constraint through a set of problem transformations. Then a budget- or cost-feasible bi-objective incentive mechanism is further proposed to solve the aforementioned bi-objective optimization problem through the combination of binary search and greedy heuristic solution under budget or cost constraint, respectively. Through both rigorous theoretical analysis and extensive simulations, the obtained results demonstrate that the mechanisms achieve computation efficiency, individual rationality, truthfulness, and budget or cost feasibility, while one mechanism obtains an approximation.

Bi-Objective Optimization of Subsurface CO2 Storage with Nonlinear Constraints Using Sequential Quadratic Programming with Stochastic Gradients

Summary This study focuses on carbon capture, utilization, and sequestration (CCUS) via the means of nonlinearly constrained production optimization workflow for a CO2-enhanced oil recovery (EOR) process, in which both the net present value (NPV) and the net present carbon tax credits (NPCTC) are bi-objectively maximized, with the emphasis on the consideration of injection bottomhole pressure (IBHP) constraints on the injectors, in addition to field liquid production rate (FLPR) and field water production rate (FWPR), to ensure the integrity of the formation and to prevent any potential damage during the life cycle injection/production process. The main optimization framework used in this work is a lexicographic method based on the line-search sequential quadratic programming (LS-SQP) coupled with stochastic simplex approximate gradients (StoSAG). We demonstrate the performance of the optimization algorithm and results in a field-scale realistic problem, simulated using a commercial compositional reservoir simulator. Results show that the workflow can solve the single-objective and bi-objective optimization problems computationally efficiently and effectively, especially in handling and honoring nonlinear state constraints imposed onto the problem. Various numerical settings have been experimented with to estimate the Pareto front for the bi-objective optimization problem, showing the trade-off between the two objectives of NPV and NPCTC. We also perform a single-objective optimization on the total life cycle cash flow, which is the aggregated quantity of NPV and NPCTC, and quantify the results to further emphasize the necessity of performing bi-objective production optimization, especially when used in conjunction with commercial flow simulators that lack the capability of computing adjoint-based gradients.