Complex Multi-objective Problems Research Articles

Two-stage stochastic multi-criteria group decision making for wind-photovoltaic-hydropower scheduling

Scheduling of wind-photovoltaic-hydropower systems is a complex multi-objective collaborative problem which requires multi-criteria decision making (MCDM) to assist in formulating the most-preferred scheduling scheme. There are uncertainties existing in criteria weights (CWs) due to the limitations of the knowledge level of decision makers and the subjectivity of preferences. This paper proposes a two-stage stochastic multi-criteria group decision making model considering the uncertainties in the decision making environment and the progression of the decision making process. For the prophase decision making (the first stage), the stochastic multi-criteria acceptability analysis (SMAA) theory and the MCDM model VIKOR are combined to construct a SMAA-VIKOR model for inverse weight space analysis on the situation that the initial CW information is completely unknown. In the second stage of decision making, the decision makers are allowed to express their fuzzy preferences based on the information provided in the first stage by coupling the intuitionistic fuzzy analytic hierarchy process (IFAHP) into the SMAA-VIKOR model to obtain the final scheme. The wind-photovoltaic-hydropower system in Yalong River Basin is selected as the case study. Results show that among the 12 alternative schemes, scheme A2 is ranked first with the probability of 0.69 in the first stage while the probability of taking the first ranking in the second stage is increased to 1. More explicit ranking results are obtained based on the results of the first stage, which effectively enhances the confidence of decision makers and improves decision making efficiency.

Multiobjective enterprise development algorithm for optimizing structural design by weight and displacement

This study presents a novel metaheuristic optimization algorithm for complex multiobjective engineering problems. By integrating advanced population and nondominated sorting techniques into the existing single-objective enterprise development algorithm, this new multiobjective approach effectively identifies Pareto-optimal solutions. The algorithm leverages these techniques to explore engineering solutions within multiobjective search spaces. We evaluated its performance using 29 multiobjective mathematical benchmark problems and conducted a comparative analysis against ten established metaheuristic optimization algorithms. The results demonstrate that the algorithm produces highly accurate approximations of Pareto-optimal fronts while maintaining a uniform distribution of solutions. Additionally, the algorithm was applied to real-world engineering challenges, including the optimization of structures such as the 942-bar tower, the 1536-bar double-layer barrel vault, and the 1410-bar double-layer dome truss, with the primary objectives of minimizing both structural weight and maximum nodal deflection. The findings highlight the algorithm's effectiveness in solving practical engineering problems and consistently achieving optimal Pareto fronts.

Facilitating Circular Transition in the Construction Industry: Optimizing a Prefabricated Construction Site Layout Using a Novel BIM-Integrated SLP-GA Model

Prefabricated construction is being developed as one of the pathways toward circularity in the construction industry. However, compared to traditional cast-in-place construction methods, the design of prefabricated construction site layouts presents unique challenges, such as managing the space for prefabricated components and lifting equipment, and coordinating the precise timing between off-site fabrication and on-site assembly. Existing research has primarily focused on traditional cast-in-place construction, leaving room for improvement in optimisation models for prefabricated site layouts. This study develops a BIM-based System Layout Planning-Genetic Algorithm (SLP-GA) model specifically tailored for prefabricated construction site optimisation. The proposed model improves the accuracy and visualisation of layout planning through BIM technology, enabling dynamic adjustments and real-time data integration. It also incorporates genetic algorithms to address complex multi-objective optimisation problems, avoiding local optima and overcoming the limitations of traditional SLP methods that rely on subjective judgements. Unlike previous studies that do not consider secondary handling, the optimisation objectives of this study focus on minimising material handling costs associated with secondary handling and maximising comprehensive relationships, including efficiency, safety and space utilisation. The application of this model in a case study shows a reduction in logistics costs of 8.58% and an improvement in comprehensive relationships of 11.61%, indicating significant improvements. This research advances optimisation methods for prefabricated construction site layouts, enriches optimisation objectives by considering secondary handling, and provides practical guidance for improving the efficiency and effectiveness of prefabricated construction projects.

Optimized scheduling of integrated community energy stations based on improved NSGA-III algorithm

To cope with the problem of building and using a large number of fast electric vehicle stations (FEVS), adding FEVS to the integrated community energy system (ICES) provides new ideas for solving the problems of interaction with the grid, overall system stability, revenue benefits, and environmental pollution. To this end, this paper designs an ICES model with FEVS (ICES-FEVS). This model considers economy, stability, and sustainability to achieve all-around consideration. To further solve the complex multi-objective problem, the multi-objective improvement strategy NSGA-III algorithm (IS-NSGA-III), combined with fuzzy comprehensive evaluation (FCE), is used to solve the model. In the solution phase, the advantages of the IS-NSGA-III algorithm are first verified by the benchmark function, and the validity of the ICES-FEVS model is verified by comparing different models. In the optimization results, daily revenue was increased by 6.3 %, daily battery life loss was increased by 26.03 %, and pollution emissions were reduced by 46.9 %. The analysis of the results shows that introducing Electric Vehicle (EV) fast charging stations in an integrated community energy system ensures economic improvement, sustainable development, and more favorable regulation of the energy storage system. The simulation results show that compared with other algorithms, the HV metrics of IS-NSGA-III are lower by about 6.8 %, Spread metrics are better by about 1.35 %, and the proposed IS-NSGA-III is better in terms of convergence and distributivity.

Single-objective and multi-objective mixed-variable grey wolf optimizer for joint feature selection and classifier parameter tuning

Feature selection plays an essential role in data preprocessing, which can extract valuable information from extensive data, thereby enhancing the performance of machine learning classification. However, existing feature selection methods primarily focus on selecting feature subsets without considering the impact of classifier parameters on the optimal subset. Different from these works, this paper considers jointly optimizing the feature subset and classifier parameters to minimize the number of features and achieve a low classification error rate. Since feature selection is an optimization problem with binary solution space while classifier parameters involve both continuous and discrete variables, our formulated problem becomes a complex multi-objective mixed-variable problem. To address this challenge, we consider a single-objective optimization method and a multi-objective optimization approach. Specifically, in the single-objective optimization method, we adopt the linear weight method to convert our multiple objectives into a fitness function and then propose a mixed-variable grey wolf optimizer (MGWO) to optimize the function. The proposed MGWO introduces Chaos-Faure initialization, Log convergence factor adjustment, and optimal solution adaptive update operators to enhance its adaptability and balance the global and local search of the algorithm. Subsequently, an improved multi-objective grey wolf optimizer (IMOGWO) is introduced to directly address the problem. The proposed IMOGWO introduces improved initialization, local search, and binary variable mutation operators to balance its exploration and exploitation abilities, making it more suitable for our mixed-variable problem. Extensive simulation results show that our MGWO and IMOGWO outperform recent and classic baselines. Moreover, we also find that jointly optimizing classifier parameters can significantly improve classification accuracy.

Multi-objective optimization of reactive power dispatch problem using fuzzy tuned mayfly algorithm

The recent multi-objective optimization problems are very complex which require an effective and robust evolutionary method for obtaining a global Pareto-optimal solutions. Most of these multi-objective evolutionary techniques are population-based methods which usually work on random search approaches and often trapped into local minima during their execution. A new fuzzy tuned mayfly algorithm (FTMA) is presented in this paper, to obtain the Pareto-optimal solutions for any complex multi-objective power system problem. It has a self-adapting global exploration capability to get the best Pareto-optimal solutions by varying two crucial parameters i.e., crossover (Pc) and mutation Pm probabilities. Moreover, a model of Pareto-dominance is employed to rank non-dominating solutions to maintain the diversity within the populations. The proposed evolutionary approach is examined on a standard ZDT benchmark test suite and its algorithmic performance is statistically compared with a few of the recent optimization techniques such as NSGA-II, NSGA-III, MMODE, MOAVOA and MMA algorithm. It is further applied to minimize two distinct objective functions (i.e., total transmission loss and voltage stability index) for IEEE-118 bus system and IEEE-24 bus RTS. A comprehensive statistical analysis is presented for the obtained numerical results, which proves that proposed FTMA has better convergence with better solution diversity in comparison to the other competing algorithms. A comprehensive analysis based on statistical results reveal that the proposed FTMA is superior for obtaining better non-dominating pareto-fronts as compared to other competing methods.

A Hybrid Strategy Guided Multi-Objective Artificial Physical Optimizer Algorithm

Artificial physical optimizer (APO), as a new heuristic stochastic algorithm, is difficult to balance convergence and diversity when dealing with complex multi-objective problems. This paper introduces the advantages of R2 indicator and target space decomposition strategy, and constructs the candidate solution of external archive pruning technology selection based on APO algorithm. A hybrid strategy guided multi-objective artificial physical optimizer algorithm (HSGMOAPO) is proposed. Firstly, R2 indicator is used to select the candidate solutions that have great influence on the convergence of the whole algorithm. Secondly, the target space decomposition strategy is used to select the remaining solutions to improve the diversity of the algorithm. Finally, the restriction processing method is used to improve the ability to avoid local optimization. In order to verify the comprehensive ability of HSGMOAPO algorithm in solving multi-objective problems, five comparison algorithms were evaluated experimentally on standard test problems and practical problems. The results show that HSGMOAPO algorithm has good convergence and diversity in solving multi-objective problems, and has the potential to solve practical problems.

A hypervolume-based cuckoo search algorithm with enhanced diversity and adaptive scaling factor

Existing multi-objective cuckoo search (MOCS) algorithms are based on either Pareto dominance or decomposition. However, when dealing with complex multi-objective problems (MOPs), the Pareto dominance-based algorithms face a decrease in selection pressure, and the decomposition-based algorithms easily gain poor distributions. The objective of this paper is to repurpose an indicator-based MOCS by combining improved diversity enhancement (IDE) and adaptive scaling factor (ASF) for MOPs. In the proposed algorithm, hypervolume is used as the indicator to guarantee better convergence and enough spread of the population. IDE chooses the large hypervolume to rebuild the parent population to compensate for the lack of population diversity. Additionally, ASF makes full use of individuals information to enhance the search ability of Lévy component in cuckoo search. Comprehensive experiments on 31 benchmark functions including two classical suites ZDT, WFG, and one challenged suite proposed in CEC2019, as well as 8 real-world problems were conducted to test the proposed algorithm. Compared with several state-of-the-art multi-objective evolutionary algorithms, the effectiveness and efficiency of our proposed method were demonstrated by the results.

A new multi-objective decision-making method with diversified weights and Pythagorean fuzzy rough sets

In reality, there are many multi-objective decision-making problems with fuzziness and uncertainty, such as the choice of clinical treatment schemes. To effectively cope with such problems, it is urgent to scientifically handle fuzzy and uncertain information. Given the fact that the Pythagorean fuzzy set is a useful tool to tackle fuzzy information, and the rough set theory is superior in dealing with uncertain data, this paper aims to establish a novel decision-making method for scheme selection from the perspective of Pythagorean fuzzy rough sets. Pythagorean fuzzy numbers (PFNs) are first employed to express fuzzy preference information, and then multi-objective Pythagorean fuzzy information systems are introduced. Subsequently, we develop a new fuzzy rough set using an improved correlation coefficient method to deal with the uncertainty of PFNs. Furthermore, considering the diversified weights, we present a weight calculation method based on approximate accuracies. Meanwhile, a weighted fuzzy rough set model is constructed to achieve multi-objective information fusion. Accordingly, a multi-objective decision-making method is put forward with the help of overlap functions. Finally, we apply the built method to three cases from different decision scenarios to illustrate the applicability of the method. By some comparative analyses, the effectiveness and superiority of the method are also exhibited. Moreover, we discuss the establishment of decision support systems regarding scheme selection. On the whole, the work of this paper is helpful to support the solution of complex multi-objective decision-making problems.

Cooperative optimization of speed planning and energy management for hybrid electric vehicles based on Nash equilibrium

The longitudinal automatic driving of hybrid electric vehicles (HEVs) is a complex multi-objective problem, and the coupling relationship between speed planning and energy management is difficult to reveal using the commonly used hierarchical control algorithm. Thus, in this paper, a collaborative control strategy is proposed for cruise speed optimization and energy management of HEVs based on Nash equilibrium. The strategy in this paper can optimize the control of vehicle-level and hybrid-system-level at the same time. First, this paper builds the key component model of HEV under the Simulink environment, which lays the foundation for vehicle control. Then, a multi-objective problem-solving framework based on game theory is proposed aiming at the economy and safety of HEV cruising. Afterward, a weight factor adjustment method is proposed based on fuzzy logic to judge the brake/drive logic. Finally, the utility functions are used for coordinated control based on Nash equilibrium. The simulation results show that the control method proposed in this paper has improved in various aspects as compared with hierarchical model predictive control, including vehicle following, safety, and comfort. In addition, this strategy can significantly reduce energy consumption costs while meeting the cruise speed requirements of vehicles. In the whole driving cycle, the strategy proposed in this paper has a high termination of SOC and a fuel consumption reduction of 15.33%. It can better deal with the relationship between speed planning and torque distribution than the traditional hierarchical control method.

A Novel Decomposition-Based Multi-Objective Symbiotic Organism Search Optimization Algorithm

In this research, the effectiveness of a novel optimizer dubbed as decomposition-based multi-objective symbiotic organism search (MOSOS/D) for multi-objective problems was explored. The proposed optimizer was based on the symbiotic organisms’ search (SOS), which is a star-rising metaheuristic inspired by the natural phenomenon of symbioses among living organisms. A decomposition framework was incorporated in SOS for stagnation prevention and its deep performance analysis in real-world applications. The investigation included both qualitative and quantitative analyses of the MOSOS/D metaheuristic. For quantitative analysis, the MOSOS/D was statistically examined by using it to solve the unconstrained DTLZ test suite for real-parameter continuous optimizations. Next, two constrained structural benchmarks for real-world optimization scenario were also tackled. The qualitative analysis was performed based on the characteristics of the Pareto fronts, boxplots, and dimension curves. To check the robustness of the proposed optimizer, comparative analysis was carried out with four state-of-the-art optimizers, viz., MOEA/D, NSGA-II, MOMPA and MOEO, grounded on six widely accepted performance measures. The feasibility test and Friedman’s rank test demonstrates the dominance of MOSOS/D over other compared techniques and exhibited its effectiveness in solving large complex multi-objective problems.

Parallel and Collaborative Passenger Flow Control of Urban Rail Transit Under Comprehensive Emergency Situation

The artificial cooperative control methods are used to fully utilize the train capacity and reduce the passenger delays by coordinating the number of entering and boarding passengers at each station, but it ignores the potential risk associated with the aggregation attributes of passengers in the station under emergency and the unfairness caused by the imbalance of travel opportunities for different origin–destination (OD) passengers. A new parallel and cooperative control model under comprehensive emergency situation is constructed from the perspective of guaranteeing travel safety, improving travel fairness, and increasing travel efficiency to generate passenger flow control strategies. The model aims to maximize passenger turnovers, minimize passenger delays and reduce the difference in the ratio of stranded passengers at stations. The complex multi-objective integer programming problem involving nonlinear equation constraints is difficult to solve numerically. A dynamic programming model taking train sequence as stage variable is then constructed as well as an NSGA-II algorithm with multiple improved strategies (MIS-NSGA-II) is proposed to solve the model. Numerical experiments on a line of Beijing Rail Transit show that the MIS-NSGA-II outperforms the traditional NSGA-II, and that increasing the overload coefficient of the train and the tolerance coefficient of each area in the station can further alleviate passenger congestion and promote the operation efficiency. Compared with other control strategies mentioned in this study, the proposed control model from a comprehensively perspective, which can ensure the travel safety and promote the travel efficiency while forcefully decongesting the bottleneck areas and improving the fairness of passenger travel.

Multi-objective robust optimization of reservoir operation for real-time flood control under forecasting uncertainty

Flood control operation is one of the effective measures to reduce flood risks. Since flood forecasting plays a critical role in real-time reservoir flood control operation, it is necessary to involve forecasting uncertainty in the optimal reservoir operation to inform decision-making. It has always been a difficult task to reduce flood risks by adjusting flood control strategies. To tackle this challenge, this study developed a multi-objective robust optimization methodology for real-time reservoir flood control operation, which mainly coped with forecast uncertainty. Three machine learning (ML) models, including back propagation neural network (BP), long short-term memory neural network (LSTM) and extreme learning machine (ELM) were adopted to forecast the short-term reservoir inflow. A stacking ensemble multi-ML model (SEM) was then applied to integrate the forecasting results of the above models. Furthermore, a multi-objective robust optimal operation model (MOROU) integrating both upstream and downstream safety was established to reduce flood risks and evaluate the impact of forecasting uncertainty on the reservoir operation. To maximize the efficiency of reservoir utilization, this study defined a new indicator of reservoir reserved capacity adaptation (RRCA) as one of the optimization indicators. To better solve the complex multi-objective problem, a scenario to point (STP) method was proposed for searching robust solutions of multi-objective optimization models. Methodologies were validated through an application to the Lishimen reservoir, China. Three main conclusions were derived from the study: (1) Three ML models performed well in flood forecasting with BP being slightly better than the other two, and the SEM method was found to be able to incorporate the characteristics of each model, outperforming the individual models; (2) MOROU showed a narrower distribution of flood risk both upstream and downstream and achieved an approximately 1.5% reduction in the maximum value of the highest water level; (3) RRCA was verified to enable to reduce the discharge flow by an average of 4.52% without occupying additional flood control reservoir capacity, confirming that it can be used as an optimization indicator to improve the utilization of the reservoir. The proposed method can provide robust strategies for real-time reservoir flood control under forecast uncertainty.

Solution of the Multi-objective Economic and Emission Load Dispatch Problem Using Adaptive Real Quantum Inspired Evolutionary Algorithm

Economic load dispatch is a complex and significant problem in power generation. The inclusion of emission with economic operation makes it a Multi-objective economic emission load dispatch (MOEELD) problem. So it is a tough task to resolve a constrained MOEELD problem with antagonistic multiple objectives of emission and cost. Evolutionary Algorithms (EA) have been widely used for solving such complex multi-objective problems. However, the performance of EAs on such problems is dependent on the choice of the operators and their parameters, which becomes a complex issue to solve in itself. The present work is carried out to solve a Multi-objective economic emission load dispatch problem using a Multi-objective adaptive real coded quantum-inspired evolutionary algorithm (MO-ARQIEA) with gratifying all the constraints of unit and system. A repair-based constraint handling and adaptive quantum crossover operator (ACO) are used to satisfy the constraints and preserve the diversity of the suggested approach. The suggested approach is evaluated on the IEEE 30-Bus system consisting of six generating units. These results obtained for different test cases are compared with other reputed and well-known techniques.

Mapping pareto fronts for efficient multi-objective materials discovery

With advancements in automation and high-throughput techniques, we can tackle more complex multi-objective materials discovery problems requiring a higher evaluation budget. Given that experimentation is greatly limited by evaluation budget, maximizing sample efficiency of optimization becomes crucial. We discuss the limitations of using hypervolume as a performance indicator and propose new metrics relevant to materials experimentation: such as the ability to perform well for complex high-dimensional problems, minimizing wastage of evaluations, consistency/robustness of optimization, and ability to scale well to high throughputs. With these metrics, we perform an empirical study of two conceptually different and state-of-the-art algorithms (Bayesian and Evolutionary) on synthetic and real-world datasets. We discuss the merits of both approaches with respect to exploration and exploitation, where fully resolving the Pareto Front provides more knowledge of the best material.

Second-Ordered Parametric Duality for the Multi-Objective Programming Problem in Complex Space

We introduced and discussed a second-ordered parametric dual model of a complex multi-objective programming problem (P). Moreover, the authors constructed and proved the weak, strong and strictly converse duality theorems by the second-ordered generalized Θ-bonvexity.

A selection scheme for energy storage to participate in primary frequency regulation of new energy

The choice of energy storage is the key content of the energy storage plan and design to participate in the primary frequency regulation of new energy. It involves many indicators such as safety, primary frequency modulation adaptability, economy, and environmental performance, and is a complex multi-objective decision-making problem. This paper analyses the characteristics of each index and constructs a two-level decision-making system. According to expert scores and practical application requirements, the weight of each decision-making index is obtained by the AHP method. The TOPSIS method is further used to select energy storage according to the weight of each index and related parameters.

Comparing chair time required for systemic agent drug reaction (DR) management to allocated chair time for systemic protocol.

40 Background: Chemotherapy scheduling and determining associated nursing resources are complex multiobjective decision problems. Management of DRs are thought to take additional chair and nurse time and should be accounted for in appointment scheduling in order to having an efficiently running clinic. BC Cancer – Victoria is a tertiary care regional site of BC Cancer in Victoria, British Columbia, Canada and currently schedules patients using a regimen-based resource intensity model (Greene et al, 2012). Methods: DRs were tracked in real time over 3 months, where BC Cancer ID, reaction, protocol, agent, cycle number and time of reaction were recorded. Our electronic medical record was interrogated to determine start and end of chair time. We then compared the actual chair time required to manage patients with a DR to scheduled chair time. Results: Thirty reactions occurred, including DRs to paclitaxel (43%), rituximab (13%), docetaxel (10%), nivolumab (7%), oxaliplatin (7%), pertuzumab (7%), bendmustine (3%), and daratumumab (3%). The reactions most commonly occurred with cycles 1 or 2. The averages for total chair time during DR, time from arrival to reaction, and time from reaction to discharge were 281 min (+79.5), 106 min (+ 55), and 171 min (+ 94), respectively. An average of 449 min/month extra were required for DR management above scheduled chair time. Conclusions: The agents precipitating DRs were common and predictable. An average of 7 hours and 29 minutes per month above scheduled chair time was required to manage DRs. This information could be used to more efficiently schedule chair and nursing time. This also highlights the need to minimize the number of DRs as management is resource intensive.[Table: see text]

Improved particle swarm optimization algorithms for aerodynamic shape optimization of high-speed train

In this paper, improved particle swarm optimization algorithms are presented for improving the aerodynamic optimization efficiency of a high-speed train head shape. A hybrid particle swarm optimization algorithm, which employs an artificial fish swarm algorithm (AFSA) and a backward learning strategy in particle swarm optimization, is first proposed for constructing an optimal least squares support vector regression (OPT-LSSVR) model. The prediction accuracy of various surrogate models was evaluated, and the results indicate that the OPT-LSSVR model has the smallest prediction errors, where the prediction error for the total aerodynamic drag coefficient is reduced to about 0.45% and reduced to within 5% for the lift coefficient. Besides, an elite-evolved multi-objective particle swarm optimizer (EMPSO), which employs a grouping-based stochastic elite competition mechanism and elite gathering behavior, is proposed to improve the multi-objective optimization efficiency. The verified results indicate that the EMPSO algorithm is more efficient and capable of tackling complex multi-objective problems. Based on the OPT-LSSVR model and the EMPSO algorithm, the aerodynamic shape optimization of the high-speed train is performed. After optimization, the aerodynamic drag coefficient and the aerodynamic lift coefficient are reduced by 3.63% and 10.59%, respectively. Improved algorithms are simple yet efficient, and they have significant implications for the research and design of high-speed trains at higher speeds.

Multi-objective sparrow search algorithm: A novel algorithm for solving complex multi-objective optimisation problems

This study proposes a multi-objective sparrow search algorithm (MOSSA) based on a 2k crowding-distance entropy and the optimal strategy of the positions to solve complex multi-objective optimisation problems (MOPs) using the excellent performance of the sparrow search algorithm (SSA). A fast non-dominated sorting approach is incorporated to permit SSA to solve MOPs. To maintain the evenness and spread of the Pareto solution set obtained in each run, a 2k crowding-distance entropy is proposed to measure the diversity of the solution set. Modified formulas for updating positions and additional adaptive parameters can improve the global search ability of MOSSA. The position archive of the population is introduced to realise the optimal strategy of the positions. This strategy ensures that the positions of the population in each generation are optimal, which significantly improves the performance of MOSSA. MOSSA is compared with three well-known algorithms using a set of complex unconstrained test problems and a complex constrained engineering optimisation problem. This study explores the effect of the 2k crowding-distance entropy and crowding distance on maintaining diversity. The impact of the k in 2k crowding-distance entropy on the performance of MOSSA is analysed. The experimental results demonstrate that MOSSA exhibits competitive performance in solving complex MOPs.