Set Of Optimal Solutions Research Articles

Constructing a MOEA approach for product form Kansei design based on text mining and BPNN

Kansei Engineering (KE) is a product design method that aims to develop products to meet users’ emotional preferences. However, traditional KE faces the problem that the acquisition of Kansei factors does not represent the real consumers demands based on manual and reports, and using traditional methods to calculate relationship between Kansei factors and specific design elements, which can lead to the omission of key information. To address these problems, this study adopts text mining and backward propagation neural networks (BPNN) to propose a product form design method from a multi-objective optimization perspective. Firstly, Term Frequency-Inverse Document Frequency (TF-IDF) and WordNet are used to extract key user Kansei requirements from online review texts to obtain more accurate Kansei knowledge. Secondly, the BPNN is used to establish the non-linear relationship between product Kansei factors and specific design elements, and a preference mapping prediction model is constructed. Finally, BPNN is transformed into an iterative prediction value of non-dominated sorting genetic algorithm-II (NSGA-II), and the model is solved through multi-objective evolutionary algorithm (MOEA) to obtain the Pareto optimal solution set that satisfies the user’s multiple emotional needs, and the fuzzy Delphi method is used to obtain the best product form design scheme that meets the user’s multiple emotional images. Using the example of electric bicycle form design could show that this proposed method can effectively complete multi-objective product solutions innovation design.

Improved Multi-objective Particle Swarm Optimization in Software Engineering Supervision

In the 21st century, the software industry has achieved great development. The development complexity and volume of software projects are also continuously increasing. The design of software engineering supervision network plans is becoming increasingly important. In response to the poor optimization performance and poor convergence and distribution of optimal solutions in existing network planning algorithms, the Pareto optimal solution set construction method, global extremum selection method, and fitness value determination method of multi-objective particle swarm optimization algorithm are improved to enhance the convergence and distribution of the algorithm. Traditional methods only optimize one or two objectives of network planning, resulting in inconsistency with actual engineering. A multi-objective model based on resources, duration, cost, and quality is established for comprehensive optimization. Based on the results, the Pareto optimal solution curves obtained by the proposed algorithm on three classic test functions are consistent with the actual theoretical Pareto frontier curves. The proposed method is applied to engineering project examples. 10 solutions that meet the schedule requirements are obtained. Most engineering projects have a quality of over 80%, which verifies the practicality of the algorithm. The algorithm has achieved good results in optimizing engineering quality. Therefore, this model has the ability to consider various indicators such as resources and costs to obtain software engineering quality improvement plans. It has certain application potential.

Study on flexible job shop scheduling problem considering energy saving

The Flexible Job Shop Scheduling Problem (FJSP) is an extension of the classical Job Shop Scheduling Problem (JSP). The research objective of the traditional FJSP mainly considers the completion time, but ignores the energy consumption of the manufacturing system. In this paper, a mathematical model of the energy-efficient flexible job shop scheduling problem is constructed. The optimization objectives are completion time, delay time, and total equipment energy consumption. To solve the model, an improved non-dominated sorting genetic algorithm (CT-NSGA-II) is proposed to obtain the optimal scheduling solution. First, the heuristic rules of GLR were used to generate the initial population with good quality and diversity. Second, different crossover and variation operators are designed for the process sequencing and equipment selection parts to enhance the diversity of the evolutionary population. The sparsity theory is introduced to find sparse solutions and three neighborhood structures are designed to perform local search on sparse solutions to improve the uniformity of the optimal solution set distribution. Finally, a competitive selection strategy based on the bidding mechanism is proposed for the Pareto optimal solution set to obtain a better scheduling scheme. The experimental results show that the proposed improved algorithm is feasible and effective in the FJSP problem considering energy consumption, and the algorithm has some application value in improving the efficiency of smart shop operation.

Optimization of responses in single and multi-point machining processes using Dragon-fly algorithm coupled with TOPSIS and VIKOR decision-making approaches

Due to complex production practices, it is becoming crucial to provide greater thermal management and friction reduction in manufacturing processes. Lubricants play a crucial role by effectively reducing friction, minimizing wear and tear thereby extending the lifespan of the tool. It is observed that there is a shortage of studies associated with the machining of hard materials like Ti-6Al-4V. The present work has therefore focused on the machining of high-grade Titanium alloy under dry and Neem oil aerosol-mist spray wet conditions. The machining is performed on two kinds of machining processes, such as plain facing with single point tool and co-axial turn-mill facing with multi-point cutting tools on computer numerical controlled Turn-mill machine tool. Furthermore, there are very few articles reported on usage of Neem oil (AzadirachtaIndicaL.) as a lubricant. This has motivated the authors to use Neem oil in a mist condition to minimize the quantity of coolant, without compromising on the tool temperature, surface quality, and tool-wear. The responses obtained are subjected to regression analysis to evolve the fitness functions. Multi-objective optimization of these functions is than adopted using Dragon-fly algorithm (MODA) under the constraints of the machining parameters. A set of pareto optimal solutions for each of the machining cases are obtained and are further evaluated using TOPSIS and VIKOR decision-making approaches to achieve the optimal values of the cutting parameters. The optimum parameters for single point cutting under wet conditions were observed as speed (592 rpm), feed (0.058 mm rev−1) and depth of cut (1.00 mm).The corresponding values of responses were tool temperature (37.05 °C), surface roughness (0.128 μm) and tool wear (155.19 μm). The equivalent values for multi-point cutting were determined as 510 rpm, 0.086 mm rev−1 and 0.25 mm. The responses for these optimal conditions are 32.17 °C, 0.725 μm and 45.72 μm in that order.

Gradient pyramid mechanism and Nelder-Mead simplex enhanced Colony Predation Algorithm for optimal power flow problems

The escalating human energy demand, particularly in the realm of electricity consumption, imposes a substantial burden on power system planning, resulting in the emergence of the optimal power flow (OPF) problem. To address this challenge, researchers have implemented a Flexible AC Transmission System (FACTS) in modern power systems to optimize network congestion. This paper presents a new application of the Colony Predation Algorithm (CPA) in the domain of Optimal Power Flow (OPF) through the introduction of an enhanced Colony Predation Algorithm (PNMCPA). PNMCPA incorporates the gradient pyramid mechanism and the Nelder-Mead simplex (NMs), marking the first utilization of CPA in the OPF field. The proposed approach presents a novel hierarchical gradient pyramid mechanism that combines the approximate gradient descent method with the construction of a pyramid fall rate, thereby optimizing the population as a whole within a framework that enhances population diversity. Additionally, the NMs algorithm is employed to optimize the optimal set of solutions for the population, thereby accelerating the convergence efficiency of the algorithm. The primary objective of this study is to optimize multiple factors, including the generation cost and transmission loss of the power system when multiple FACT components are present. Utilizing the Weibull probability density function, the model captures the uncertain and unstable nature of wind energy resources, encompassing direct, penalty, and standby costs. The proposed algorithm is applied to the IEEE30 bus test system, and the experimental results demonstrate that PNMCPA achieves a final optimization cost of 806.0132 $/h, surpassing other optimization algorithms. Concerning the power loss matter within the bus system, the PNMCPA algorithm significantly effectively mitigates total power loss, reducing from 1.44 MW to 1.41 MW instead of the initial CPA and substantially enhancing convergence speed. Empirical simulation outcomes clearly endorse PNMCPA as a highly efficient approach to tackling optimal power flow problems in the presence of multiple FACTS devices. The significant advancements presented in this paper mark a significant contribution to the field, offering a novel and superior solution to optimize power systems in the face of escalating energy demands.

Evaluation of Design Parameters for Daylighting Performance in Secondary School Classrooms Based on Field Measurements and Physical Simulations: A Case Study of Secondary School Classrooms in Guangzhou

The quality of natural lighting within secondary school classrooms can significantly affect the physical and mental well-being of both teachers and students. While numerous studies have explored various aspects of daylighting performance and its related factors, there is no universal standard for predicting and optimizing daylighting performance from a design perspective. In this study, a method was developed that combines measurements and simulations to enhance the design parameters associated with daylighting performance. This approach facilitates the determination of precise ranges for multiple design parameters and allows for the efficient attainment of optimal daylighting performance. Daylight glare probability (DGP), point-in-time illuminance (PIT), daylight factor (DF), and lighting energy consumption were simulated based on existing control parameters of operational classrooms. The simulation results were then validated using field measurements. Genetic algorithms (GAs) were employed to optimize the control parameters, yielding a set of optimal solutions for improving daylight performance. The differences between daylighting performance indicators corresponding to the optimal solution set and those of the basic model were compared to test the performance of the optimized parameters. The proposed method is a robust process for optimizing daylight design parameters based on GAs, which not only enhances daylighting performance but also offers scientifically grounded guidelines for the design phase. It is a valuable framework for creating healthier and more productive educational environments within secondary school classrooms.

Environmental performance driven optimization of urban modular housing layout in Singapore

ABSTRACT With the growing size of cities and the need to renew residential areas, architects are calling for more efficient use of already settled areas. This paper presents a performance-driven architectural design (PDAD) workflow for shape generation and genetic optimization based on environmental data, using public housing in the Singapore region as a case study. It integrates three-dimensional cellular automata, parametric performance simulation, genetic optimization algorithms, and hierarchical clustering algorithms. The results show that the average value of Useful Daylight Illuminance (UDI) is 85.19%, the average value of Energy Use Intensity (EUI) is 159.41 kWh/m2, and the average value of Predicted Mean Vote (PMV) is 0.64 for the optimal set of solutions produced after genetic optimization. The optimal solution set was further classified into 4 categories by a hierarchical clustering algorithm and was visualized for further evaluation and selection by the architect. The study helps architects to integrate data analysis results with human decision-making as a design research method in the early stages of design and leads to further discussion on bottom-up design approaches in the urban renewal process.

MORSA: Multi-objective reptile search algorithm based on elite non-dominated sorting and grid indexing mechanism for wind farm layout optimization problem

The proposal of the wind farm layout optimization (WFLO) problem aims to better utilize wind energy. A multi-objective reptile search algorithm (MORSA) based on elite non-dominated sorting and grid indexing mechanism was proposed to solve the multi-objective optimization problem of wind farm layout under the Jansen wake model to maximize power generation while minimizing costs. Firstly, the elite non-dominated sorting method was used to sort the population, and then the crowding distance method was used to maintain the diversity between the optimal sets. By calculating the crowding distance, the same level of non-dominated populations are sorted. Then, the grid index mechanism is added to the archive for selection and deletion. Leaders can use the roulette wheel to select and delete some solutions in high-density grids. By obtaining the optimal Pareto solution set while maintaining the diversity of the population, the effectiveness of solving multi-objective optimization problems is improved. The improved algorithm solves the WFLO problem based on the Jansen wake model by using two different initial self-flow winds for performance testing while considering the effects of single wake and multiple wake with or without partial wake occlusion. The performance of the WFLO (output power and cost) was compared without considering wake obstruction, MORSA can obtain the minimum turbine cost of 26.3601 and the maximum power generation of 2.3078E-08 with a single wake flow of 16 m/s. The experimental results show that the proposed MORSA has better convergence and applicability, and has shown good results in multi-objective layout optimization of wind farms.

Dominance relation selection and angle-based distribution evaluation for many-objective evolutionary algorithm

In many-objective optimization, most existing evolutionary algorithms struggle to effectively balance the convergence and diversity of population. Given the failure of Pareto-dominance-based selection mechanism in high-dimensional spaces and the growing recognition of the advantages of angle-based similarity evaluation, we propose a Many-objective Evolutionary Algorithm using Dominance Relation Selection and Angle-based Distribution Evaluation (DSAE). Firstly, based on both traditional Pareto dominance and a newly proposed Angle-dominance with higher selection pressure, a Dominance Relation Selection (DRS) strategy is designed, which dynamically adjusts the selection pressure by assessing the overall proximity between parent and offspring populations. Then, an Angle-based Distribution Evaluation is proposed to determine the distribution levels of solutions, so as to adaptively maintain promising distribution performance of population in objective space. Furthermore, a Pareto-dominance-based global optimal solution set is introduced to save solutions with the best diversity throughout the iteration as the final output. Finally, DSAE is compared with 7 state-of-the-art algorithms by using benchmark test suites DTLZ and WFG with 5, 8 and 10 objectives, and the experimental results demonstrate that DSAE has the most advanced performance.

Evolutionary multimodal multiobjective optimization guided by growing neural gas

Evolutionary multimodal multiobjective optimization aims to search for a set of Pareto optimal solutions that are well distributed in both the objective and decision spaces. In recent years, there has been a growing interest in enhancing the search ability of evolutionary algorithms using machine learning techniques. However, there are few studies on machine learning-assisted evolutionary multimodal multiobjective optimization. In this paper, we propose an evolutionary multimodal multiobjective algorithm guided by growing neural gas, which learns the topological structure of the obtained good solutions during the evolution process. These good solutions are well-converged and well-distributed in the decision space, which indicate the shape of the Pareto optimal solution set. The proposed algorithm employs three novel mating selection operators based on the topological structure to efficiently and effectively search for Pareto optimal solutions. The first operator exploits Pareto optimal solutions within the topological structure, while the others explore Pareto optimal solutions around and far away from the topological structure, respectively. The proposed algorithm is compared with eight state-of-the-art evolutionary multimodal multiobjective algorithms on 20 test problems. Experimental results demonstrate that the proposed algorithm is competitive in solving these problems.

Multi-Objective Optimization of the Microchannel Heat Sink Used for Combustor of the Gas Turbine

This research presents a surrogate model and computational fluid dynamic analysis-based multi-objective optimization approach for microchannel heat sinks. The Non-dominated Sorting Genetic Algorithm is suggested to obtain the optimal solution set, and the Kriging model is employed to lower the simulation’s computational cost. The physical model consists of a coolant chamber, a mainstream chamber, and a solid board equipped with staggered Zigzag cooling channels. Five design variables are examined in relation to the geometric characteristics of the microchannel heat sinks: the length of inlet of the cooling channels, the width of the cooling channels, the length of the “zigzag”, the height of the cooling channels, and the periodic spanwise width. The optimal geometry is established by choosing the averaged cooling effectiveness and coolant mass flow rate which enters the mainstream chamber through the microchannel heat sinks as separate objectives. From the Pareto front, the optimal microchannel heat sinks structures are obtained. Three optimized results are studied, including the maximum cooling effectiveness, minimum coolant mass flow rate, and a compromise between the both objectives; a reference case using the median is compared as well. Numerical assessments corresponding to the four cases are performed, and the flow and cooling performance are compared. Furthermore, an analysis is conducted on the mechanisms that impact the ideal geometric parameters for cooling performance.

Desirability-based post-hoc selection of Pareto solutions

ABSTRACT Generating a set of optimal solutions is a recommended practice when solving a multiresponse problem. However, it is known that some optimal solutions may yield unexpected outcomes when implemented in practice. Thus, to avoid wasting resources and time in implementing a theoretical optimal solution that does not produce the expected outcomes, a new approach to select a solution from the Pareto front is proposed. This approach employs a desirability-based function to aggregate all the desired response characteristics, namely the responses’ Bias, Resilience, Quality of Predictions, and Robustness. Two case studies illustrate the usefulness of the proposed approach.

Two-stage evolutionary algorithm with fuzzy preference indicator for multimodal multi-objective optimization

Multimodal multi-objective optimization problems (MMOPs) are multi-objective optimization problems (MOPs) involving multiple equivalent global or local Pareto optimal solution sets (PSs). For decision-makers, not only the global optimal solution sets need to be found, but also the value of local optimal solution sets cannot be ignored. However, most multimodal multi-objective evolutionary algorithms (MMOEAs) tend to select solutions with better convergence, and it is difficult to obtain the global PSs and local PSs at the same time. Therefore, we propose a fuzzy preference indicator-based two-stage evolutionary algorithm (FPITSEA) in this paper. To evaluate more comprehensively the potential of each solution in the population for locating the global and local PS during the evolutionary process, a fuzzy preference indicator is designed in FPITSEA. The fuzzy preference indicator is used to guide the evolution of the population in the first stage to find the global and local Pareto optimal regions. Subsequently, an independent evolution strategy is implemented in the second stage to distinguish different PSs as accurately as possible while also ensuring the convergence quality of the solution set. In addition, an improved distance-based subset selection method is proposed, aiming to simultaneously improve the distribution of the solution set in the decision space and objective space. Experimental results on several test sets of MMOPs show the advantages of FPITSEA over several state-of-the-art MMOEAs.

Multi-objective particle swarm optimization for optimal scheduling of household microgrids

Addressing the challenge of household loads and the concentrated power consumption of electric vehicles during periods of low electricity prices is critical to mitigate impacts on the utility grid. In this study, we propose a multi-objective particle swarm algorithm-based optimal scheduling method for household microgrids. A household microgrid optimization model is formulated, taking into account time-sharing tariffs and users’ travel patterns with electric vehicles. The model focuses on optimizing daily household electricity costs and minimizing grid-side energy supply variances. Specifically, the mathematical model incorporates the actual input and output power of each distributed energy source within the microgrid as optimization variables. Furthermore, it integrates an analysis of capacity variations for energy storage batteries and electric vehicle batteries. Through arithmetic simulation within the Pareto optimal solution set, the model identifies the optimal solution that effectively mitigates fluctuations in energy input and output on the utility side. Simulation results confirm the effectiveness of this strategy in reducing daily household electricity costs. The proposed optimization approach not only improves the overall quality of electricity consumption but also demonstrates its economic and practical feasibility, highlighting its potential for broader application and impact.

A multi-objective optimization method for enclosed-space lighting design based on MOPSO

With the rapid development of underground spaces and manned cabins, the design of enclose-space has received attention. Humans working in enclosed-space for a long period of time are prone to fatigue, which in serious cases can lead to human errors and major accidents. Therefore, the optimized design of enclosed-space is of great research significance to enhance the efficiency and comfort of workers. The lighting environment is one of the important objectives of the optimized design of enclosed-space, and the current research on lighting design often focuses on single-objective reduction of energy consumption or improvement of visual effects, and lacks attention to non-visual effects. We propose multi-objective optimal control strategy for enclosed-space lighting systems, taking the visual effects, non-visual effects, and energy efficiency of lighting as the optimization objectives and constraints, combined with multi-objective particle swarm optimization algorithm. Firstly, we obtain a set of optimal Pareto front solution for the dimming level by improving the algorithm. Secondly, to select appropriate lighting strategies according to different working scenarios, we introduce the fuzzy integrated evaluation method of experts to find the best compromise. Finally, we used a manned simulated enclosed cabin based on DIALux evo for a case study to compare the optimization results with baseline solutions. The results show that when we employed the improved dimming strategy, the energy efficiency and visual comfort were significantly improved compared with the baseline lighting design. The proposed method can satisfy human non-visual effects requirements, providing a research reference for future enclosed-space lighting optimization.

Multi-objective optimization of regional integrated energy system matrix modeling considering exergy analysis and user satisfaction

Integrated energy system achieves the collaborative optimization of different energy forms such as electricity/gas/heat/cold, and it is an important strategic development direction in the international energy field in the future. However, with the development of smart grid technology and the increase of renewable energy penetration, it needs more flexible load to adapt to the changing energy supply–demand relationship. Considering the impact of user-side load fluctuations on the system, this paper establishes a two-tier closed-loop system model formed by users and the market. The upper-layer is based on the user’s perspective. A comprehensive user satisfaction model is established by the radar chart area method and consumer preference theory. The lower-layer is based on the market perspective. It proposes an improved layering matrix Energy Hub model and conducts the regional integrated energy system exergy efficiency evaluation study. Then, taking economy, carbon emission and exergy efficiency as objective functions, a multi-objective optimization model is constructed. Non-dominated Sorting Genetic Algorithms-II is applied to solve the model, and the output parameters is a Pareto front surface. A combination weighting TOPSIS method is used to select a compromise solution of multi-objective optimization from the optimal solution set. Compared with the primary energy utilization efficiency as the objective function, the exergy efficiency reduces the system cost by 8.64%. Finally, the multi-objective optimization solution based on different user satisfaction is obtained. Through the analysis of the examples, compared with the original load, the introduction of the upper-layer user satisfaction model reduces the system cost by 2.8%. The reasonable setting of user satisfaction and load adjustment amount can improve the economy of system, which verifies the effectiveness of the two-tier closed-loop system based on user satisfaction model.

Long-term multi-objective optimal scheduling for large cascaded hydro-wind-photovoltaic complementary systems considering short-term peak-shaving demands

The effective synergy among hydropower, wind power, and photovoltaic enhances variable renewable energy (VRE) utilization. However, existing long-term hydropower operating rules that consider runoff uncertainty neglect escalating peak-shaving demands. This paper optimizes the long-term decision-making of hydropower by supplementing the demand to buffer short-term VRE uncertainty. Latin hypercube sampling and K-means clustering reduction are utilized to generate coupling scenario sets to quantify long-term runoff and short-term VRE uncertainties. Then, a double-layer multi-objective optimization model is developed, the outer layer maximizes the long-term expected energy production of the whole system, and the inner layer minimizes hourly residual load fluctuation of power grids under daily electricity boundaries. The daily electricity is dependent on the load profile and monthly generation. Moreover, A power-electricity coupling approach is proposed to bridge long- and short-term operations and reduce the computational burden. An optimal set of pareto solutions is finally obtained with different constraint boundaries, where a compromise solution is selected by a fuzzy decision method. The model has been implemented on the Lancang River hydro-wind-photovoltaic complementary system in Southwest China. The results indicate that: (1) the model can transfer hydropower electricity from flood season to dry season, facilitate VRE integration, increase overall benefits, and improve short-term hydropower regulation capacity, especially in wet years; (2) the obtained Pareto solution set has significant advantages. Under multi-year average conditions, energy production increases by 11 million kWh, hydropower curtailment decreases by 751 million kWh, and residual load fluctuations reduce by 2200 MW, and (3) increasing transmission capacity is more conducive to improving system efficiency in wet years than in dry years, and is helpful to enhance hydropower flexibility.

A convenient-accurate optimization method of the multi-effect evaporation system

In this work, a convenient-accurate multi-effect evaporation system optimization method that integrates regression analysis and a multi-objective genetic algorithm has been proposed to optimize the design of the multi-effect evaporation system. Firstly, a multitude of numerical simulation calculations are conducted employing precise thermodynamic models. Secondly, regression analysis is performed on the experimental data to establish the approximate model between the design variables and performance parameters. Finally, NSGA-II, a non-dominated sorting genetic algorithm with an elite strategy, is employed to optimize and solve the approximate model derived from regression analysis. Consequently, a series of Pareto solutions satisfying the given conditions are obtained. The two initial schemes of the FF-MEE (forward-feed) system and the PF-MEE (parallel-feed) system are optimized using the proposed optimization method. The results show that following optimization, the Gained Output Ratio (GOR) of the FF-MEE system is increased by 3.6%, while the specific heat transfer area (As) is reduced by 16%. Similarly, for the PF-MEE system, the GOR is enhanced by 7.8%, and As is decreased by 19%. The proposed method provides a comprehensive set of optimization solutions, ensuring rapid solution speed, straightforward application, and high solution accuracy.

An energy consumption optimization strategy for Wireless sensor networks via multi-objective algorithm

Deploying relay nodes is a significant mechanism to prolong the network lifetime of wireless sensor networks (WSNs). However, most existing studies overlook the energy consumption of relay nodes, leading to imperfections in the optimization process. Additionally, there is also a lack of analysis of conflicts between different optimization objectives. In this regard, a multi-objective antlion with fuzzy clustering algorithm (MOALO-FCM) is designed to obtain a better trade-off between different optimization objectives. And an adaptive membership function revision strategy is introduced to improve the energy balance of relay nodes. To verify the performance of the proposed algorithm, simulation experiments are set in 2-dimensional and 3-dimensional scenes with correlative algorithms, respectively. The main evaluation indexes include performance of Pareto optimal solution sets, the life cycle of network, the energy consumption of sensor nodes, the energy consumption of relay nodes, the number of living nodes, and the running time of algorithms. The results indicate that the proposed algorithm has better performance in various indexes.

Multi-objective optimization of the dynamic performance of a suspended monorail vehicle based on an effective surrogate model

This work presents the multi-objective optimization (MOO) of the dynamic performance of a suspended monorail vehicle (SMV) moving on a curved bridge, based on an effective surrogate model. First, the vehicle-bridge dynamic interaction features are analysed through a dynamic model. Then, an MOO method is developed based on an effective surrogate model. In this method, the accuracy and stability of the radial basis function are enhanced by proposing an innovative improvement strategy and adopting the particle swarm optimization algorithm. The proposed method is validated by a few numerical tests. Based on this verification, the MOO model between key parameters and several optimization objectives is formulated, and the optimization solution set of the vehicle key parameters is obtained using the non-dominated sorting genetic algorithm II. Finally, the optimization effects are revealed by comparing the dynamic performance of the vehicle obtained from the original values and the optimal solution set.