Pareto Optimal Solutions Research Articles

Plowing operation: labor productivity and specific operating costs. Part 1. Multifactor simulation of plowing operation

One of the most important problems in grain production in the Republic of Belarus is increasing labor productivity, which is 4–5 times less than labor productivity in the EU countries. A great influence on labor productivity and specific operating costs is exerted by energyand material-intensive operations, such as plowing and harvesting. The main patterns of the plowing operation, which is a complex technical system, is connected with the use of a large volume of agrotechnological, technical, operational, resource and economic information (operation duration, working length of the harrow, physical and mechanical properties of soil, depth of treatment, permissible interval of the unit speed, fuel and energy, engine power and traction characteristics, width of the unit, economic indicators, etc.) are considered. Currently, as a result of introduction of computer mathematics systems, there are effective methods available for studying complex technical systems, allowing for multi-factor modeling and multi-criteria optimization of the production processes and formation of a set of machines by system analysis. A prerequisite for a complete and comprehensive description of the functioning of a complex technical system is the presence of conflicting optimization parameters, as well as a complete set of independent control factors significantly affecting these parameters. A distinctive feature of the proposed method is to determine not one optimal solution, but a set of Paretooptimal solutions, giving the producer new opportunities of choice when organizing the production processes, increasing the efficiency of plowing operation and, consequently, the profitability of grain production in general. Therefore, increasing productivity at permissible specific operating costs through the formation of a rational set of machines and modes of its operation under specific conditions of production is an important scientific and engineering task. A mathematical illustration of the method is provided for natural-production conditions of the Republic of Belarus.

Optimising the inherent fire capacity of structures

This paper introduces a structural design optimisation methodology aimed at minimising the consequences of a fire. The methodology considers the trade-off between implementing passive fire protection measures and enhancing a structure’s “inherent fire capacity”, defined as its ability to retain integrity/functionality without additional fire safety measures. The feasibility of the methodology is demonstrated through the fire safety design of a single-span, steel girder bridge. The optimisation process generates multiple Pareto-optimal solutions for minimising the maximum bridge deflection after a given fire exposure time. Passive protection ensures the bridge’s functionality when facing a heavy goods vehicle fire. In the case of exposure to a car fire, solutions requiring fire protection in specific limited girder regions are identified. The decision-making process is further supported by investigating the robustness of the solutions to uncertainties in material properties and the heat flux model.

Multi-objective optimization design of TRISO-based fully ceramic microencapsulated fuel

Fully Ceramic Microencapsulated (FCM) fuel is a new type of material in nuclear energy field. It has become a promising accident tolerant fuel (ATF) candidate due to its advantages of high radiation stability, high fission product containment capacity and excellent thermo-mechanical performance. During operation, the temperature, stress, deformation and other key parameters will change significantly, which directly affect the safety of nuclear reactor. Therefore, it is necessary to carry out a multi-physics fully-coupled analysis suitable for the multi-scale, multi-component, multi-phase and nonlinear coupling processes in the reactor, so as to sort out the influences of material properties, radiation behavior, thermo-mechanical performance from numerous influencing factors. In this paper, based on the irradiation-thermo-mechanical coupling method, the performance of TRISO-based FCM fuel under irradiation conditions was analyzed, key thermo-mechanical parameters and other influencing factors of the fuel were obtained, failure behavior of the fuel element was evaluated. On this basis, the theoretical and numerical model of multi-objective optimization method were established, the optimum parameters including material properties, fuel geometry and particle arrangement were found by optimization method. The optimization results showed that the multi-objective optimization results could provide multiple Pareto optimal solutions for the FCM fuel. Specifically, when the TRISO particle spacing is 200 µm and 150 µm, the objective function difference between the optimal heat transfer solutions is only about 1.7%, meanwhile the mechanical properties vary significantly (the difference between the objective functions of the optimal solutions is about 12.4% ∼26.5%), indicating the response of stress is more sensitive than temperature. When the TRISO particles are tightly packed (particle spacing less than 100 µm), the difference of objective function between the optimal solutions is less than 5%, illustrating the optimization has limited improvement on the thermo-mechanical performance of the fuel, namely the optimization space is limited.

Flexible Job Shop Scheduling Optimization for Green Manufacturing Based on Improved Multi-Objective Wolf Pack Algorithm

Green manufacturing has become a new production mode for the development and operation of modern and future manufacturing industries. The flexible job shop scheduling problem (FJSP), as one of the key core problems in the field of green manufacturing process planning, has become a hot topic and a difficult issue in manufacturing production research. In this paper, an improved multi-objective wolf pack algorithm (MOWPA) is proposed for solving a multi-objective flexible job shop scheduling problem with transportation constraints. Firstly, a multi-objective flexible job shop scheduling model with transportation constraints is established, which takes the maximum completion time and total energy consumption as the optimization objectives. Secondly, an improved wolf pack algorithm is proposed, which designs individual codes from two levels of process and machine. The precedence operation crossover (POX) operation is used to improve the intelligent behavior of wolves, and the optimal Pareto solution set is obtained by introducing non-dominated congestion ranking. Thirdly, the Pareto solution set is selected using the gray relational decision analysis method and analytic hierarchy process to obtain the optimal scheduling scheme. Finally, the proposed algorithm is compared with other algorithms through a variety of standard examples. The analysis results show that the improved multi-objective wolf pack algorithm is superior to other algorithms in terms of solving speed and convergence performance of the Pareto solution, which shows that the proposed algorithm has advantages when solving FJSPs.

A Methodology for Fault-tolerant Pareto-optimal Approximate Designs of FPGA-based Accelerators

Approximate Computing Techniques (ACTs) take advantage of resilience computing applications to trade off among output precision, area, power, and performance. ACTs can lead to significant gains at affordable costs when efficiently implemented on Field Programmable Gate Array– (FPGA) based accelerators. Although several novel ACTs works have been proposed for FPGA accelerators, their applicability to high-assurance systems has not been explored as much. ACTs are becoming necessary in many critical Edge computing systems, such as self-driving cars and Earth observation satellites, to increase computational efficiency. However, an important question comes to mind when targeting critical systems: Does ACT optimization negatively affect the reliability of the system and how can one find optimal design architectures that blend classic mitigation techniques like Triple Modular Redundancy with approximation- and precise-based arithmetic hardware units to achieve the best possible computational efficiency without compromising dependability? This work aims to solve this research problem by introducing a Design Space Exploration (DSE) methodology that employs ACTs in arithmetic units of the design and identifies Pareto-optimal microarchitectures that balance all relevant gains of ACTs, such as area, speed, power, failure rate, and precision, by inserting the correct amount of approximation in the design. In a nutshell, our DSE methodology has formulated the DSE with a Multi-Objective Optimization Problem (MOP). Each Pareto-optimal solution of our tool finds which arithmetic units of the design to implement with precise and approximate circuits and which units to selectively triplicate to remove single points of failure that compromise system reliability below acceptable thresholds. We also suggest another formulation of the DSE into a Single-Objective constraint Optimization Problem (ScOP) producing a single optimal point, and that the user may demand, as a less time-consuming alternative to the MOP if a complete Pareto-front is not needed. Our methodology generates fault-tolerant versions of the Pareto-optimal approximate designs (or simple optimized approximate designs if the ScOP choice is picked) by selectively applying mitigation techniques in a way that the overheads of redundant resources for fault-tolerance do not negate the gains of approximation in comparison to the fault-tolerant versions of the precise design. We evaluate our method on two FPGA-based accelerators: a JPEG encoder and an H.264/Advanced Video Coding decoder. Our experimental results show significant gains in area, frequency, and power consumption without compromising output quality and system reliability compared to classic solutions that replicate all or a part of the resources of the precise design to increase dependability metrics.

Cost‐ and performance‐aware resource selection for parallel software on heterogeneous cloud

SummaryCloud providers offer flexible infrastructures and on‐demand services, including the capability to deploy low cost virtual resources of many different types. However, the diversity of cloud resources followed by the important trade‐off between cost and performance makes the resource selection a challenging task for users in the case of parallel communication‐intensive software. The paper presents cost‐ and performance‐aware resource selection for parallel discrete element method (DEM) software as a service (SaaS) on heterogeneous OpenStack cloud. The developed resource selection uses preliminary application‐specific benchmarks of size smaller than targeted problems and the performance prediction based on speedup of parallel computations to obtain Pareto optimal solutions and to select the best configuration of containers from user's perspective. Hybrid parallelization of DEM software is developed by using OpenCL for shared‐memory multi‐core architectures and MPI for internode communications on distributed‐memory computer clusters. Round up and proportional pricing schemes are examined and compared from a user's perspective. Lower cost of computations obtained by using the proportional pricing scheme is always preferable for users. However, the difference approaches 1.0% of the cost calculated by using proportional pricing scheme, when long lasting computations are performed. The prediction tends to underestimate the execution time of DEM SaaS, but its accuracy is sufficient to obtain the same Pareto optimal solutions by using measured and predicted execution times. Pareto front and linear scalarization propose to select configurations of containers capable of exploiting higher memory bandwidth, which is specific to memory bandwidth bound DEM computations.

A near-optimum multi-objective optimization approach for structural design

Multi-objective design optimization problems offer a set of solution alternatives within a Pareto-front. In structural design, the design variables are typically the section properties. The outcomes of these design variables are usually used in selecting standard sections. However, the properties of the selected standard sections normally have different values from the determined design variables. Accordingly, the values of the objective functions for these solutions will change after selecting standard sections. This change may be different among these solutions. Thus far, only Pareto-optimal solutions have been standardized in the literature. The effects of the inclusion of non-Pareto solutions in the standardization process have never been examined. In this paper, the differences between including the near-optimal solutions and not including them in the final structural design optimization set are explored. The paper investigates the impact of selecting standard sections on both Pareto-front solutions and near-optimal solutions, and it studies the importance of keeping track of the near-optimal solutions. A modified version of a multiple-objective particle swarm optimization method, enhanced with a proposed computationally efficient section standardization algorithm, is used to solve multi-objective system-reliability design optimization problems. The concepts of the paper are applied to examples of bridge structures. The results demonstrate the efficiency of the proposed technique in capturing final design solutions that would have been otherwise missed due to standardization.

A Zoning Search-Based Multimodal Multi-Objective Brain Storm Optimization Algorithm for Multimodal Multi-Objective Optimization

For multimodal multi-objective optimization problems (MMOPs), there are multiple equivalent Pareto optimal solutions in the decision space that are corresponding to the same objective value. Therefore, the main tasks of multimodal multi-objective optimization (MMO) are to find a high-quality PF approximation in the objective space and maintain the population diversity in the decision space. To achieve the above objectives, this article proposes a zoning search-based multimodal multi-objective brain storm optimization algorithm (ZS-MMBSO). At first, the search space segmentation method is employed to divide the search space into some sub-regions. Moreover, a novel individual generation strategy is incorporated into the multimodal multi-objective brain storm optimization algorithm, which can improve the search performance of the search engineering. The proposed algorithm is compared with five famous multimodal multi-objective evolutionary algorithms (MMOEAs) on IEEE CEC2019 MMOPs benchmark test suite. Experimental results indicate that the overall performance of the ZS-MMBSO is the best among all competitors.

A clustering-based competitive particle swarm optimization with grid ranking for multi-objective optimization problems

The goal of the multi-objective optimization algorithm is to quickly and accurately find a set of trade-off solutions. This paper develops a clustering-based competitive multi-objective particle swarm optimizer using the enhanced grid for solving multi-objective optimization problems, named EGC-CMOPSO. The enhanced grid mechanism involved in EGC-CMOPSO is designed to locate superior Pareto optimal solutions. Subsequently, a hierarchical-based clustering is established on the grid for improving the accuracy rate of the grid selection. Due to the adaptive division of clustering centers, EGC-CMOPSO is applicable for solving MOPs with various Pareto front (PF) shapes. Particularly, the inferior solutions are discarded and the leading particles are identified by the comprehensive ranking of particles in each cluster. Finally, the selected leading particles compete against each other, and the winner guides the update of the current particle. The proposed EGC-CMOPSO and the eight latest multi-objective optimization algorithms are performed on 21 test problems. The experimental results validate that the proposed EGC-CMOPSO is capable of handling multi-objective optimization problems (MOPs) and obtaining superior performance on both convergence and diversity.

Multi-objective architecture for strategic integration of distributed energy resources and battery storage system in microgrids

Microgrids with integrated renewable energy-based distributed generation (RDG) and battery energy storage systems (BESS) should be effectively designed and controlled to reap the potential benefits. In this context, this study recommends a novel Multi-objective Artificial Hummingbird Algorithm (MOAHA) based framework for optimal RDG allocation and sizing, along with BESS operation strategy, to enhance the voltage stability margin (VSM) and reduce the overall yearly expenses. In this work, the developed formulation has been evaluated on the IEEE 33-bus system, IEEE 69-bus system, and the Masirah Island distribution grid of Oman. Furthermore, the proposed method’s Pareto fronts are concluded to be superior to four of the recent metaheuristics employed in this research domain: Multi-objective Multiverse Optimization method (MOMVO), Multi-objective Equilibrium Optimization Technique (MOEOT), Multi-objective Particle Swarm Optimization (MOPSO), and Non-dominated Sorting Genetic Algorithm-III (NSGA-III). According to the findings, the MOAHA optimal Pareto solution candidates (PSC) for the three test systems satisfied the VSM constraints and cost objectives while providing substantial energy transfer during off-peak and peak demand hours. Additionally, all PSCs effectively avoided voltage violations, and the active power losses during each optimization period and the total energy losses were significantly reduced.

Dual objective bounded abstaining model to control performance for safety-critical applications

Abstaining models have been widely used in safety-critical fields to avoid uncertain classification and reduce misclassification costs. Previous abstaining models have two main disadvantages. First, the costs of classification and rejection need to be set. Unfortunately, it is difficult to obtain or estimate costs in practical applications. When costs change, the trained model will be no longer applicable. Second, a single indicator, such as the error rate or AUC, is optimized, which has poor robustness for different application requirements. To solve such problems, a dual objective bounded abstaining (DOBA) model is proposed. DOBA optimizes the binary confusion matrix with rejection by minimizing the false positive and negative rates under class-specific reject constraints. The DOBA model is solved using an evolutionary multi-objective optimization algorithm. The requirement-oriented abstaining classifier can be selected from a set of Pareto-optimal solutions. Extensive experiments prove the effectiveness and superiority of DOBA compared to other abstaining models.

Modelling and application of joint maintenance grouping and workload smoothing for an automotive plant

In the maintenance optimisation framework, grouping maintenance is a promising solution for maintenance planning of multi-component systems, in which maintenance activities are performed together to reduce maintenance costs. One of the most widely identified challenges in real applications of grouping maintenance is that it may disturb the maintenance workload balance (smoothness), causing many difficulties in production and/or labour scheduling and inventory management. In this study, we propose a joint optimisation approach for maintenance grouping and workload balancing to address the above challenge. First, a mathematical model of the joint optimisation problem was derived. A multi-objective grouping optimisation approach based on the Weighted Sum model and Genetic Algorithm was implemented to determine the Pareto-optimal grouping solution. The proposed approach was applied to a real case study of an automotive plant comprising 40 production lines with 1090 components. The results highlighted the advantages, effectiveness, and flexibility of the proposed maintenance approach in real-world applications.

Bi-sided facility location problems: an efficient algorithm for k-centre, k-median, and travelling salesman problems

This study introduces a general framework, called Bi-sided facility location, for a wide range of problems in the area of combined facility location and routing problems such as locating test centres and designing the network of supermarkets. It is based on a multi-objective optimisation model to enhance the service quality which the clients received, called client-side, and enhance the interconnection quality and eligibility among the centres, called center-side. Well-known problems such as k-median and k-centre for the client-side and the travelling salesman problem for the centre-side are taken into account in this paper. After discussing the complexity of this kind of combination, we propose a heuristic approximation algorithm to find approximation Pareto-optimal solutions for the problem. The algorithm is an efficient local search utilising geometric objects such as the Voronoi diagram and Delaunay triangulation as well as algorithms for computing approximation travelling salesman tour. In addition to the comprehensive theoretical analysis of the proposed models and algorithm, we apply the algorithm to different instances and benchmarks, and compare it with NSGA-II based on set coverage and spacing metrics. The results confirm the efficiency of the algorithm in terms of running time and providing a diverse set of efficient trade-off solutions. Highlights Introducing a general bi-side location model considering centres and clients’ utilities Discussing and proving the NP-hardness of the model in the general framework Considering two instances; k-centre and k-median for client-side and TSP for centre-side Proposing an efficient geometric-based algorithm for solving the problems Implementing, testing, and comparing the proposed algorithm on several benchmarks

Ecosystem Service Optimisation in the Central Plains Urban Agglomeration Based on Land Use Structure Adjustment

By using the methods of scenario analysis, model simulation, and the multi-objective spatial optimisation algorithm Non-dominated Sorting Genetic Algorithm-II (NSGA-II), the Pareto optimal solutions for water supply, water purification (N retention), as well as carbon storage and sequestration service (carbon service) of the Central Plains Urban Agglomeration (CPUA) were sought by adjusting the land use structure. It showed that, to reach the Pareto optimal solution goal, (1) in Scenario 1 (S1), the water supply service needs to increase by 10.682 billion cubic metres, the water purification (N retention) service needs to decrease by 11,400 tons, and the carbon service need to decrease by 2.487 billion tons. In Scenario 2 (S2), the water supply service needs to increase by 8.243 billion cubic metres, the water purification (N retention) service needs to decrease by 11,000 tons, and the carbon service needs to decrease by 2.466 billion tons. In Scenario 3 (S3), the water supply service needs to increase by 4.089 billion cubic metres, the water purification (N retention) service needs to decrease by 10,800 tons, and the carbon service needs to decrease by 2.380 billion tons. (2) After land use optimisation and adjustment, the S3 ecological land structure is complete and consistent with the vision of ecological protection and urban development in the study area, which is the optimal scenario. (3) Optimising the ecosystem service supply pattern through land use structure adjustment could balance the overall ecosystem service supply pattern of the study area In regions wherein ecosystem supply is insufficient and there is a spatial mismatch between supply and demand for ecosystem services, this study can guide regional land planning and assist in the formulation of ecosystem service management policies.

Compensation and profit allocation for collaborative multicenter vehicle routing problems with time windows

With the growing interest in win–win cooperation within the logistics industry recently, collaborative multicenter logistics networks have witnessed the establishment of numerous alliances aimed at achieving cost savings. However, alliance members may choose to withdraw from an alliance due to changes in market positioning strategies and short-term profit considerations. Such withdraws often lead to the disintegration of the alliance and result in financial losses for the remaining non-defaulting members. This study focuses on addressing the issues of compensation and profit allocation in a specific scenario known as the collaborative multicenter vehicle routing problem with time windows and defaulting members withdrawal (CMVRPTWDMW). The objective is to ensure alliance stability and fair profit distribution among its members. To achieve this, a tri-objective mathematical model is proposed to optimize the re-formed alliances by considering the total operating cost, number of vehicles, and service waiting time. Additionally, an improved minimum cost remaining saving method is introduced to accurately quantify the deserved profits of non-defaulting members. Compensation quantification and default cost allocation models are then developed based on this analysis. To solve the CMVRPTWDMW and obtain Pareto optimal solutions, a hybrid heuristic algorithm is designed. This algorithm combines a 3D k-means clustering algorithm for customer reassignment after the withdrawal of defaulting members, effectively reducing the complexity of the problem. Furthermore, the algorithm employs a Clarke-Wright saving method-based non-dominated sorting genetic algorithm-III (CW-NSGA-III) to search for optimal solutions. To enhance the algorithm’s search ability, an elite alteration strategy and a penalty-based boundary intersection approach are incorporated into CW-NSGA-III. Finally, a real-world case study conducted in Chongqing City, China, is presented to demonstrate the feasibility of the proposed models and solution algorithms. The study contributes valuable insights into the sustainable operation of urban logistics networks that may experience unpredictable defaults, providing guidance for the stability of logistics alliances in the transportation sector.

Minimizing Single-Family Homes’ Carbon Dioxide Emissions and Life Cycle Costs: An Improved Billiard-Based Optimization Algorithm Approach

In recent years, research has focused on designing buildings with higher energy efficiency and lower emissions by considering multiple objectives. This can impact financial savings, smaller environmental footprints, and energy consumption optimization. The purpose of the current study is to develop a new technique to solve this challenging multiple-objective optimization problem. While there are different methods to solve optimization problems, based on the NLP theory, there is not any metaheuristic algorithm that can solve all the problems accurately. Sometimes, the outcome of a basic algorithm is a local optimum. Therefore, to reach the global optimum, we propose the Improved Billiard-based Optimization Algorithm (IBOA). Moreover, in some cases, the basic model suffers from premature convergence, which prevents reaching an accurate result. Hence, this study aims to solve this problem and attain better convergence results using the proposed method to minimize CO2-eq emissions and life cycle costs. The design variables include some parameters of the envelope of a single-family residential dwelling to indicate the efficiency of the presented method. Based on the Pareto optimum solutions achieved, it is proved that the method is effective.

Multi-objective optimal dispatch strategy for power systems with Spatio-temporal distribution of air pollutants

Accurate and effective pollutant emission control models are key in mitigating the environmental impact of energy supply systems. This paper proposes a novel high-dimensional multi-objective optimal dispatching strategy for power systems considering the spatial and temporal distribution of multiple pollutants. Firstly, a spatial and temporal distribution model of pollutants in thermal power plants is constructed, which is truly applicable to power dispatch. For modeling the pollution situation, the daily changes in the atmospheric boundary layer are taken into account, fully reflecting the pollutant dispersion characteristics of thermal power plants and improving the result accuracy. Next, a high-dimensional multi-objective optimization model is developed to simultaneously reduce the cost of power generation, carbon emission and the impact air quality from VOCs (volatile organic compounds), SO2 and NO2. This model combines the spatial and temporal distribution characteristics of various pollutants and environmental capacity. Finally, a representative high-dimensional multi-objective optimization algorithm is employed to obtain an approximate Pareto-optimal solution set. And a multi-objective decision method is proposed to filter the compromise solution. The results show that the APCs of VOCs, SO2 and NO2 are reduced by 27.5%, 10.13% and 23.16%, respectively, in the pollution day model. On non-pollution days, the proposed scheduling method not only effectively improves air quality, but also achieves cost savings of $1276.59 and reduces CO2 emission by 0.168 × 104t compared to the emission limitation method. The proposed scheduling method can not only effectively improve air quality, but also make corresponding adjustments according to the spatial and temporal changes of environmental capacity, which can truly realize economic and environmental-friendly power scheduling.

Optimization of headway and bus stop spacing for low demand bus routes

ABSTRACT We propose a methodology for optimization of service headway and stop spacing along a low-demand bus route that minimizes operator and user costs. This study develops analytical cost models that are representative of low-demand routes by using negative binomial distribution for passenger demand for boarding and alighting pattern to estimate the probability of stopping and both random and planned arrival of passengers are considered to estimate the waiting time. Pareto optimal solutions obtained using multi-objective evolutionary algorithm, NSGA-II indicate that optimal values of headway and stop spacing are underestimated if optimized based on assumptions typical of high-demand routes which is passenger demand for boarding and alighting at bus stops randomly following a Poisson process. With the aid of the study methodology, transit planners will be able to improve the service utilization and passenger accessibility along an under-performing low demand routes by recommending minimal modifications to the existing route and bus schedule.

DPGWO Based Feature Selection Machine Learning Model for Prediction of Crack Dimensions in Steam Generator Tubes

The selection of an appropriate number of features and their combinations will play a major role in improving the learning accuracy, computation cost, and understanding of machine learning models. In this present work, 22 gray-level co-occurrence matrix features extracted from magnetic flux leakage images captured in steam generator tubes’ cracks are considered for developing a machine learning model to predict and analyze crack dimensions in terms of their length, depth, and width. The performance of the models is examined by considering R2 and RMSE values calculated using both training and testing data sets. The F Score and Mutual Information Score methods have been applied to prioritize the features. To analyze the effect of different machine learning models, their number of features, and their selection methods, a Taguchi experimental design has been implemented and an analysis of variance test has been conducted. The dynamic population gray wolf algorithm (DPGWO) has been adopted to select the best features and their combinations. Due to the two contradictory natures of performance metrics, Pareto optimal solutions are considered, and the best one is obtained using Deng’s method. The effectiveness of DPGWO is proved by comparing its performance with Grey Wolf Optimization and Moth Flame Optimization algorithms using the Friedman test and performance indicators, namely inverted generational distance and spacing.

MOIMPA: multi-objective improved marine predators algorithm for solving multi-objective optimization problems

This paper introduces a multi-objective variant of the marine predators algorithm (MPA) called the multi-objective improved marine predators algorithm (MOIMPA), which incorporates concepts from Quantum theory. By leveraging Quantum theory, the MOIMPA aims to enhance the MPA’s ability to balance between exploration and exploitation and find optimal solutions. The algorithm utilizes a concept inspired by the Schrödinger wave function to determine the position of particles in the search space. This modification improves both exploration and exploitation, resulting in enhanced performance. Additionally, the proposed MOIMPA incorporates the Pareto dominance mechanism. It stores non-dominated Pareto optimal solutions in a repository and employs a roulette wheel strategy to select solutions from the repository, considering their coverage. To evaluate the effectiveness and efficiency of MOIMPA, tests are conducted on various benchmark functions, including ZDT and DTLZ, as well as using the evolutionary computation 2009 (CEC’09) test suite. The algorithm is also evaluated on engineering design problems. A comparison is made between the proposed multi-objective approach and other well-known evolutionary optimization methods, such as MOMPA, multi-objective ant lion optimizer, and multi-objective multi-verse optimization. The statistical results demonstrate the robustness of the MOIMPA approach, as measured by metrics like inverted generational distance, generalized distance, spacing, and delta. Furthermore, qualitative experimental results confirm that MOIMPA provides highly accurate approximations of the true Pareto fronts.