Multi-objective Multi-verse Optimization Research Articles

A pareto strategy based on multi-objective optimal integration of distributed generation and compensation devices regarding weather and load fluctuations

In this study, we present a comprehensive optimization framework employing the Multi-Objective Multi-Verse Optimization (MOMVO) algorithm for the optimal integration of Distributed Generations (DGs) and Capacitor Banks (CBs) into electrical distribution networks. Designed with the dual objectives of minimizing energy losses and voltage deviations, this framework significantly enhances the operational efficiency and reliability of the network. Rigorous simulations on the standard IEEE 33-bus and IEEE 69-bus test systems underscore the effectiveness of the MOMVO algorithm, demonstrating up to a 47% reduction in energy losses and up to a 55% improvement in voltage stability. Comparative analysis highlights MOMVO's superiority in terms of convergence speed and solution quality over leading algorithms such as the Multi-Objective Jellyfish Search (MOJS), Multi-Objective Flower Pollination Algorithm (MOFPA), and Multi-Objective Lichtenberg Algorithm (MOLA). The efficacy of the study is particularly evident in the identification of the best compromise solutions using MOMVO. For the IEEE 33 network, the application of MOMVO led to a significant 47.58% reduction in daily energy loss and enhanced voltage profile stability from 0.89 to 0.94 pu. Additionally, it realized a 36.97% decrease in the annual cost of energy losses, highlighting substantial economic benefits. For the larger IEEE 69 network, MOMVO achieved a remarkable 50.15% reduction in energy loss and improved voltage profiles from 0.89 to 0.93 pu, accompanied by a 47.59% reduction in the annual cost of energy losses. These results not only confirm the robustness of the MOMVO algorithm in optimizing technical and economic efficiencies but also underline the potential of advanced optimization techniques in facilitating the sustainable integration of renewable energy resources into existing power infrastructures. This research significantly contributes to the field of electrical distribution network optimization, paving the way for future advancements in renewable energy integration and optimization techniques for enhanced system efficiency, reliability, and sustainability.

Multi-objective Geometric Mean Optimizer (MOGMO): A Novel Metaphor-Free Population-Based Math-Inspired Multi-objective Algorithm

This research introduces a novel multi-objective adaptation of the Geometric Mean Optimizer (GMO), termed the Multi-Objective Geometric Mean Optimizer (MOGMO). MOGMO melds the traditional GMO with an elite non-dominated sorting approach, allowing it to pinpoint Pareto optimal solutions through offspring creation and selection. A Crowding Distance (CD) coupled with an Information Feedback Mechanism (IFM) selection strategy is employed to maintain and amplify the convergence and diversity of potential solutions. MOGMO efficacy and capabilities are assessed using thirty notable case studies. This encompasses nineteen multi-objective benchmark problems without constraints, six with constraints and five multi-objective engineering design challenges. Based on the optimization results, the proposed MOGMO is better 54.83% in terms of GD, 64.51% in terms of IGD, 67.74% in terms of SP, 70.96% in terms of SD, 64.51% in terms of HV and 77.41% in terms of RT. Therefore, MOGMO has a better convergence and diversity for solving un-constraint, constraint and real-world application. Statistical outcomes from MOGMO are compared with those from Multi-Objective Equilibrium Optimizer (MOEO), Decomposition-Based Multi-Objective Symbiotic Organism Search (MOSOS/D), Non-dominated Sorting Genetic Algorithm (NSGA-II), Multi-Objective Multi-Verse Optimization (MOMVO) and Multi-Objective Plasma Generation Optimizer (MOPGO) algorithms, utilizing identical performance measures. This comparison reveals that MOGMO consistently exhibits robustness and excels in addressing an array of multi-objective challenges. The MOGMO source code is available at https://github.com/kanak02/MOGMO.

Multi-objective multiverse optimization for optimal allocation of distributed energy resources: The optimal parallel processing schemes

Utilizing Distributed Generators (DGs) and Energy Storage Systems (ESSs) enhances power system reliability, drawing significant research attention. However, these systems pose challenges, compelling scientists to explore optimization methods. Our paper presents an innovative solution, Parallel Multi-Objective Multi-Verse Optimization (PMOMVO), aimed at optimizing DGs and Battery Energy Storage Systems (BESSs) allocation. This optimization addresses voltage violations and operation costs, crucial concerns for system operators and consumers. By leveraging a parallel approach, PMOMVO significantly accelerates the optimization process. We compared its results with a base case scenario, demonstrating the superior efficiency of our parallel method. It not only enhances the optimization performance but also proves its efficacy by generating optimal solutions from the Pareto front set. This research showcases the benefits of PMOMVO, offering a faster, more efficient, and reliable way to optimize power systems, benefiting both operators and consumers.

Multi-objective liver cancer algorithm: A novel algorithm for solving engineering design problems

This research introduces the Multi-Objective Liver Cancer Algorithm (MOLCA), a novel approach inspired by the growth and proliferation patterns of liver tumors. MOLCA emulates the evolutionary tendencies of liver tumors, leveraging their expansion dynamics as a model for solving multi-objective optimization problems in engineering design. The algorithm uniquely combines genetic operators with the Random Opposition-Based Learning (ROBL) strategy, optimizing both local and global search capabilities. Further enhancement is achieved through the integration of elitist non-dominated sorting (NDS), information feedback mechanism (IFM) and Crowding Distance (CD) selection method, which collectively aim to efficiently identify the Pareto optimal front. The performance of MOLCA is rigorously assessed using a comprehensive set of standard multi-objective test benchmarks, including ZDT, DTLZ and various Constraint (CONSTR, TNK, SRN, BNH, OSY and KITA) and real-world engineering design problems like Brushless DC wheel motor, Safety isolating transformer, Helical spring, Two-bar truss and Welded beam. Its efficacy is benchmarked against prominent algorithms such as the non-dominated sorting grey wolf optimizer (NSGWO), multiobjective multi-verse optimization (MOMVO), non-dominated sorting genetic algorithm (NSGA-II), decomposition-based multiobjective evolutionary algorithm (MOEA/D) and multiobjective marine predator algorithm (MOMPA). Quantitative analysis is conducted using GD, IGD, SP, SD, HV and RT metrics to represent convergence and distribution, while qualitative aspects are presented through graphical representations of the Pareto fronts. The MOLCA source code is available at: https://github.com/kanak02/MOLCA.

Multi-Objective Stochastic Paint Optimizer for Solving Dynamic Economic Emission Dispatch with Transmission Loss Prediction Using Random Forest Machine Learning Model

Dynamic economic emission dispatch problems are complex optimization tasks in power systems that aim to simultaneously minimize both fuel costs and pollutant emissions while satisfying various system constraints. Traditional methods often involve solving intricate nonlinear load flow equations or employing approximate loss formulas to account for transmission losses. These methods can be computationally expensive and may not accurately represent the actual transmission losses, affecting the overall optimization results. To address these limitations, this study proposes a novel approach that integrates transmission loss prediction into the dynamic economic emission dispatch (DEED) problem. A Random Forest machine learning model was offline-trained to predict transmission losses accurately, eliminating the need for repeated calculations during each iteration of the optimization process. This significantly reduced the computational burden of the algorithm and improved its efficiency. The proposed method utilizes a powerful multi-objective stochastic paint optimizer to solve the highly constrained and complex dynamic economic emission dispatch problem integrated with random forest-based loss prediction. A fuzzy membership-based approach was employed to determine the best compromise Pareto-optimal solution. The proposed algorithm integrated with loss prediction was validated on widely used five and ten-unit power systems with B-loss coefficients. The results obtained using the proposed algorithm were compared with seventeen algorithms available in the literature, demonstrating that the multi-objective stochastic paint optimizer (MOSPO) outperforms most existing algorithms. Notably, for the Institute of Electrical and Electronics Engineers (IEEE) thirty bus system, the proposed algorithm achieves yearly fuel cost savings of USD 37,339.5 and USD 3423.7 compared to the existing group search optimizer algorithm with multiple producers (GSOMP) and multi-objective multi-verse optimization (MOMVO) algorithms.

Multiobjective Multiverse Optimizer for Multirobotic U-Shaped Disassembly Line Balancing Problems

The development of technology accelerates the upgrade of products, which results in a significant number of obsolete products. This research aims to solve the Multi-robotic Multi-product U-shaped Disassembly-line-balancing Problem (M2UDP), in which different products are disassembled on a U-shaped model in a pre-set cycle time and assigned tasks to robots in each workstation reasonably. A linear mixed-integer model is established to maximize disassembly profit and minimize carbon emissions. An improved multi-objective multi-verse optimizer (IMMO) that utilizes the sigmoid activation function in neural networks is proposed to find the optimal plan for the model. The improved algorithm is verified via a set of real-life instances and compared with three classical multi-objective optimization algorithms. The experimental results show that the proposed IMMO performs better than those peers in solving the M2UDP problems.

A new decomposition-based multi-objective symbiotic organism search algorithm for solving truss optimization problems

This study presents a comprehensive study on the potential and efficacy of decomposition-based multi-objective symbiotic organism search (MOSOS/D) algorithm for truss structure optimization. The investigation is carried out on five benchmark truss structures, e.g., 37-bar, 60-bar, 72-bar, 120-bar, and 200-bar truss problems. The optimization performance of MOSOS/D is compared with other established algorithms, such as Multi-Objective Evolutionary Algorithm Based on Decomposition, Non-Dominated Sorting Genetic Algorithm-II, Multi-Objective Equilibrium Optimizer, Multi-Objective Marine Predator Algorithm, Decomposition-Based Multi-Objective Heat Transfer Search, Multi-Objective Passing Vehicle Search, Multi-Objective Evolutionary Algorithm Based on Decomposition Differential Evaluation, Multi-Objective Symbiotic Organisms Search, and Multi-Objective Multi-Verse Optimizer considering several metrics, including Generational Distance, Spacing, Spread, Inverted Generational Distance, Hypervolume and Runtime. The findings demonstrate MOSOS/D’s competitiveness in providing non-dominated solutions with less space between them. It also achieves a good balance between convergence and coverage and, thus, delivers diverse solutions with less computational complexity. However, the efficiency of the MOSOS/D algorithm varies depending on the complexity of the considered truss structure, with some algorithms occasionally outperforming it in one or two aspects for specific benchmarks. This study provides valuable insights to engineers and designers aiming to achieve optimal truss structure design.

Comparison of ethane recovery processes for lean gas based on a coupled model

Ethane recovery from natural gas is crucial for improving the economic efficiency of enterprises, saving energy and reducing emissions. This study analyses the characteristics of process parameters based on three lean gas ethane recovery processes. A prediction and multiobjective optimization model for ethane recovery and system energy consumption is established. Based on this framework, a new method for ethane recovery process comparison for lean gas is proposed. In the process analysis, two additional coolers are added to the cold residue recycling process to improve ethane recovery. Seven main process parameters are determined based on the three processes. According to the prediction results, support vector regression is the most effective model among the individual models. The prediction accuracy of the support vector regression model based on grey wolf optimization is the highest. Compared with traditional support vector regression, this approach yields average reductions in the mean absolute error, mean absolute percentage error and root mean square error of 63.95%, 64.21% and 47.98%, respectively, reflecting significantly improved prediction accuracy and stability. The multiobjective multiverse optimization algorithm displays the best optimization performance and the highest solution diversity among the optimization results. Additionally, it yields high-quality solutions at the shortest run time. Based on the optimization results, the supplemental rectification with compression process yields the lowest system energy consumption of any method considered and meets the ethane recovery requirements real projects.

Efficient Solutions for Electronic Chip Cooling: Multi-Objective Optimization Using Evolutionary Algorithms with Boron Nitride Nanotube-Based Nanofluid

Optimization algorithms have significantly evolved because of advancements in computational capacity. This increase aids in the availability of data to train various artificial intelligence models and can be used in optimizing solutions for electronic chip cooling. In the current study, such a microchannel heat sink (MCHS) is optimized using a Boron Nitride Nanotube (BNN)-based nanofluid as a coolant. Thermal resistance and pumping power are chosen as the objective functions, while geometric parameters such as the channel aspect and width ratio are used as the design variables. Multi-objective multiverse optimizer (MOMVO), an evolutionary algorithm, is used to optimize both objective functions, which are minimized simultaneously. The primary objective of this study is to study the applicability of such advanced multi-objective optimization algorithms, which have not previously been implemented for such a thermal design problem. Based on the study, it is found that the optimal results are obtained with a population size of only 50 and within 100 iterations. Using the MOMVO optimization, it is also observed that thermal resistance and pumping power do not vary significantly with respect to the channel aspect ratio, while pumping power varies linearly with the channel width ratio. An optimum thermal resistance of 0.0177 °C/W and pumping power of 10.65 W are obtained using the MOMVO algorithm.

A heterogeneous ensemble architecture coupling model selection sorting and residual error iterative correction for crude oil price forecasting

Although crude oil price forecasts can provide policymakers, investors, consumers, and producers with scientific and reliable guidance, the nonlinearity and complexity of crude oil markets still pose serious challenges to this work. To this end, we propose a crude oil price ensemble prediction model that combines model selection sorting, multi-objective heterogeneous ensemble learning, and residual error iterative correction. First, a selection strategy based on the weighted information criterion is used to screen benchmark models in the model pool. Subsequently, candidate models are heterogeneously integrated using the multi-objective multi-verse optimization algorithm. VIseKriterijumska Optimizacija I Kompromisno Resenje, Technique for Order Preference by Similarity to Ideal Solution, and Grey Relational Analysis are utilized to select the optimal non-dominated solution of the Pareto surface. Finally, correction technology is designed to adaptively correct the residual error. Optimum error shrinkage and the number of corrections ensure maximum predictable component development. West Texas Intermediate and Europe Brent spot price data are utilized for experimental verification. Results show that the model can accurately describe crude oil price fluctuations, and has excellent robustness and stability. The forecasting method can be used as a reliable and promising energy economic decision algorithm.

Efficient Red Kite Optimization Algorithm for Integrating the Renewable Sources and Electric Vehicle Fast Charging Stations in Radial Distribution Networks

The high penetration of renewable energy resources’ (RESs) and electric vehicles’ (EVs) demands to power systems can stress the network reliability due to their stochastic natures. This can reduce the power quality in addition to increasing the network power losses and voltage deviations. This problem can be solved by allocating RESs and EV fast charging stations (FCSs) in suitable locations on the grid. So, this paper proposes a new approach using the red kite optimization algorithm (ROA) for integrating RESs and FCSs to the distribution network through identifying their best sizes and locations. The fitness functions considered in this work are: reducing the network loss and minimizing the voltage violation for 24 h. Moreover, a new version of the multi-objective red kite optimization algorithm (MOROA) is proposed to achieve both considered fitness functions. The study is performed on two standard distribution networks of IEEE-33 bus and IEEE-69 bus. The proposed ROA is compared to dung beetle optimizer (DBO), African vultures optimization algorithm (AVOA), bald eagle search (BES) algorithm, bonobo optimizer (BO), grey wolf optimizer (GWO), multi-objective multi-verse optimizer (MOMVO), multi-objective grey wolf optimizer (MOGWO), and multi-objective artificial hummingbird algorithm (MOAHA). For the IEEE-33 bus network, the proposed ROA succeeded in reducing the power loss and voltage deviation by 58.24% and 90.47%, respectively, while in the IEEE-69 bus it minimized the power loss and voltage deviation by 68.39% and 93.22%, respectively. The fetched results proved the competence and robustness of the proposed ROA in solving the problem of integrating RESs and FCSs to the electrical networks.

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.

A multi-objective multi-verse optimizer algorithm to solve environmental and economic dispatch

The combustion and emission of coal have always been a concern. A class of multi-objective Environmental Economic Dispatch (EED) problems has been widely studied to reduce the pollution problem of fossil fuel power plants. In this study, a multi-objective Multi-Verse Optimization algorithm based on Gridded Knee Points and Plane Measurement technique (GKPPM-MVO) is proposed for the multi-objective EED problems. Knee points are usually considered as the most critical points in unbiased decision-making, while plane measurement can find the largest distant points in the population neighborhood. We apply the knee and maximum plane distance points in the local search phase. The original mechanism of parameter control in local search is replaced by using the two above points to exploit the pretty information and inherit it to the next generation. The algorithm is applied to various EED problems. The four algorithms, including MOMVO, NSGA-ii, MOABC, and MOEGO are also used to compare the performance of the algorithms thoroughly. Results show that the GKPPM-MVO algorithm has good convergence performance, high stability, and high uniformity of the Pareto Front.

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.

An Enhanced Multi-Objective Optimizer for Stochastic Generation Optimization in Islanded Renewable Energy Microgrids

A microgrid is an autonomous electrical system that consists of renewable energy and efficiently achieves power balance in a network. The complexity in the distribution network arises due to the intermittent nature of renewable generation units and varying power. One of the important objectives of a microgrid is to perform energy management based on situational awareness and solve an optimization problem. This paper proposes an enhanced multi-objective multi-verse optimizer algorithm (MOMVO) for stochastic generation power optimization in a renewable energy-based islanded microgrid framework. The proposed algorithm is utilized for optimum power scheduling among various available generation sources to minimize the microgrid’s generation costs and power losses. The performance of MOMVO is assessed on a 6-unit and 10-unit test system. Simulation results show that the proposed algorithm outperforms other metaheuristic algorithms for multi-objective optimization.

A two-archive multi-objective multi-verse optimizer for truss design

Multi-objective structure optimization is a complex design issue that involves dealing with multiple conflicting objectives and various constraints. Although metaheuristics have been successful in resolving such issues, their stochastic nature and limitations can make implementation challenging. To address this challenge, an efficient and powerful optimizer called the multi-objective multi-verse optimizer (MOMVO) has been proposed in this study. The MOMVO algorithm is based on a two-archive concept focused on convergence and diversity, respectively, and is termed MOMVO2arc. The effectiveness of MOMVO2arc was evaluated by applying it to five conventional planar and spatial real-world structural optimization problems. These problems had conflicting objectives, such as minimizing structural mass and minimizing maximum nodal deflection, while imposing safety and size constraints related to stress on components and discrete cross-sectional areas. The results were then compared with those of seven advanced optimization techniques, including MOEA/D and NSGA-II, using four globally accepted performance indicators, including Hypervolume, Inverted Generational Difference, Spacing to Extent matrices, and the qualitative behavior of the best Pareto-front plots that each algorithm can produce. The comparative analysis and average Friedman rank test revealed that MOMVO2arc was more effective in solving large structure optimization problems with less computation time. The suggested approach not only found and maintained more Pareto-optimal sets but also achieved good diversity and convergence in both the decision and objective spaces. Therefore, MOMVO2arc can be a promising tool for resolving complex multi-objective structure optimization problems.

Scheduling an Energy-Aware Parallel Machine System with Deteriorating and Learning Effects Considering Multiple Optimization Objectives and Stochastic Processing Time

Currently, energy conservation draws wide attention in industrial manufacturing systems. In recent years, many studies have aimed at saving energy consumption in the process of manufacturing and scheduling is regarded as an effective approach. This paper puts forwards a multi-objective stochastic parallel machine scheduling problem with the consideration of deteriorating and learning effects. In it, the real processing time of jobs is calculated by using their processing speed and normal processing time. To describe this problem in a mathematical way, a multi-objective stochastic programming model aiming at realizing makespan and energy consumption minimization is formulated. Furthermore, we develop a multi-objective multi-verse optimization combined with a stochastic simulation method to deal with it. In this approach, the multi-verse optimization is adopted to find favorable solutions from the huge solution domain, while the stochastic simulation method is employed to assess them. By conducting comparison experiments on test problems, it can be verified that the developed approach has better performance in coping with the considered problem, compared to two classic multi-objective evolutionary algorithms.

Parallel Multiobjective Multiverse Optimizer for Path Planning of Unmanned Aerial Vehicles in a Dynamic Environment with Moving Obstacles

Path planning with collision avoidance for unmanned aerial vehicles (UAVs) in environments with moving obstacles is a complex process of navigation, often considered a hard optimization problem. Ordinary resolution algorithms may fail to provide flyable and collision-free paths under the time-consumption constraints required by the dynamic 3D environment. In this paper, a new parallel multiobjective multiverse optimizer (PMOMVO) is proposed and successfully applied to deal with the increased computation time of the UAV path planning problem in dynamic 3D environments. Collision constraints with moving obstacles and narrow pass zones were established based on a mathematical characterization of any intersection with lines connecting two consecutive drones’ positions. For the implementation, a multicore central processing unit (CPU) architecture was proposed according to the concept of master–slave processing parallelization. Each subswarm of the entire PMOMVO population was granted to a corresponding slave, and representative solutions were selected and shared with the master core. Slaves sent their local Pareto fronts to the CPU core representing the master that merged the received set of nondominated solutions and built a global Pareto front. Demonstrative results and nonparametric ANOVA statistical analyses were carried out to show the effectiveness and superiority of the proposed PMOMVO algorithm compared to other homologous, multiobjective metaheuristics.

Multi-objective optimization of reinforced concrete cantilever retaining wall: a comparative study

This paper investigates the performance of four multi-objective optimization algorithms, namely non-dominated sorting genetic algorithm II (NSGA-II), multi-objective particle swarm optimization (MOPSO), strength Pareto evolutionary algorithm II (SPEA2), and multi-objective multi-verse optimization (MVO), in developing an optimal reinforced concrete cantilever (RCC) retaining wall. The retaining wall design was based on two major requirements: geotechnical stability and structural strength. Optimality criteria were defined as reducing the total cost, weight, CO2 emission, etc. In this study, two sets of bi-objective strategies were considered: (1) minimum cost and maximum factor of safety, and (2) minimum weight and maximum factor of safety. The proposed method's efficiency was examined using two numerical retaining wall design examples, one with a base shear key and one without a base shear key. A sensitivity analysis was conducted on the variation of significant parameters, including backfill slope, the base soil’s friction angle, and surcharge load. Three well-known coverage set measures, diversity, and hypervolume were selected to compare the algorithms’ results, which were further assessed using basic statistical measures (i.e., min, max, standard deviation) and the Friedman test with a 95% level of confidence. The results demonstrated that NSGA-II has a higher Friedman rank in terms of coverage set for both cost-based and weight-based designs. SPEA2 and MOPSO outperformed both cost-based and weight-based solutions in terms of diversity in examples without and with the effects of a base shear key, respectively. However, based on the hypervolume measure, NSGA-II and MVO have a higher Friedman rank for examples without and with the effects of a base shear key, respectively, for both the cost-based and weight-based designs.

A Decomposition based Multi-Objective Heat Transfer Search algorithm for structure optimization

Multi-objective (MO) problems are complex and challenging to solve due to multiple conflicting objectives and incommensurate constraints. Heat Transfer Search is a recently introduced thermodynamic laws-based algorithm for solving many single objective problems. But it faces criticism due to its shortcomings including local optima trap, computational complexity, and reliability issues while solving MO problems. Decompositions is a simple yet efficient framework that aids in resolving fitness assignments and diversity maintenance issues of MO problems. It is also popular for reducing computational complexity and improving solution quality. Therefore, this work proposes and investigates a novel, simple, and robust Decomposition-based Multi-Objective Heat Transfer Search (MOHTS/D) for solving real-world structural problems. To achieve the Pareto optimal solutions and to confirm their coverage behaviour, the evenly generated weight vectors sorting and Euclidean distance strategies were employed in the proposed posteriori method. The performance of MOHTS/D is investigated through eight constrained widely accepted benchmarks. The results contrast with the MOHTS, MO evolutionary algorithm based on decomposition, MO passing vehicle search, MO slime mould, MO symbiotic organisms search, and MO multi-verse optimization. The efficacy of MOHTS/D is evaluated based on hyper-volume, coverage, inverted generational distance, pure diversity, spacing, spread, coverage Pareto front, diversity maintenance, generational distance, and runtime metrics. The results reveal that MOHTS/D is a robust optimization approach compared to others for optimizing real-life structural problems. MOHTS/D was able to find the optimal solution with minor computational complexity, and the obtained solutions demonstrate a better convergence, coverage, diversity, and spread behaviour over Pareto fronts