Multi-objective Optimization Problem Research Articles

Multi-Objective Routing and Categorization of Urban Network Segments for Cyclists

This study develops a progressive navigation and guidance model for the route selection of cyclists executed in a designated area. The route selection of cyclists is modeled as a Pareto multi-objective optimization problem which is solved with the NSGA-II algorithm. The study aims to contribute to the ongoing efforts to create efficient and cyclist-friendly navigation tools to promote sustainable urban mobility. Data collection methods include GPS tracking, field measurements, and qualitative approaches to understand cyclists’ behavior and preferences. Nine objective functions are constructed based on criteria related to safety and comfort, incorporating decision variables related to cyclists riding on sidewalks, capturing the complexity of urban cycling infrastructure. Tests are performed in a defined area in the center of Athens, Greece. The NSGA-II algorithm is executed with modifications and the Pareto front is constructed, which consists of 28 alternative routes between two origin–destination points. The four routes that optimize the nine criteria of the objective functions are presented, with most routes passing through the Zappeion Gardens. The NSGA-II algorithm is proven to be a suitable approach for applications in networks with complex characteristics and for capturing cyclists’ choices when they face conflicting options. The study presents how a novel approach for the multi-objective optimization of cyclists’ route choice, which considers a wide range of cyclists’ needs and preferences, can be implemented in an urban environment with a lack of cycle infrastructure.

Quantum Genetic Algorithm-Driven Optimization of Triple-Glazed Window Thickness for Enhanced Light Reduction

Abstract. Glass, a common construction material, generally lacks significant thermal properties. As technology rapidly advances, the demand for glass materials with superior heat preservation and thermal insulation capabilities increases, driven by the need to reduce building energy consumption. Multi-objective optimization problems, particularly in complex multilayered systems, require advanced numerical optimization algorithms. The quantum-inspired genetic algorithm (QIGA) offers advantages such as fast solving speed and high precision, utilizing quantum coding, variation, rotation gates, and crossing techniques. This study focuses on designing the optimal thickness of triple-layer glass to minimize sunlight penetration through windows, using QIGA to achieve this goal. The results demonstrate that triple glazing effectively reduces solar radiation entering a room, though different layer combinations lead to significant variations in total energy reduction. The study also emphasizes the importance of concurrent research in glass layer splicing technology, coating film techniques, and new glass materials to enhance overall performance. These findings contribute to the development of energy-efficient building materials that meet modern standards for thermal insulation and light control.

Research on Microgrid Optimal Scheduling Based on an Improved Honey Badger Algorithm

As global energy demands continue to grow and environmental protection pressures increase, microgrids have garnered widespread attention due to their ability to effectively integrate distributed energy sources, improve energy utilization efficiency, and enhance grid stability. Due to the complexity of internal structure, variety of energy sources, and uncertainty of load demand, the optimal scheduling problem of microgrids becomes extremely complicated. Traditional optimization methods often perform poorly in complex and dynamic microgrid environments, and it is assumed that the complexity is low or that more simplification is needed, which leads to poor convergence and local optimality when dealing with uncertainty and nonlinear problems, making intelligent optimization algorithms a crucial solution to this problem. To address the shortcomings of the traditional honey badger algorithm, such as the slow convergence speed and a tendency to fall into local optima in complex microgrid optimal scheduling problems, this paper proposes a multi-strategy improved honey badger algorithm. During the population initialization phase, a combined opposition-based learning strategy is introduced to enhance the algorithm’s exploration and exploitation capabilities. Additionally, the introduction of variable spiral factors and a linearly decreasing strategy for parameters improves the overall efficiency of the algorithm and reduces the risk of local optima. To further enhance population diversity, a hunger search strategy is employed, providing stronger adaptability and global search capabilities in varying environments. The improved honey badger algorithm is then applied to solve the multi-objective optimal scheduling problem in grid-connected microgrid modes. The simulation results indicate that the improved honey badger algorithm effectively enhances the economic and environmental benefits of microgrid operations, improving system operational stability.

Multiobjective Route Optimization for Multimodal Cold Chain Networks Considering Carbon Emissions and Food Waste

The cold chain logistics industry faces significant challenges in terms of transportation costs and carbon emissions. It is imperative to plan multimodal transportation routes efficiently to address these issues, minimize food waste, and reduce carbon emissions. This paper focuses on four key optimization objectives for multimodal cold chain transport: minimizing total transportation time, costs, carbon emissions, and food waste. To tackle these objectives, we propose a high-dimensional multiobjective route optimization model for multimodal cold chain networks. Our approach involves the development of a multiobjective evolutionary algorithm, utilizing Monte Carlo simulation and a one-by-one selection strategy. We evaluate the proposed algorithm’s performance by analyzing various convergence and distribution indicators. The average values for the minimum total transportation time, transportation cost, carbon emission cost, and cargo loss rate derived from the proposed algorithm ultimately converge to 6721.7, 5184.4, 301.5, and 0.21, respectively, demonstrating the effectiveness of the algorithmic solution. Additionally, we benchmark our algorithm against the existing literature to showcase its efficiency in solving high-dimensional multi-objective route optimization problems. Furthermore, we investigate the impact of different parameters, such as carbon tax rates, temperature, and cargo activation energy, on carbon emissions, and food waste. Moreover, we conduct a real-world case study to apply our approach to solving a practical business problem related to multimodal cold chain transportation. The insights gained from this research offer valuable decision-making support for multimodal carriers in developing low-carbon and environmentally friendly transportation strategies to efficiently transport perishable goods.

Steepest descent method for uncertain multiobjective optimization problems under finite uncertainty set

In this paper, a steepest descent method is developed for the robust counterpart of uncertain multiobjective optimization problems under finite uncertainty. The robust counterpart under consideration is the minimum of objective wise worst case, which is a nonsmooth deterministic multiobjective optimization problem. To solve this robust counterpart with the help of the steepest descent method, a subproblem is constructed and solved to find a descent direction. An Armijo-type inexact line search technique is employed to find a suitable step length. With the help of the descent direction and step length, a sequence is generated. The convergence of the proposed method is justified under some common assumptions. Finally, the algorithm is verified and compared with one existing method with the help of some numerical problems.

Multi-Objective Optimization of Three-Stage Turbomachine Rotor Based on Complex Transfer Matrix Method

This study presents the complex transfer matrix method (CTMM) as an advanced mathematical model, providing significant advantages over the finite element method (FEM) by yielding rapid solutions for complex optimization problems. In order to design a more efficient structure of a three-stage turbomachine rotor, we integrated this method with various optimization algorithms, including genetic algorithm (GA), differential evolution (DE), simulated annealing (SA), gravitational search algorithm (GSA), black hole (BH), particle swarm optimization (PSO), Harris hawk optimization (HHO), artificial bee colony (ABC), and non-metaheuristic pattern search (PS). Thus, the best rotor geometry can be obtained fast with minimum bearing forces and disk deflections within design limits. In the results, the efficiency of the CTMM for achieving optimized designs is demonstrated. The CTMM outperformed the FEM in both speed and applicability for complex rotordynamic problems. The CTMM was found to deliver results of comparable quality much faster than the FEM, especially with higher element quality. The use of the CTMM in the iterative optimization process is shown to be highly advantageous. Furthermore, it is noted that among the different optimization algorithms, ABC provided the best results for this multi-objective optimization problem.

Modeling and Solving the Knapsack Problem with a Multi-Objective Equilibrium Optimizer Algorithm Based on Weighted Congestion Distance

The knapsack problem is a typical bi-objective combinatorial optimization issue, wherein maximizing the value of the packed items is achieved concurrently with minimizing the weight of the load. Due to the conflicting objectives of the knapsack problem and the typical discrete property of the items involved, swarm intelligence algorithms are commonly employed. The diversity of optimal combinations in the knapsack problem has become a focal point, which involves finding multiple packing solutions at the same value and weight. For this purpose, this paper proposes a Multi-Objective Equilibrium Optimizer Algorithm based on Weighted Congestion Distance (MOEO_WCD). The algorithm employs a non-dominated sorting method to find a set of Pareto front solutions rather than a single optimal solution, offering multiple decision-making options based on the varying needs of the decision-makers. Additionally, MOEO_WCD improves the balance pool generation mechanism and incorporates a weighted congestion incentive, emphasizing the diversity of packing combination solutions under the objectives of value and weight to explore more Pareto front solutions. Considering the discrete characteristics of the knapsack combination optimization problem, our algorithm also incorporates appropriate discrete constraint handling. This paper designs multiple sets of multi-objective knapsack combinatorial optimization problems based on the number of knapsacks, the number of items, and the weights and values of the items. This article compares five algorithms suitable for solving multi-objective problems: MODE, MO-PSO-MM, MO-Ring-PSO-SCD, NSGA-II, and DN-NSGAII. In order to evaluate the performance of the algorithm, this paper proposes a new solution set coverage index for evaluation. We also used the hypervolume indicator to evaluate the diversity of algorithms. The results show that our MOEO-WCD algorithm achieves optimal coverage of the reference composite Pareto front in the decision space of four knapsack problems. The experimental results indicate that our MOEO_WCD algorithm achieves the optimal coverage of the reference composite Pareto front in the decision space for four sets of knapsack problems. Although our MOEO_WCD algorithm covers less of the composite front in the objective space compared with the MODE algorithm for knapsack problem 1, its coverage of the integrated reference solutions in the decision space is greater than that of the MODE algorithm. The experiments demonstrate the superior performance of the MOEO_WCD algorithm on bi-objective knapsack combinatorial optimization problem instances, which provides an important solution to the search for diversity in multi-objective combinatorial optimization solutions.

Wind Farm Layout Optimization/Expansion of Real Wind Turbines with a Parallel Collaborative Multi-Objective Optimization Algorithm

The objective of this paper is to study the Wind Farm Layout Optimization/expansion problem. This problem is formulated here as a Multi-Objective Optimization Problem considering the total power output and net efficiency of Wind Farms as objectives along with specific constraints. Once formulated, this problem needs to be solved efficiently. For that, a new approach based on a combination of five Multi-Objective Optimization algorithms, which is named the Parallel Collaborative Multi-Objective Optimization Algorithm, is developed and implemented. This technique is checked on seven test cases; for each case, the goal is to find a set of optimal solutions called the Pareto Front, which can be exploited later. The acquired solutions were compared with other approaches and the proposed approach was found to be the better one. Finally, this work concludes that the proposed approach gives, in a single run, a set of optimal solutions from which a designer/planner can select the best layout of a designed Wind Farm using expertise and applying technical and economic constraints.

A Review of Algorithms and Platforms for Offloading Decisions in Mobile Cloud Computing

With the substantial growth of mobile applications and the emergence of cloud computing concepts, therefore mobile Cloud Computing (MCC) has been introduced as a potential mobile service technology. Mobile has limited resources, battery life, network bandwidth, storage, and processor, avoid mobile limitations by sending heavy computation to the cloud to get better performance in a short time, the operation of sending data, and get the result of computation call offloading. In this paper, a survey about offloading types is discussed that takes care of many issues such as offloading algorithms, platforms, metrics (that are used with this algorithm and its equations), mobile cloud architecture, and the advantages of using the mobile cloud. The trade-off between local execution of tasks on end-devices and remote execution on the cloud server for minimizing delay time and energy saving. In the form of a multi-objective optimization problem with a focus on reducing overall system power consumption and task execution latency, meta-heuristic algorithms are required to solve this problem which is considered as NP-hardness when the number of tasks is high. To get minimum cost (time and energy) apply partial offloading on specific jobs containing a number of tasks represented in sequences of zeros and ones for example (100111010), when each bit represents a task. The zeros mean the task will be executed in the cloud and the ones mean the task will be executed locally. The decision of processing tasks locally or remotely is important to balance resource utilization. The calculation of task completion time and energy consumption for each task determines which task from the whole job will be executed remotely (been offloaded) and which task will be executed locally. Calculate the total cost (time and energy) for the whole job and determine the minimum total cost. An optimization method based on metaheuristic methods is required to find the best solution. The genetic algorithm is suggested as a metaheuristic Algorithm for future work.

Evolutionary Optimization with a Simplified Helper Task for High-Dimensional Expensive Multiobjective Problems

In recent years, surrogate-assisted evolutionary algorithms (SAEAs) have been sufficiently studied for tackling computationally expensive multiobjective optimization problems (EMOPs), as they can quickly estimate the qualities of solutions by using surrogate models to substitute for expensive evaluations. However, most existing SAEAs only show promising performance for solving EMOPs with no more than 10 dimensions, and become less efficient for tackling EMOPs with higher dimensionality. Thus, this article proposes a new SAEA with a simplified helper task for tackling high-dimensional EMOPs. In each generation, one simplified task will be generated artificially by using random dimension reduction on the target task (i.e., the target EMOPs). Then, two surrogate models are trained for the helper task and the target task, respectively. Based on the trained surrogate models, evolutionary multitasking optimization is run to solve these two tasks so that the experiences of solving the helper task can be transferred to speed up the convergence of tackling the target task. Moreover, an effective model management strategy is designed to select new promising samples for training the surrogate models. When compared to five competitive SAEAs on four well-known benchmark suites, the experiments validate the advantages of the proposed algorithm on most test cases.

Dynamic multi-objective optimization based on classification response of decision variables

In recent years, many dynamic multi-objective optimization algorithms (DMOAs) have been proposed to address dynamic multi-objective optimization problems (DMOPs). Most existing DMOAs treat all decision variables uniformly and respond to them in an identical manner. This paper proposes a dynamic multi-objective optimization algorithm based on the classification response of decision variables (CRDV-DMO). Firstly, CRDV-DMO categorizes the decision variables into convergence variables and diversity variables. Different decision variables adopt distinct response strategies. The response strategy of diversity variable (RSDV) uses Latin hypercube sampling to generate the diversity variables of the new environment. For each dimensional convergence variable, the response strategy of convergence variable (RSCV) first evaluates whether the basic center prediction strategy (CPS) yields positive feedback or negative feedback, further determining the predictability of that dimensional convergence variable. RSCV then decides to either use the basic CPS to generate the convergence variable for that dimension or to retain that dimensional convergence variable from the current environment, based on the predictability of that dimensional convergence variable. The proposed algorithm is extensively studied through comparison with several advanced DMOAs, demonstrating its effectiveness in dealing with the benchmark DMOPs and the parameter-tuning problem of the PID controller on a dynamic system.

Optimized design of energy absorption of aluminum foam filled CFRP thin-walled square tube based on agent model

PurposeAluminum foam-filled thin-walled unit structures have received much attention for their excellent energy absorption properties. To improve the energy absorption effect of car energy absorption box under axial compression, this paper optimizes the fiber lay-up sequence, fiber angle and aluminum foam density of aluminum foam filled carbon fiber reinforced plastic (CFRP) thin-walled square tubes.Design/methodology/approachDesign of sample points required to construct the proxy model using design of experiments (DOE) method, and the data sample points of different models are obtained through Abaqus simulation and test. A double high-precision proxy model with the maximum specific energy absorption (SEA) and the minimum initial peak crash force (PCF) as the evaluation index is constructed based on the response surface function method. The NSGA-II multi-objective genetic algorithm was used to optimize the design parameters and obtain the optimal solution for the Pareto front, and the results were verified by using the multi-objective optimization toolbox in design-expert.FindingsThe results show that the optimal solution to the multi-objective optimization problem with the inclusion of the lay-up sequence is ρ = 0.5g/cm3 for a fiber lay-up angle varying in the range ±15–90° and an aluminum foam density varying in the range 0.2g/cm3-0.5g/cm3, with a lay-up method of [±87°/±16°/±15°/±89°]. The two optimization methods correspond to SEA and PCF errors of 2.109% and 4.1828%, respectively. The optimized SEA value is 18.2 J/g and the PCF value is 18,230 N. The optimized design reduces the peak impact force and increases the specific energy absorption, which improves the energy absorption effect of thin-walled energy-absorbing boxes for automobiles.Originality/valueIn this paper, the impact resistance of CFRP thin-walled square tubes filled with aluminum foam is optimized. Based on numerical simulations and experiments to obtain the sample point data for constructing the dual-agent model, we investigate the effect of filling with different densities of aluminum foam under the simultaneous change of fiber lay-up angle and order on its mechanical properties in this process, and carry out the multi-objective optimization design with NSGA-II algorithm.

A Multimodal Multi-Objective Coati Optimization Algorithm Based on Spectral Clustering

Multimodal multi-objective problems refer to situations where more than one Pareto set in the decision space corresponds to the same Pareto front in the objective space. In this paper, we propose a multimodal multi-objective coati optimization algorithm based on spectral clustering (MMOCOA-SC) for use in multimodal multi-objective problems. The algorithm starts by creating stable subpopulations via a spectral clustering method, grouping similar individuals within each subpopulation. Then, an improved coati optimization algorithm is proposed in order to increase the diversity of the population and continuously search for near-Pareto optimal solutions. Finally, we use an improved crowding distance method combined with a non-dominated sorting method to maintain and retain multiple near-Pareto optimal solutions. The MMOCOA-SC is evaluated alongside five state-of-the-art algorithms using the 2020 CEC test suite, IDMP test problems, and twelve classic engineering application problems. In comparison to the other five state-of-the-art algorithms, the experimental results show that MMOCOA-SC exhibits a superior performance when applied to the problems. This study explores multimodal multi-objective optimization algorithms with a focus on the concept of symmetry, which is crucial for multimodal multi-objective optimization problems in terms of achieving a balanced decision space and a diversity of solutions in the objective space.

Efficiently Constructing Convex Approximation Sets in Multiobjective Optimization Problems

Convex approximation sets for multiobjective optimization problems are a well-studied relaxation of the common notion of approximation sets. Instead of approximating each image of a feasible solution by the image of some solution in the approximation set up to a multiplicative factor in each component, a convex approximation set only requires this multiplicative approximation to be achieved by some convex combination of finitely many images of solutions in the set. This makes convex approximation sets efficiently computable for a wide range of multiobjective problems: even for many problems for which (classic) approximations sets are hard to compute. In this article, we propose a polynomial-time algorithm to compute convex approximation sets that builds on an exact or approximate algorithm for the weighted sum scalarization and is therefore applicable to a large variety of multiobjective optimization problems. The provided convex approximation quality is arbitrarily close to the approximation quality of the underlying algorithm for the weighted sum scalarization. In essence, our algorithm can be interpreted as an approximate version of the dual variant of Benson’s outer approximation algorithm. Thus, in contrast to existing convex approximation algorithms from the literature, information on solutions obtained during the approximation process is utilized to significantly reduce both the practical running time and the cardinality of the returned solution sets while still guaranteeing the same worst-case approximation quality. We underpin these advantages by the first comparison of all existing convex approximation algorithms on several instances of the triobjective knapsack problem and the triobjective symmetric metric traveling salesman problem. History: Accepted by Andrea Lodi, Area Editor for Design & Analysis of Algorithms–Discrete. Funding: This research was supported by the German Research Foundation [Project 398572517]. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information ( https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2023.0220 ) as well as from the IJOC GitHub software repository ( https://github.com/INFORMSJoC/2023.0220 ). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/ .

Multi-objective optimization and multi-attribute decision-making support for optimal operation of multi stakeholder integrated energy systems

To efficiently tackle the optimal operation problem of multi-stakeholder integrated energy systems (IESs), this paper develops a multi-objective optimization and multi-attribute decision-making support method. Mathematically, The optimal operation of IESs interconnected with distributed district heating and cooling units (DHCs) via the power grid and gas network, can be formulated as a multi-objective optimization problem considering both economic, reliability and environment-friendly objectives with numerous constraints of each energy stakeholder. Firstly, a multi-objective group search optimizer with probabilistic operator and chaotic local search (MPGSO) is proposed to balance global and local optimality during the random search iteration. The MPGSO utilizes a crowding probabilistic operator to select producers to explore areas with higher potential but less crowding and reduce the number of fitness function calculations. Moreover, a new parameter selection strategy based on chaotic sequences with limited computational complexity is adopted to escape the local optimal solutions. Consequently, a set of superior Pareto-optimal fronts could be obtained by the MPGSO. Subsequently, a multi-attribute decision-making support method based on the interval evidential reasoning (IER) approach is used to determine a final optimal solution from the Pareto-optimal solutions, taking multiple attributes of each stakeholder into consideration. To verify the effectiveness of the MPGSO, the DTLZ suite of benchmark problems are tested compared with the original GSOMP, NSGA-II and SPEA2. Additionally, simulation studies are conducted on a modified IEEE 30-bus system connected with distributed DHCs and a 15-node gas network to verify the proposed approch. The quality of the obtained Pareto-optimal solutions is assessed using a set of criteria, including hypervolume (HV), generational distance (GD), and Spacing index, among others. Simulation results show that the number of Pareto-optimal solutions (NPS) of MPGSO are higher by about 32.6 %-62.1%, computation time (CT) are lower by about 2.94 %-46.1 % compared with other algorithms. Besides, to further evaluate the performance of the proposed approach in addressing larger-scale issues, the study employs the modified IEEE 118-bus system of greater magnitude. The proposed MPGSO algorithm effectively handles multi-objective and non-convex optimization problems with Pareto sets in terms of better convergence and distributivity.

The principle of compromise-in-competition: understanding mesoscale complexity of different levels

This perspective is not meant to be a complete summary of the full series of our studies over decades, rather it aims to look back across the entire process to outline: What inspired this work at its beginning? How did the mindset gradually evolve from a solely engineering study to the new concept of Mesoscience? And where is the research currently being focused and to be extended? This approach elucidates the central importance of correlating precise engineering problems to be resolved with associated missing links in the underlying, fundamental science while exploring a notable commonality, namely, the universality of Mesoscience. Inspired by the physical phenomenon of the coexistence and interaction between a gas-rich dilute phase and a solid-rich dense phase with different physical mechanisms dominating the behaviour for each phase in gas–solid fluidization, it was recognized that an underlying compromise-in-competition (CIC) exists between these two physically dominant mechanisms. This, then, is the CIC principle. We believe that this is the origin of inherent structural complexity in these and other systems. We have shown that this CIC principle can be formulated as a multi-objective optimization problem through the so-called energy-minimization multi-scale model, leading to a massive improvement in both the accuracy and scalability of computation and its wide application in both academia and industries. Furthermore, this approach was extended to formulate and understand other complex systems in many apparently disparate fields, indicating the wide applicability of the CIC principle and then resulting in the proposition and advancement of the concept of Mesoscience. Furthermore, within the main body of this perspective article, future directions for identifying, developing and applying the concept of Mesoscience will be prospected. This includes extending its possible generality and applications in many different disciplines and fields, even to analysing global challenging issues and promoting CIC-informed AI. In this way, many challenging problems in engineering—identified through their underlying mesoscale complexity—will be closely correlated with the development of future fundamental science. Through this approach, we hope to illustrate that fundamental research can now tackle the intrinsic complexity existing in a multitude of engineering problems. Through the concept of Mesoscience, we aim to explore the possible commonality from complexity. The deduction of commonality from diversity is possible in resolving global challenges, shifting paradigms in science and filling in the existing gaps at the mesoscales of different levels of our knowledge, though there are difficulties and uncertainty coming from diversity.

A hierarchical clustering algorithm for addressing multi-modal multi-objective optimization problems

Many evolutionary multi-modal multi-objective algorithms (MMEAs) have been proposed to solve multi-modal multi-objective optimization problems (MMOPs). Unfortunately, the environmental selection process causes many algorithms to place too much emphasis on solution variety in the decision space, which leads to solutions with low convergence quality. As a result, not only are all local Pareto fronts reversed, but objective values are also far lower than the global Pareto Fronts. To tackle these tasks, this paper proposes a hierarchical clustering-based MMOEA_DC_HR model that uses decision space clustering methods to group neighborhood solutions into several local clusters, preserving local Pareto Sets. And secondary clustering is performed in the objective space to select temporary populations from these local clusters to maintain the diversity of the objective space. Additionally, a hierarchical ranking method is introduced to update the convergence archive aiding in maintaining the convergence of the algorithm and controlling the quality of the Pareto Front. The test results show that this novel algorithm exhibits competitive performance in solving selected benchmark problems when compared to other cutting-edge MMEAs.

Dynamic Multiobjective Optimization Based on Multi-Environment Knowledge Selection and Transfer

Background: Dynamic multiobjective optimization problems (DMOPs) involve multiple conflicting and time-varying objectives, and dynamic multiobjective algorithms (DMOAs) aim to find Pareto optima that are closer to the real one in the new environment as soon as possible. In particular, the introduction of transfer learning in DMOAs has led to good results in solving DMOPs. However, the selection of valuable historical knowledge and the mitigation of negative transfer remain important problems in existing transfer learning-based DMOAs. Method: A DMOA based on multi-environment knowledge selection and transfer (MST-DMOA) is proposed in this article. First, by clustering historical Pareto optima, some representative solutions that can reflect the main evolutionary information are selected as knowledge of the environment. Second, the similarity between the historical and current environments is evaluated, and then the knowledge of multiple similar environments is selected as valuable historical knowledge to construct the source domain. Third, solutions with high quality in the new environment are obtained to form the target domain, which can better help historical knowledge to adapt to the current environment, thus effectively alleviating negative transfer. Conclusions: We compare the proposed MST-DMOA with five state-of-the-art DMOAs on fourteen benchmark test problems, and the experimental results verify the excellent performance of MST-DMOA in solving DMOPs.

Reliability-based multi-objective optimization design of composite patch repair structure using artificial neural networks

Due to the parameter differences and the existence of random factors, the performance of composite repair structure shows a large dispersion. In order to obtain stronger, lighter and more reliable repair structure, multi-objective optimization design of carbon fiber reinforced polymers (CFRP) laminate repair structure is investigated by combining the reliability theory, artificial neural networks and the genetic algorithm. First, a 3D simulation model of the composite laminate patch repair structures is established using the 3D Hashin criterion and the cohesive region model. Then, the Latin Hypercube sampling (LHS) method is used to realize the random sampling, and the strength proxy model of the repair structure is established by using Back-propagation artificial neural network, further a multi-objective optimization model with tensile strength, reliability and weight as objective functions is built considering the design parameters and the random parameters. Finally, NSGAⅡalgorithm is used to solve the multi-objective optimization problem, and a set of solutions on the Pareto front surface are obtained, also the optimal design parameters of the composite repair structure meets the requirements is obtained.

Multi-objective cooperation search algorithm based on decomposition for complex engineering optimization problems

This study introduces a novel multi-objective cooperation search algorithm based on decomposition (MOCSA/D) to address multi-objective competitive challenges in engineering problem. Inspired by the optimization strategy of single-objective Cooperation Search Algorithm (CSA) and the decomposition framework of MOEA/D, MOCSA/D algorithm randomly generates initial solutions in the optimization space, and then repeatedly executes four search strategies until the end of iteration: Cooperative updating strategy gathers high-quality information to update solutions with balanced distribution. Reflective adjustment strategy expands the exploration range of the population, enabling the acquisition of solutions with strong optimization capabilities. Internal competition strategy selects superior individuals with better performance for subsequent optimization. Density updating strategy improves the competitiveness of optimized individuals within the population, fostering a more diverse solution set. Three numerical experiments (including DTLZ, WFG unconstrained test problems, ZXH_CF constrained test problems and RWMOP real-world multi-objective optimization problems) are tested to further comprehensively evaluate the dominant performance of MOCSA/D. The test results in different problem scenarios show that compared with the existing excellent evolutionary algorithms, MOCSA/D can always obtain a better, stable and uniform distribution of non-dominated solutions, and has higher solving efficiency and optimization quality under different performance evaluation metrics with the increasing difficulty of solving problems. Finally, the proposed algorithm is applied to the multi-objective reservoir engineering optimization problem to verify the feasibility of the decision scheme and the comprehensive benefit optimization of MOCSA/D. Overall, MOCSA/D can simplify the problem optimization difficulty based on decomposition mechanism, and improve the global optimization of population, path diversity and individual competition through different search strategies, which provides an advantageous tool for addressing multi-objective competitive challenges.