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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, CO 2 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.

In this study, efficient global optimization (EGO) with a multi-fidelity hybrid surrogate model for multi-objective optimization is proposed to solve multi-objective real-world design problems. In the proposed approach, a design exploration is carried out assisted by surrogate models, which are constructed by adding a local deviation estimated by the kriging method and a global model approximated by a radial basis function. An expected hypervolume improvement is then computed on the basis of the model uncertainty to determine additional samples that could improve the model accuracy. In the investigation, the proposed approach is applied to two-objective and three-objective optimization test functions. Then, it is applied to aerodynamic airfoil design optimization with two objective functions, namely minimization of aerodynamic drag and maximization of airfoil thickness at the trailing edge. Finally, the proposed method is applied to aerodynamic airfoil design optimization with three objective functions, namely minimization of aerodynamic drag at cruising speed, maximization of airfoil thickness at the trialing edge and maximization of lift at low speed assuming a landing attitude. XFOILis used to investigate the low-fidelity aerodynamic force, and a Reynolds-averaged Navier–Stokes simulation is applied for high-fidelity aerodynamics in conjunction with a high-cost approach. For comparison, multi-objective optimization is carried out using a kriging model only with a high-fidelity solver (single fidelity). The design results indicate that the non-dominated solutions of the proposed method achieve greater data diversity than the optimal solutions of the kriging method. Moreover, the proposed method gives a smaller error than the kriging method.

In recent years, when solving MOPs, especially discrete path optimization problems, MOACOs concerning other meta-heuristic algorithms have been used and improved often, and they have become a hot research topic. This article will start from the basic process of ant colony algorithms for solving MOPs to illustrate the differences between each step. Secondly, we provide a relatively complete classification of algorithms from different aspects, in order to more clearly reflect the characteristics of different algorithms. After that, considering the classification result, we have carried out a comparison of some typical algorithms which are from different categories on different sizes TSP (traveling salesman problem) instances and analyzed the results from the perspective of solution quality and convergence rate. Finally, we give some guidance about the selection of these MOACOs to solve problem and some research works for the future.

In the multi-objective optimization design of automotive seats based on Approximation-Based Design Optimization, a single approximation model may not adequately address the requirement of accurately fitting highly nonlinear feature data. For this reason, the Hybrid Approximation Models based on the Multi-Species Approximation Model (HAM-MSAM) is proposed to meet the requirement for high fitting accuracy. Subsequently, this study introduces a HAM-MSAM-based Approximation-Based Global Multi-Objective Optimization Design (ABGMOOD) strategy. This strategy is employed in the multi-objective optimization of the rear seat of a passenger car. HAM-MSAM was constructed from an experimentally validated finite element model and a training set generated through experimental design. The advantages of HAM-MSAM in capturing the highly nonlinear response under seat crash conditions were validated through comparison with hybrid model construction methods reported in existing literature. Finally, the optimization results obtained by the ABGMOOD strategy were compared to those of the classical local multi-objective optimization strategy, demonstrating the substantial advantages of the ABGMOOD optimization scheme in economy and weight reduction. In addition, the safety of the rear seats is slightly lower than that of the local optimization scheme but remains in compliance with regulatory requirements. The final optimized rear seat demonstrates notable improvements in safety, economy, and weight reduction, validating the feasibility of the ABGMOOD strategy and providing valuable insights for similar engineering optimization challenges.

Over the past years, wind energy has been considered as a promising solution for clean and sustainable energy development, but wind curtailment remains a challenge to wind power development. On this basis, utilization of non‐grid‐connected wind power becomes crucial and necessary as it can mitigate wind curtailment and improve energy efficiency. This paper proposes the collaboration strategy and optimization model of wind farm‐hybrid energy storage system (WF‐HESS) for non‐grid‐connected wind power based on battery and superconducting magnetic energy storage (SMES) whose combination can effectively cope with fluctuation and intermittence of wind input. The optimization problem is simultaneously investigated by the minimization of total cost, wind curtailment magnitude, and loss of power supply probability (LPSP). The multi‐objective particle swarm optimization (MOPSO) is introduced to find available solutions, and Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) is applied to determine the optimal one. Results are obtained for a case study, and the effectiveness and the feasibility of proposed model are verified by a comparative analysis and a sensitivity analysis. Results analysis and discussion show that the WF‐HESS model and the application of HESS have important influence on promoting utilization of non‐grid‐connected wind power and mitigating wind curtailment. This paper proposes a collaboration strategy and optimization model of wind farm‐hybrid energy storage system (WF‐HESS) for non‐grid‐connected wind power based on battery and superconducting magnetic energy storage (SMES). The optimization problem is investigated by minimization of total cost, wind curtailment magnitude, and loss of power supply probability (LPSP) simultaneously. The multi‐objective particle swarm optimization (MOPSO) is introduced to find available solutions, and Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) is applied to determine the optimal one.

This work considers the design‐for‐control of water distribution networks (WDN) for the joint optimization of performance and cost‐related objectives. In particular, we focus on the problem of optimizing the placement (design) and settings (control) of pressure reducing valves to minimize leakage at minimum cost. We present an integrative hybrid method combining the complementary advantages of deterministic and evolutionary algorithms (EA) to efficiently approximate the Pareto front of the resulting non‐convex bi‐objective mixed‐integer non‐linear program. Design decisions are fixed by an outer multi‐objective EA, while a non‐linear programming solver is called during the fitness evaluation stage to compute continuous control settings. The algorithm is applied to case study and operational networks and evaluated against alternative heuristic methods based on computational performance and quality of the solutions returned. Our results show that the proposed method converges faster and more consistently than existing approaches, producing better trade‐offs between cost and leakage reduction. In particular, the Pareto front approximations computed using the proposed integrative hybrid method are characterized by a more marked knee (i.e., more efficient trade‐offs), while the achieved computational improvements facilitate the integration of expert feedback into the design‐for‐control of WDNs during offline planning.

Water distribution systems (WDSs) are increasingly required to respond to dynamic financial and regulatory signals. This study presents a computationally tractable multi‐objective optimization framework for minimizing time‐variant electricity costs, carbon intensity, and water age. We apply this framework in a large, complex WDS over monthly time periods to demonstrate computational tractability and describe tradeoffs in energy costs, carbon emissions, and water quality under realistic operating and billing conditions. We achieve computational tractability by combining a novel model reduction approach with search space reduction (domain targeting) and algorithmic efficiency tools (search‐integrated feasibility prescreening). The result was a 43% reduction in hydraulic simulation time and a 20% reduction in water quality simulation time for our case study system. By modifying a combination of tank level and time control set points in our case study, we identify opportunities for reducing energy costs by up to 5% without compromising GHG emissions and water age and up to 8% with increases in water age. This work underscores the importance of multi‐objective formulations for dynamic WDS optimization and the imperative of computationally efficient optimization workflows for practical application in large systems with monthly billing cycles.

Hydrological forecasts have significantly improved in skill over recent years, encouraging their systematic exploitation in multipurpose reservoir operations to improve reliability and resilience to extreme events. Despite the growing availability of multi‐timescale forecasts, there is still a lack of transparent and integrated methods for selecting the most suitable forecast products, variables, and lead times for specific operational challenges. In this work, we propose a holistic approach based on Reinforcement Learning (RL) to design multipurpose dam operating policies informed by available multi‐timescale forecast products. Our approach extends the traditional Evolutionary Multi‐Objective Direct Policy Search method by parametrizing both the operating policy and the forecast information extraction process. We compare our RL approach with a state‐of‐the‐art two‐step procedure in which the forecast selection and processing are performed before the policy optimization. We demonstrate the value of the method for the multipurpose operation of Lake Como (Italy) by considering multi‐timescale forecasts from short to seasonal lead times to manage flood‐ and drought‐related operational objectives. Our approach identifies solutions achieving an 18% improvement in hypervolume indicator compared to policies not informed by forecasts and a 6% improvement over those designed using the two‐step reference methodology. These improvements are accompanied by increased flexibility in policy design and trade‐off analysis by directly extracting forecast information within the multi‐objective optimization. This study demonstrates the feasibility and benefits of integrating policy design with forecast information extraction, particularly when multiple operational forecasts are available. Key Points Multi‐timescale hydro‐meteorological forecast information helps in multi‐purpose reservoir operations A new methodology is proposed to learn the most valuable information from multiple forecasts and jointly design operating policies With the available operational products, more skillful short‐range lead times are preferred to ideally more informative extended‐range ones

This work proposes multi-objective Rao algorithms. The basic Rao algorithms are modified for solving multi-objective optimization problems. The proposed algorithms have no algorithm-specific parameters and no metaphorical meaning. Based on the interaction of the population with best, worst, and randomly selected solutions, the proposed algorithms explore the search space. The proposed algorithms handle multiple objectives simultaneously based on dominance principles and crowding distance evaluation. In addition, multi-attribute decision-making method-based selection scheme for identifying the best solutions from the Pareto fronts is included. The proposed algorithm performances are investigated on a case study of solar-assisted Brayton heat engine system and a case study of Stirling heat engine system to see whether there can be any improvement in the performances of the considered systems. Furthermore, the efficiencies of the Rao algorithms are evaluated in terms of spacing, hypervolume, and coverage metrics. The results obtained by the proposed algorithms are compared with those obtained by the latest advanced optimization algorithms. It is observed that the results obtained by the proposed algorithms are superior. The performances of the considered case studies are improved by the application of the proposed optimization algorithms. The proposed optimization algorithms are simple, robust, and can be easily implemented to solve different engineering optimization problems.