A multiobjective beam angle optimization framework for intensity-modulated radiation therapy

The intensity-modulated radiation therapy (IMRT) treatment planning is usually a sequential process where initially a given number of beam directions are selected followed by the fluence map optimization (FMO) considering those beam directions. The beam angle optimization (BAO) problem consists on the selection of appropriate radiation incidence directions in radiation therapy treatment planning and may be decisive for the quality of the treatment plan, both for appropriate tumor coverage and for enhancement of better organs sparing. This selection must be based on the optimal value of the FMO problem otherwise the resulting beam angle set has no guarantee of optimality and has questionable reliability. Pattern search methods (PSM) have been used successfully to address the BAO problem driven by the optimal fluence value of the FMO problem. PSM are iterative methods generating a sequence of non-increasing iterates such that iterate progression is solely based on a finite number of function evaluations in each iteration, without explicit or implicit use of derivatives. Typically, in IMRT optimization, the quality of the solutions obtained is not simply related to the final value of an objective function but rather judged by dose-volume histograms or considering a set of physical dose metrics. These dose metrics can be simply described as obtaining a minimum prescribed dose for the target volumes (the regions that have to be irradiated) and a maximum or mean tolerance dose values for the remaining surrounding structures (the regions that should be spared). The goal of this paper is to present a non-descent PSM that can be guided both by an objective function formulation of the FMO problem and by physical dose metrics. Four retrospective treated cases of head-and-neck tumors at the Portuguese Institute of Oncology of Coimbra are used to discuss the benefits of non-descent PSM for the optimization of the BAO problem.

A Tchebycheff-based multi-objective combined with a PSO–SQP dynamic real-time optimization framework for cycling energy systems

The transition from fossil fuels to renewable energy demands energy systems that are not only technically and economically sound but also environmentally and socially sustainable. This study proposed a novel multi-objective optimisation (MOO) framework for the design of a grid-connected hybrid renewable energy system (GC-HRES) that explicitly integrated Job Creation (JC) as a fourth objective along with traditional technical, economic, and environmental objectives, such as Loss of Power Supply Probability (LPSP), Cost of Energy (COE), and Renewable Energy Fraction (REF). Prior studies often treated JC as a post-optimisation metric, while this study incorporated JC into the MOO using employment technology-specific factors. Metaheuristic algorithms, Multi-Objective Particle Swarm Optimisation (MOPSO) and Non-Dominated Sorting Genetic Algorithm II (NSGA-II), were applied to find the optimal number of solar panels, wind turbines, and battery banks under scenarios which excluded and included JC. The results demonstrated that including JC reshaped the Pareto front, revealed new objective compromises and led to diverse configurations. MOPSO favoured solutions with higher JC and REF at the expense of cost and reliability, while NSGA-II achieved more balanced, cost-effective and reliable solutions with competitive JC values. Additional constraint sensitivity analysis further demonstrated the influence of battery bank constraints on solution feasibility. The results highlighted that integrating JC into the optimisation framework enriched design possibilities and fostered a more inclusive transition to renewable energy with a focus on GC-HRESs. This paper provided a flexible and replicable MOO framework that sets the foundation for socially attuned GC-HRES designs that align with broader sustainability goals.

Floating offshore wind energy will play a key role in the clean energy transition scenario. The number of projects deploying large-scale wind farms is growing in multiple regions, from Northern Europe to the East Coast of the United States, and extending to the Mediterranean Sea. Offshore wind farms face fewer constraints in layout design, as they do not need to consider orography and can generally be situated in vast, open sea areas. Consequently, offshore wind turbines could be arranged in simple layouts, such as grid patterns or staggered rows, spaced uniformly. However, this regular turbine arrangement would result in significant annual energy production (AEP) losses due to wake-rotor interaction. Although increasing spacing between turbines can mitigate this issue, it is not always feasible due to marine space availability. Moreover, when feasible, it can lead to higher costs for additional cabling and maintenance. This paper aims to introduce a multi-objective wind farm optimization framework that employs a genetic algorithm (NSGA II). This framework seeks to maximize the energy production while minimizing OPEX and CAPEX costs, taking into account the wind resource and bathymetry of a specific region. In the paper, two case studies are presented for the optimization of wind farms in the Mediterranean Sea assuming 15MW wind turbines. AEP evaluation of each individual wind farm is obtained with the open-source library FLORIS, while the optimization algorithm relies on the library PyMoo for multi-objective optimization.

Pressure swing adsorption (PSA) is an energy-efficient technology for gas separation, while the multi-objective optimization of PSA is a challenging task. To tackle this, we propose a hybrid optimization framework, which integrates three steps. In the first step, we establish surrogate models for the constraints using Gaussian processes (GPs) and employ multi-objective Bayesian optimization to search for feasible points that satisfy the constraints. In the second step, we establish surrogate models for the objective function and constraints using GPs and utilize constrained multi-objective Bayesian optimization to search for an approximate Pareto front. In the third step, we perform a local search based on the approximate Pareto front. By employing the trust region filter method, we construct quadratic models for each constraint and objective function and refine the Pareto front to achieve local optimality. This framework demonstrates the efficiency of Bayesian optimization and the local optimality of the trust region method. A comparison with the popular evolutionary algorithm, Nondominated Sorting Genetic Algorithm II (NSGA-II), showed that this framework had a higher hypervolume of the Pareto front while halving the runtime and reducing the number of simulations by a factor of 20.

A novel multiobjective adaptive surrogate modeling-based optimization (MO-ASMO) framework is proposed to utilize a minimal number of training samples efficiently for sequential model updates. All the sample points are enforced to be feasible, and to provide coverage of sparsely explored sparse design regions using a new optimization subproblem. The MO-ASMO method only evaluates high-fidelity functions at feasible sample points. During an exploitation sample phase, samples are selected to enhance solution accuracy rather than the global exploration. Sampling tasks are especially challenging for multiobjective optimization; for an n-dimensional design space, a strategy is required for generating model update sample points near an (n − 1)-dimensional hypersurface corresponding to the Pareto set in the design space. This is addressed here using a force-directed layout algorithm, adapted from graph visualization strategies, to distribute feasible sample points evenly near the estimated Pareto set. Model validation samples are chosen uniformly on the Pareto set hypersurface, and surrogate model estimates at these points are compared to high-fidelity model responses. All high-fidelity model evaluations are stored for later use to train an updated surrogate model. The MO-ASMO algorithm, along with the set of new sampling strategies, are tested using two mathematical and one realistic engineering problems. The second mathematical test problems is specifically designed to test the limits of this algorithm to cope with very narrow, non-convex feasible domains. It involves oscillatory objective functions, giving rise to a discontinuous set of Pareto-optimal solutions. Also, the third test problem demonstrates that the MO-ASMO algorithm can handle a practical engineering problem with more than 10 design variables and black-box simulations. The efficiency of the MO-ASMO algorithm is demonstrated by comparing the result of two mathematical problems to the results of the NSGA-II algorithm in terms of the number of high fidelity function evaluations, and is shown to reduce total function evaluations by several orders of magnitude when converging to the same Pareto sets.

A novel multi-objective optimization based multi-agent deep reinforcement learning approach for microgrid resources planning

With the increasing amount of distributed generation (DG) integrated into electrical distribution networks, various operational problems, such as excessive power losses, over-voltage and thermal overloading issues become gradually remarkable. Innovative approaches for power flow and voltage controls are required to ensure the power quality, as well as to accommodate large DG penetrations. Using power electronic devices is one of the approaches. In this paper, a multi-objective optimization framework was proposed to improve the operation of a distribution network with distributed generation and a soft open point (SOP). An SOP is a distribution-level power electronic device with the capability of real-time and accurate active and reactive power flow control. A novel optimization method that integrates a Multi-Objective Particle Swarm Optimization (MOPSO) algorithm and a local search technique – the Taxi-cab method, was proposed to determine the optimal set-points of the SOP, where power loss reduction, feeder load balancing and voltage profile improvement were taken as objectives. The local search technique is integrated to fine tune the non-dominated solutions obtained by the global search technique, overcoming the drawback of MOPSO in local optima trapping. Therefore, the search capability of the integrated method is enhanced compared to the conventional MOPSO algorithm. The proposed methodology was applied to a 69-bus distribution network. Results demonstrated that the integrated method effectively solves the multi-objective optimization problem, and obtains better and more diverse solutions than the conventional MOPSO method. With the DG penetration increasing from 0 to 200%, on average, an SOP reduces power losses by 58.4%, reduces the load balance index by 68.3% and reduces the voltage profile index by 62.1%, all compared to the case without an SOP. Comparisons between SOP and network reconfiguration showed the outperformance of SOP in operation optimization.

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.

Multi-objective optimization strategy for industrial catalytic cracking units: Kinetic model and enhanced SPEA-2 algorithm with economic, CO2, and SO2 emission considerations

The present paper investigates the trade‐offs between the energy efficiency (EE) and spectral efficiency (SE) in the full‐duplex (FD) multiuser multi‐input multioutput (MU‐MIMO) cloud radio access networks (CRANs) with simultaneous wireless information and power transfer (SWIPT). In the considered network, the central unit (CU) intends to concurrently not only transfer both energy and information toward downlink (DL) users using power splitting structures but also receive signals from uplink (UL) users. This communication is executed via FD radio units (RUs) which are distributed nearby users and connected to the CU through limited capacity fronthaul (FH) links. In order to unveil interesting trade‐offs between the EE and SE metrics, we first introduce three conventional single‐objective optimization problems (SOOPs) including (i) system sum rate maximization, (ii) total power minimization, and (iii) fractional energy efficiency maximization. Then, by making use of the multiobjective optimization (MOO) framework, the MOO problem (MOOP) with the objective vector of the achievable rate and power consumption is addressed. All considered problems are nonconvex with respect to designing variables comprising precoding matrices, compression matrices, and DL power splitting factors; thus, it is extremely intractable to solve these problems directly. To overcome these issues, we develop iterative algorithms by utilizing the sequential convex approximation (SCA) approach for the first two SOO problems and the SCA‐based Dinkelbach method for the fractional EE problem. Regarding the MOOP, we first rewrite it as an SOOP by applying the modified weighted Tchebycheff method and, then, propose the iterative algorithm‐based SCA to find its optimal Pareto set. Various numerical simulations are conducted to study the system performance and appealing EE‐SE trade‐offs in the considered system.

An improved multi-objective optimization approach for performance-based design of structures using nonlinear time-history analyses

Optimizing urban spatial form has become an important research topic for promoting urban sustainable development and improving energy efficiency. This study selects 164 high-rise residential blocks in the Changsha area as the research object and constructs three multi-objective optimization frameworks and mathematical models for the spatial form of high-rise residential blocks based on the Rhino and Grasshopper parametric platform. The TOPSIS comprehensive evaluation method is combined to further screen the Pareto front solutions, and global sensitivity analysis of spatial form parameters is conducted using Simlab to explore the multi-objective optimization strategies for the spatial form of high-rise residential blocks in the Changsha area, guided by energy performance. Practical cases are selected for verification. The results show that, (1) after multi-objective optimization, the optimal scheme for the determinant type reduces EUI by 7.22%, increases PVP by 28.84%, and reduces CGR by 2.21%. The optimal scheme for the point-cluster type reduces EUI by 3.80%, increases PVP by 7.34%, and reduces CGR by 2.30%. The optimal scheme for the staggered type reduces EUI by 6.66%, increases PVP by 17.65%, and reduces CGR by 2.26%. (2) The potential order of spatial form optimization for the three types of high-rise residential blocks in the Changsha area is determinant type > staggered type > point-cluster type. (3) The spatial form parameters most sensitive to the three architectural performance goals of EUI, PVP, and CGR are floor area ratio and average number of floors. The research results will provide quantifiable references for scientific decision-making in the design practice of high-rise residential blocks in the Changsha area and even in regions with hot summers and cold winters.

We propose a fairness-constrained curriculum adaptation framework for AI-enhanced education that integrates natural language processing (NLP) with multi-objective optimization to dynamically tailor learning materials while ensuring cultural responsiveness and ethical alignment. The proposed method employs a Transformer-based language model to analyze student-generated text, extracting latent cultural and demographic features, which are then clustered using a fairness-sensitive algorithm to mitigate biased representations. These features are combined with conventional performance metrics to formulate a multi-objective optimization problem that simultaneously maximizes pedagogical effectiveness and minimizes disparities across demographic groups. The optimization framework incorporates differentiable fairness constraints, such as equalized odds, to ensure equitable learning outcomes while adhering to institutional guidelines. Moreover, the system interfaces with existing educational platforms through input and output substitution mechanisms, enabling seamless integration with conventional modules. A key novelty lies in the coupling of NLP-driven cultural analysis with constrained optimization, which provides a transparent and auditable approach to curriculum adaptation. Furthermore, the framework includes a human-in-the-loop component, allowing educators to override recommendations and refine the system iteratively. Experimental validation demonstrates that the method achieves superior fairness-performance trade-offs compared to baseline approaches, offering a scalable solution for equitable education. The work contributes to the growing discourse on ethical AI in education by addressing both technical and societal challenges through a mathematically rigorous yet interpretable framework.

• Multi-objective optimization applied to achieve NZEB in Prague. • Integration of passive, active, and renewable strategies. • Energy savings drop from 70 % to 32 % under future climates. • Emphasis on adaptive, resilient building designs. • NZEB strategies need regular optimization for future climates. This study applies a Multi-Objective Optimization (MOO) framework to enhance the energy performance of a typical high-rise residential building in Prague and assess its resilience under future climate change scenarios. A total of 18 passive strategies—including external wall and roof insulation (0.08–0.20 m), optimized Window-to-Wall Ratios (10–90 % by orientation), triple low-E glazing, and dynamic shading overhangs—were evaluated alongside two active strategies (heating and cooling COP optimization) and three renewable strategies (roof-mounted photovoltaic (PV) panels with tilt, spacing, and orientation optimization). Results show that integrating these strategies can reduce annual energy demand by up to 68.7 % under current climate conditions and by 56 %, 42 %, and 32 % in the 2020s, 2050s, and 2080s, respectively. The optimized configuration maintained acceptable indoor comfort, with Predicted Percentage Dissatisfied (PPD) values reduced by up to 18 % compared to the baseline. PV panels generated 53,875 kWh annually under current conditions, covering 69 % of thermal and electrical demand, though coverage declined under future climate scenarios due to rising cooling loads. These findings demonstrate that a comprehensive integration of passive, active, and renewable strategies can significantly improve building performance and provide a resilient pathway toward Near-Zero Energy Buildings (NZEBs) under changing climatic conditions.