Multiple Optimization Problems Research Articles

Maximum load for medium voltage lines in N-1 conditions

This paper proposes a methodology able to assess the maximum value of the load that can be connected to a medium voltage (MV) feeder in addition to the existing one without impairing the N-1 security criterion. A simplified approach is pursued, the original problem is split into several separate subproblems, and the maximum additional load is calculated solving multiple optimization problems. The proposed method is simple and practically applicable by distribution system operators (DSOs) that, after a request by a customer to connect a load, must know if an MV feeder is fit to host the additional demand or if a new infrastructure is needed. The application of the methodology to the whole MV distribution grid of Rome, in Italy, is presented; execution times show that the DSO can apply the model daily, to follow the load growth day by day.

Parallel Beam Search Algorithms for Domain-Independent Dynamic Programming

Domain-independent dynamic programming (DIDP), a model-based paradigm based on dynamic programming, has shown promising performance on multiple combinatorial optimization problems compared with mixed integer programming (MIP) and constraint programming (CP). The current DIDP solvers are based on heuristic search, and the state-of-the-art solver, complete anytime beam search (CABS), uses beam search. However, the current DIDP solvers cannot utilize multiple threads, unlike state-of-the-art MIP and CP solvers. In this paper, we propose three parallel beam search algorithms and develop multi-thread implementations of CABS. With 32 threads, our multi-thread DIDP solvers achieve 9 to 39 times speedup on average and significant performance improvement over the sequential solver, finding the new best solutions for two instances of the traveling salesperson problem with time windows. In addition, our solvers outperform multi-thread MIP and CP solvers in four of the six combinatorial optimization problems evaluated.

Multi-Objective Operating Parameters Optimization for the Start Process of Proton Exchange Membrane Fuel Cell Stack with Non-Dominated Sorting Genetic Algorithm II

Proton exchange membrane fuel cell (PEMFC) is one of the most promising energy conversion devices in the world. Performance, durability, and cost are the key issues currently limiting its large-scale commercial application. This paper proposes a non-dominated sorting genetic algorithm II (NSGA-II) for optimizing operating parameters of the start process to improve the output performance of a PEMFC stack. First, a Simulink model of the PEMFC stack including the anode module, cathode module, water transfer module, output voltage module, and output net power module is established, and the accuracy of the stack model is verified through experiments. The three performances are then optimized simultaneously based on NSGA-II. The results show that the optimized operating parameters for the start process results in a PEMFC stack that outperforms the base case in steady-state voltage, percentage of undershoot, and net power these three indicators with the same response time, demonstrating the success of the method in solving multiple optimization problems. This study presents an effective approach for the multi-objective optimization of the PEMFC stack, which is of guidance for engineering practice.

FLC-Based Ultra-Low-Frequency Oscillation Suppression Scheme for Interconnected Power Grids

The appearance of ultra-low-frequency oscillations in the grid at the sending end, after asynchronous grid interconnection, poses a significant threat to the stable operation of the system. For post-asynchronous interconnection in a multi-DC transmission system, an investigation is conducted to analyze the causes of ultra-low-frequency oscillations and the utilization of a Frequency Limit Controller (FLC) which aims to suppress these oscillations. Furthermore, a method is developed to rank DC sensitivity, considering the hydroelectric distribution in the sending-end grid, by combining the DC FLC impact factor and DC control sensitivity. Subsequently, a novel approach for ultra-low-frequency oscillation suppression is proposed. This approach employs the stochastic subspace method for parameter estimation and the NSGA-II optimization algorithm to convert the multi-DC optimization challenge into multiple sequential cyclic optimization problems, each focusing on a single DC, ensuring a more effective suppression of ultra-low-frequency oscillations. The proposed scheme’s effectiveness is validated through simulations using a specific locations’ interconnected power grid.

STUDY ON MECHANICAL PROPERTIES OF DEVELOPED ECO-FRIENDLY BRAKE PADS USING GRAY RELATIONAL ANALYSIS IN BOX BEHNKEN DESIGN OF EXPERIMENT

Over the years, asbestos has been a leading material for developing automobile brake pads. However, due to its hazardous nature to human health, many researchers have found that organic materials possess the potential for replacement. The organic materials used in this research were the hybrid of coconut fruit fibre CFF and oyster sea shell OSS. These materials were gathered from the river bank, dried, crushed, washed, ground, sieved, and moulded with different additives: CuO (abrasive), graphite (friction modifier or solid Lubricant), epoxy resin (binder), hardener (catalyst) by Box Behnken design BBD of L27 experiment. Therefore, an experimental test on mechanical properties was performed to check the developed brake pad's characterization. Then, grey relational analysis was used to analyze grey relational grade GRG to convert a multiple response process optimization problem into a single response optimization using maximization of maximum GRG. The optimum parameter values producing the highest value of grey relational grade were chosen as rank one, pertained to the factors setup for experiment number S3232 having moulding pressure of 11.25MPa, moulding temperature of 180oC, and heat treatment time of 180min. The optimized response values obtained from the experiment sample S3232 give the highest values on all the responses, i.e., density of 3.483g/cm3, hardness of 52.91BHN, compressive strength of 2.78MPa, ultimate tensile strength of 3.92MPa, impact energy of 17.87N, cold water absorption of 0.2863%, hot water absorption of 0.4785%, and oil absorption of 0.4402%. After that, the optimized brake pad sample (S3232) was applied to the automobile and was suitable for braking owing to its high mechanical properties.

Modified proportional topology optimization algorithm for multiple optimization problems

Three modified proportional topology optimization (MPTO) algorithms are presented in this paper, which are named MPTOc, MPTOs and MPTOm, respectively. MPTOc aims to address the minimum compliance problem with volume constraint, MPTOs aims to solve the minimum volume fraction problem under stress constraint, and MPTOm aims to tackle the minimum volume fraction problem under compliance and stress constraints. In order to get rid of the shortcomings of the original proportional topology optimization (PTO) algorithm and improve the comprehensive performance of the PTO algorithm, the proposed algorithms modify the material interpolation scheme and introduce the Heaviside threshold function based on the PTO algorithm. To confirm the effectiveness and superiority of the presented algorithms, multiple optimization problems for the classical MBB beam are solved, and the original PTO algorithm is compared with the new algorithms. Numerical examples show that MPTOc, MPTOs and MPTOm enjoy distinct advantages over the PTO algorithm in the matter of convergence efficiency and the ability to obtain distinct topology structure without redundancy. Moreover, MPTOc has the fastest convergence speed among these algorithms and can acquire the smallest (best) compliance value. In addition, the new algorithms are also superior to PTO concerning suppressing gray-scale elements.

A Comprehensive Survey on Feature Selection with Grasshopper Optimization Algorithm

Recent growth in data dimensions presents challenges to data mining and machine learning. A high-dimensional dataset consists of several features. Data may include irrelevant or additional features. By removing these redundant and unwanted features, the dimensions of the data can be reduced. The feature selection process eliminates a small set of relevant and important features from a large data set, reducing the size of the dataset. Multiple optimization problems can be solved using metaheuristic algorithms. Recently, the Grasshopper Optimization Algorithm (GOA) has attracted the attention of researchers as a swarm intelligence algorithm based on metaheuristics. An extensive review of papers on GOA-based feature selection algorithms in the years 2018–2023 is presented based on extensive research in the area of feature selection and GOA. A comparison of GOA-based feature selection methods is presented, along with evaluation strategies and simulation environments in this paper. Furthermore, this study summarizes and classifies GOA in several areas. Although many researchers have introduced their novelty in the feature selection problem, many open challenges and enhancements remain. The survey concludes with a discussion about some open research challenges and problems that require further attention.

Computation Offloading and Resource Allocation for E2E Tasks in Satellite Edge Computing Networks

Satellite edge computing shows promise in delivering seamless, low-latency services in challenging contexts such as deserts, oceans, and during natural disasters. Previous studies focused on the selection of suitable offloading nodes for task processing and result transmission to the original node. However, for end-to-end tasks, exemplified by applications like satellite-based remote sensing and forestry monitoring, the disparity between source and destination nodes emphasizes the importance of routing selection in data transmission. This aspect substantially limits the effectiveness of traditional computation offloading methods. In this paper, we formulate a joint computation offloading, routing, and multiple resource allocation optimization problem for end-to-end tasks in satellite edge computing networks. Moreover, to reduce the complexity of this nondeterministic polynomial-time hard (NP-hard) problem, we decompose it into the multidimensional resource allocation in fixed offloading and routing condition and the computation offloading and routing selection problem. An algorithm based on binary particle swarm optimization for joint computation offloading, routing, and multiple resource allocation optimization problem is proposed. Simulation results are presented to demonstrate the performance of our scheme compared with other baseline schemes.

Supported nondominated points as a representation of the nondominated set: An empirical analysis

AbstractThe nondominated set of a multiple objective discrete optimization problem is known to contain unsupported nondominated points, which outnumber the supported ones and are more difficult to obtain. We treat supported nondominated points as a representation and analyse their quality using different metrics beyond their sheer numbers. Under different data generation schemes on multiobjective knapsack and assignment problems, we observe that supported nondominated points almost always provide a good representation of the entire nondominated set.

Modeling of Proton Exchange Membrane Fuel Cell Stack and Start Strategy Optimization with a Multi-Objective Genetic Algorithm

This paper proposes a non-dominated ranking genetic algorithm (NSGA-II) method for fast optimizing the loading strategy at the start of a proton exchange membrane fuel cell (PEMFC) stack to optimize the dynamic response capability, power density and system efficiency. First, a Simulink model of the PEMFC stack including anode module, cathode module, water transfer module and output voltage module is established as the base model for optimization, and the accuracy of the stack model is verified through experiments. The power consumption of the air compressor is the main parasitic power considered, and it is modelled using the air compressor map by taking a table look-up method directly. The three performance indicators of dynamic response capability, power density and system efficiency are then optimized simultaneously based on NSGA-II. The results show that the optimized start-up loading strategy results in a PEMFC stack that outperforms the base model in all three indicators, demonstrating the success of the method in solving time-consuming multiple optimization problems. This study presents an effective and rapid approach for the multi-objective optimization of PEMFC stack, which is of guidance for engineering practice.

A Consensus-Based Alternating Direction Method for Mixed-Integer and PDE-Constrained Gas Transport Problems

We consider dynamic gas transport optimization problems, which lead to large-scale and nonconvex mixed-integer nonlinear optimization problems (MINLPs) on graphs. Usually, the resulting instances are too challenging to be solved by state-of-the-art MINLP solvers. In this paper, we use graph decompositions to obtain multiple optimization problems on smaller blocks, which can be solved in parallel and may result in simpler classes of optimization problems because not every block necessarily contains mixed-integer or nonlinear aspects. For achieving feasibility at the interfaces of the several blocks, we employ a tailored consensus-based penalty alternating direction method. Our numerical results show that such decomposition techniques can outperform the baseline approach of just solving the overall MINLP from scratch. However, a complete answer to the question of how to decompose MINLPs on graphs in dependence of the given model is still an open topic for future research. History: Accepted by Andrea Lodi, Area Editor for Design & Analysis of Algorithms–Discrete. Funding: This work was supported by Deutsche Forschungsgemeinschaft [Grant TRR 154].

Optical heterodyne detection system for a high-speed camera based on the HSA phase compensation method.

This study proposes an innovative active optical heterodyne detection system to address the limitations of existing swarm intelligence algorithms in resolving phase compensation issues within coherent detection systems. The design incorporates a high-speed camera array detector, offering improved practicality and a simplified structure. Employing a heuristic search algorithm (HSA) transforms the high-dimensional problem into multiple one-dimensional optimization problems, significantly enhancing algorithmic running speed. The HSA maintains excellent performance even with increased array elements, allowing for real-time phase correction in large arrays. Experimental results using shot peening comparison samples reveal a substantial amplification of the heterodyne signal spectrum amplitude peak, approximately 60 times greater than the original signal. This innovative approach holds great potential for active optical heterodyne detection of dim targets, paving the way for further research in the field.

Modeling of Proton Exchange Membrane Fuel Cell Stack and Start Strategy Optimization with a Multi-Objective Genetic Algorithm

This paper proposes a non-dominated sorting genetic algorithm II (NSGA-II) for optimizing the startup strategy of a proton exchange membrane fuel cell (PEMFC) stack to improve the dynamic response capability, output voltage, and net power. First, a Simulink model of the PEMFC stack including the anode module, cathode module, water transfer module, output voltage module, and output net power module is established, and the accuracy of the stack model is verified through experiments. The three performances are then optimized simultaneously based on NSGA-II. The results show that the optimized start-up loading strategy results in a PEMFC stack that outperforms the base model in steady-state voltage, undershoot percent, and net power these three indicators with the same response time, demonstrating the success of the method in solving multiple optimization problems. This study presents an effective approach for the multi-objective optimization of the PEMFC stack, which is of guidance for engineering practice.

Integrated velocity optimization and energy management for FCHEV: An eco-driving approach based on deep reinforcement learning

Ecological driving (eco-driving) is a promising technology for transportation sector to save energy and reduce emission, which works by improving vehicle behaviors in traffic scenarios. Fuel cell hybrid electric vehicles (FCHEV) are receiving extensive attentions due to global fossil energy crisis, but whose implementations for eco-driving result in multiple objective collaborative optimization problems. In this paper, an eco-driving framework for FCHEV is proposed based on deep deterministic policy gradient (DDPG) algorithm. And it combines adaptive cruise control (ACC) and energy management strategy (EMS) into an integrated architecture. Firstly, in order to achieve excellent balance between driving behaviors and fuel economy, an appropriate weight coefficient value is determined after adequate explorations. Secondly, power-varying equivalent hydrogen conversion coefficient function is constructed to save fuel consumption by 8.97%. Thirdly, ablation experiments for health state of fuel cell system present 19.95% decrease in terms of health degradation. Then, comparison experiments indicate that the DDPG-based eco-driving strategy can reach 94.16% of that of dynamic programming with respect to equivalent hydrogen consumption, meanwhile with best ride comfortability. Moreover, simulation results under validation driving cycle manifest its excellent adaptability.

New Algorithm Permitting the Construction of an Effective Spanning Tree

Abstract In this paper, we have done a rapid and very simple algorithm that resolves the multiple objective combinatorial optimization problem. This, by determining a basic optimal solution, which is a strong spanning tree constructed, according to a well-chosen criterion. Consequently, our algorithm uses notions of Bellman’s algorithm to determine the best path of the network, and Ford Fulkerson’s algorithm to maximise the flow value. The Simplex Network Method that permits to reach the optimality conditions manipulates the two algorithms. In short, the interest of our work is the optimization of many criteria taking into account the strong spanning tree, which represents the central angular stone of the network. To illustrate that, we propose to optimize a bi-objective distribution problem.

An optimization algorithm based on forward recursion with applications to variable horizon MPC

We consider optimization algorithms designed for variable horizon model predictive control. Traditionally, such problems are considered intractable for real-time applications that require fast computations, as they need to solve multiple optimal control problems with varying horizons at each sampling instance. The main contribution is an algorithm that efficiently solves multiple optimal control problems with different prediction horizons in a recursive manner. This algorithm has been successfully implemented and integrated into the OSQP solver, resulting in a real-time controller that is both fast and reliable. To assess the effectiveness of the approach, we conducted evaluations in both a realistic simulation environment and on real hardware during outdoor flight experiments. Specifically, we focused on two distinct rendezvous maneuvers for autonomous landings of unmanned aerial vehicles. The results obtained from these evaluations further validate the practicality and efficacy of the proposed algorithm.

Joint well-placement and well-control optimization for energy-efficient water flooding of oil fields

Hydrocarbon production driven by water flooding is energy-intensive. This paper presents well-placement and joint well-placement-and-control optimization studies with objective function taking into account CO2 emissions, pursuing more energy-efficient water flooding. To assess the effect of emission cost on the optimal drainage strategy, multiple optimization problems implementing different CO2 tax levels are solved. The solutions for higher tax levels usually inject less water and proportionally emit less CO2. The trade-off between emissions and oil production is non-linear: For lower tax levels, we obtain solutions providing large emission reductions with limited reductions in production. Increasing the CO2 tax further, any additional emission reduction leads to a larger reduction in oil production due to reduced opportunities for energy efficiency. Enforcement of higher tax levels usually produces optimal drainage strategies with higher injection effectiveness and lower emission intensity. However, some increases in CO2 tax, particularly above the critical level, have negligible impact on the optimal solution, hence they only affect the profitability negatively without further reducing emissions or improving emission intensity. Compared to the well-placement solutions, the solutions for our joint optimization emit less CO2 and provide higher profit. They also have lower emission intensity due to lower injection pressure. The adjustable well-control enables our joint optimization to stop field production after some years which could be more profitable than continuing the production at high CO2 tax. These clearly demonstrate the advantages of incorporating the well-control variables, giving more freedom to our joint optimization. In well-placement optimization, reductions in water injection and emissions are obtained by decreasing well productivity and injectivity and by increasing inter-well distance. In joint optimization, water injection can also be reduced by adjusting the well-control, hence there is no clear trend in well productivity and inter-well distance with changes in injection volume. The trends in well characteristics concluded from the well-placement solutions could mislead the search for more energy-efficient drainage as they are different from the trends observed in the joint optimization solutions, indicating the importance of joint optimization in this study.

Optimization of integrated energy system considering transmission and distribution network interconnection and energy transmission dynamic characteristics

The traditional hierarchical scheduling and operational model of transmission and distribution networks has failed to fully utilize the adjustable resources of the entire grid, consequently limiting the integration of renewable energy. To fully excavate the potential of transmission and distribution (T&D) coordination in enhancing the level of renewable energy assimilation and operational efficiency, in this paper, transmission grid and distribution network in the framework of synergetic unit commitment (TDS-UC) considering the dynamic characteristics of the electricity-gas-heat integrated energy system is proposed. The framework developed in this paper allows for the integration of multiple energy sources, including electricity, gas, and heat, into the dispatch strategy of the TG. To improve scheduling flexibility, the dynamic characteristics of the natural gas and heating networks are also considered in the TDS-UC model. A coordinated interactive optimization model for T&D is formulated, taking into account the multi-energy coupling relationship of the IES. To solve the TDS-UC model, a decentralized analytical target cascading algorithm is used to obtain an independent TG optimization problem and multiple ADNs local optimization problems that can be solved in parallel. The proposed model is transformed into an easy-to-solve mixed-integer linear programming (MILP) problem using an improved one-dimensional approximation piecewise linearization method to deal with the non-convexity nonlinear natural gas Weymouth equation. Numerical experiments are conducted on both a T6D2 and a T118D10 test system to demonstrate the efficiency and practicality of the proposed methodology.© 2017 Elsevier Inc. All rights reserved.

Multitask Particle Swarm Optimization With Dynamic Transformation

Multitask optimization (MTO) mainly utilizes knowledge transfer among tasks to address multiple optimization problems in parallel. However, the decision space dimensions of different tasks often differ, which leads to the failure of knowledge transfer. Therefore, it is a challenging problem to transfer knowledge among tasks with different dimensions to achieve parallel optimization of multiple tasks. To address this problem, multitask particle swarm optimization with a dynamic transformation strategy (MTPSO-DTS) is proposed to improve the performance of MTO. First, an intertask similarity index based on gradient information and location information is designed to dynamically assess the degree of similarity among different tasks. Then, the intertask similarity is determined to assist the transformation of dimensions. Second, a dynamic transformation strategy based on intertask similarity is developed to achieve a uniform representation of different dimension knowledge, including dimension supplementation and dimension reduction. Then, the MTPSO-DTS algorithm, which takes advantage of the search characteristics of particle swarm optimization, can facilitate knowledge transfer among tasks with different dimensions. Third, the convergence of the MTPSO-DTS algorithm is analyzed to verify the validity theoretically. Finally, numerical comparison experiments on benchmark problems and a practical application are carried out to demonstrate the effectiveness of the MTPSO-DTS algorithm. The results indicate that the proposed MTPSO-DTS algorithm can facilitate knowledge transfer among tasks of different dimensions to promote parallel optimization of multiple tasks.

Manta ray foraging optimization based on mechanics game and progressive learning for multiple optimization problems

Metaheuristic algorithms are currently being studied in depth by many scholars, and it is an important task to improve the learning and adaptive capabilities of the algorithms so that they can be of great use in a wide range of optimization problems. The Manta ray foraging optimization (MRFO) has made certain achievements in optimization problems, but it still has shortcomings, such as its insufficient intra-population communication and poor learning ability, so the optimization capability of MRFO needs further improvement. To address these shortcomings, this paper proposes a manta ray foraging optimization based on mechanics game and progressive learning for multiple optimization problems, which is abbreviated as MGL-MRFO, introducing variable spiral factors and dynamic adjustment of internal parameters; then proposes progressive learning to enhance the learning ability of MRFO; and finally proposes a matching game-based update mechanism to eliminate intra-population repetition as a feasible solution. It is validated in terms of move step size and time complexity. The results are compared with variants of the algorithm proposed in recent years in 18 benchmark test functions and the CEC 2022 test set, as well as with the TOP algorithm in the CEC competition, and show that MGL-MRFO has strong advantages, validating the novelty and competitiveness of MGL-MRFO. At the end of the paper, the feasibility and practicality of MGL-MRFO is further validated by three engineering optimization problems.