Mathematical Programming Algorithms Research Articles

Matheuristic and learning-oriented multi-objective artificial bee colony algorithm for energy-aware flexible assembly job shop scheduling problem

With the increase of mass customization, flexible job shop scheduling problem considering assembly stage has widely existed in many manufacturing industries, such as die-casting mould factories. This problem is to find a reasonable machine assignment and operation sequence both in fabrication and assembly stages and simultaneously maximize production efficiency. In reality, energy shortages and environmental pollution have given an impetus to the development of energy-aware production scheduling problems. In this study, we address an energy-aware flexible assembly job shop scheduling problem (EFAJSP) with the objectives of minimizing flow time and energy consumption and first develop a mixed-integer linear programming (MILP) model to solve EFAJSP problem. Then, the model-specific characteristics are extracted and applied to a matheuristic decoding method for exploring the Pareto optimal solution. Due to the complexity of EFAJSP problem, a matheuristic and learning-oriented multi-objective artificial bee colony algorithm (MLABC), which combines the advantages of mathematical programming, reinforcement learning and meta-heuristic algorithm, is proposed. In addition, an initialization, destruction/construction operator and population update operator are proposed and work together to improve the exploration and exploitation performance of the proposed MLABC. Finally, numerical experimental results demonstrate the effectiveness of the proposed MILP model and the superiority of the MLABC over other algorithms in the literature.

Overview of Distribution System Reliability Optimization Against Lightning

The reliability of the distribution system relies on the occurrence of lightning phenomena, which can significantly affect the distribution of electricity and result in power service disruptions. Therefore, ensuring the reliability of the distribution system is an ongoing challenge that necessitates continuous research for optimal solutions. Researchers have always developed solutions that are always up to date by leveraging advancements in mathematics, engineering technology, and management strategies. This paper presents a comprehensive summary and discussion of various optimization models for enhancing system reliability. It offers an overview of commonly employed mathematical programming techniques and algorithms for Lightning Protection Systems (LPSs), while also highlighting the influence of lightning phenomena on these solutions. The focus of this paper is to present the engineering aspects behind the development of modern LPSs. It encompasses historical reliability data, technical limitations, and economic considerations. By utilizing operations research and optimization theory, researchers have been able to devise more effective approaches for addressing reliability issues, even in highly intricate systems across different domains. Technological advancements have prompted researchers to adopt a new perspective on solving reliability problems, based on practical engineering requirements. In conclusion, the continuous progress in mathematics, engineering technology, and management approaches has enabled researchers to tackle the challenges associated with distribution system reliability. This paper serves as a valuable resource, providing insights into the development of modern LPSs and offering guidance on optimizing system reliability in various practical engineering scenarios.

Static Analysis and Optimization Design of Bridge Structures under Different Load Conditions

The research is the optimization design of the bridge from the structure of the bridge, proper material utilization, and improving the performance of the bridge. First, the static model of the bridge structure was established, and then the finite analysis and rigid body mechanics models were utilized to separately detail the dead load, live load, and exceptional load. Based on the above analyses, optimization methods such as mathematical programming and genetic algorithms were used for optimizing the design of bridge structures. The tests demonstrated that the bridge’s weight can be significantly reduced by optimal design, the efficiency of usage in materials is enhanced, and the rigidity and stability of the structure advanced significantly. It is verified through checking the comparative analysis before and after optimization that the efficiency of the optimization method has been proved and the critical application value of optimization design in bridge engineering. The research conclusions provide new ideas and methods for bridge structure design, which has important theoretical and practical significance.

Research on IoT-based hybrid electrical vehicles energy management systems using machine learning-based algorithm

Electric vehicles (EVs) are quickly becoming a staple of smart transportation in applications involving smart cities due to their ability to reduce carbon footprints. However, the widespread use of electric vehicles significantly strains the nation's electrical system. In-depth descriptions of the EV's energy management system (EMS) should highlight the vehicle's powertrain's vital role. The energy for propulsion in electric automobiles comes from a rechargeable battery. The safe and dependable operation of batteries in electric vehicles relies heavily on online surveillance and status estimations of charges. An energy management strategy (EMS) that considers the electric vehicle's battery and ultra-capacitor may lessen the vehicle's reliance on external power sources and extend the battery's lifespan. A machine learning-based mathematical dynamic programming algorithm is used in designing the energy management system to teach the system how to respond appropriately to various situations without resorting to predefined rules. Therefore, this research aims to use Machine Learning to create a Smart Energy Management System for Hybrid Electrical Vehicles (SEMS-HEV) with energy storage. Energy optimization techniques and algorithms are necessary in this setting to reduce expenses and length of charging and appropriately arrange the EV charging process to prevent bursts in the electrical supply that may impact the transmission network. To improve the performance of an energy management system, this study employs an IoT-based smart charging system for scheduling V2G connections for hybrid electrical vehicles. It allows for more precise and effective control and greater efficiency by enabling the system to learn from its surroundings.

Random update particle swarm optimizer (RUPSO): A novel robust optimization algorithm

Achieving an optimal design, especially those with numerous variables, is a tedious process. It is regularly achieved by mathematical programming or Metaheuristic algorithm methods. A novel metaheuristic optimization algorithm is presented in this research. The proposed algorithm is based on the well-known Particle Swarm Optimization (PSO) algorithm, in which the updating process has been improved. The efficiency of the new method, named Random Update Particle Swarm Optimizer (RUPSO), has been verified for problems with continuous variables as well as problems with discrete variables. It is shown that RUPSO converges to better optimum solutions than PSO and other existing metaheuristic algorithms. It is for its capability of searching through the entire feasible search spaces and going over the local optima. Random updating process, which has been utilized in RUPSO, decreases the sensitivity of the algorithm and increases its stability in solving optimization problems. High stability of the method is also shown in the paper. The RUPSO algorithm finds the optimized answers with a very high convergence rate for problems with discrete or even continuous variables.

Economic and environmental optimal design of a multi-vector energy hub feeding a Local Energy Community

One of the main ways to reach the important targets of the European Commission in the energy field set by 2030 is to implement sustainable energy systems to cover electrical and thermal energy demands, as well as transportation needs, in urban areas. In the aforesaid scenario, multi-vector energy hubs consist of installing small and medium size power plants, mainly fed by renewable sources, and charging infrastructures for electric vehicles in sustainable urban districts. The optimal design of such systems can be faced from different points of view and using different methods, one of the most adopted being the development of mathematical programming algorithms typically aimed to minimize global costs and emissions. The contribution of this paper is to propose an innovative methodology to optimally design a multi-vector energy hub able to supply electricity and thermal energy, for space heating and cooling, to a set of buildings within a sustainable district acting as a local energy community. The developed mixed integer linear programming model is characterized by very detailed models of the technologies and by a multi-objective function which is proposed to evaluate the impact of the optimal solution on global costs and emissions. The proposed mathematical model is very comprehensive as it involves a wide range of energy technologies with detailed modelling by considering the impact of external ambient conditions and energy vector temperature values on the plant conversion efficiency, thus showing high replicability potential in real contexts. In the case study, the model is applied to a university campus in the North of Italy.

Modification of the Bellman–Ford Algorithm for Finding the Optimal Route in Multilayer Network Structures

One of the actual tasks of the contemporary logistics business using the “just in time” supply planning concept, is to distribute manufactured goods among the objects of the distribution network in the most efficient manner at the lowest possible cost. The article is devoted to the problem of finding the optimal path in network structures. The problem statement for multilayer data transmission networks (MDTN), which is one of the possible representations of multimodal transport networks, is considered. Thus, each MDTN layer can be represented as a separate type of transport. The problem is solved by modifying the Bellman–Ford mathematical programming algorithm. Load testing of the modified method was performed, and a comparative analysis was given, including an assessment of speed and performance, proving the effectiveness of the results of the study. Based on the results of comparative analysis, recommendations for using a modified version of the Bellman–Ford algorithm for application in practical problems in optimizing logistics networks are proposed. The results obtained can be used in practice not only in logistics networks but also in the construction of smart energy networks, as well as in other subject areas that require optimization of multilayer graph structures.

Shape and non-shape unified isogeometric optimal design for extremal band gaps

A unified shape and non-shape design optimization for lattice structures is performed to obtain extremal band gaps in an isogeometric computational framework, which uses the same NURBS basis functions as used in CAD description. Using a precise numerical model in both response and shape sensitivity analyses, enhanced response and sensitivity can be obtained, which leads to a precise optimal design. A plane wave propagation in infinite periodic lattice is analyzed within a representative unit cell using the Bloch theory with periodic boundary conditions. The ligaments of lattice structures are modeled using geometrically exact beams whose cross-sectional area and configuration are regarded as design variables, which are parameterized by the NURBS basis functions. The design variables are controlled by a mathematical programming algorithm with efficient adjoint design sensitivity. The obtained optimal lattice structures of triangular, squared, hexagonal, and Kagomé structures are fabricated using a 3D printing machine to be validated by physical experiments. Through harmonic response analysis and physical experiment for the optimal and the original designs, the wave attenuation properties are compared to demonstrate the validity of the obtained optimal design.

Real-time large-scale supplier order assignments across two-tiers of a supply chain with penalty and dual-sourcing

Supplier selection and order allocation (SSOA) are key strategic decisions in supply chain management which greatly impact the performance of the supply chain. Although, the SSOA problem has been studied extensively but less attention paid to scalability presents a significant gap preventing adoption of SSOA algorithms by industrial practitioners. This paper presents a novel multi-item, multi-supplier double order allocations with dual-sourcing and penalty constraints across two-tiers of a supply chain, resulting in cooperation and in facilitating supplier preferences to work with other suppliers through bidding. We propose Mixed-Integer Programming models for allocations at individual-tiers as well as an integrated allocations. An application to a real-time large-scale case study of a manufacturing company is presented, which is the largest scale studied in terms of supply chain size and number of variables so far in literature. The use case allows us to highlight how problem formulation and implementation can help reduce computational complexity using Mathematical Programming (MP) and Genetic Algorithm (GA) approaches. The results show an interesting observation that MP outperforms GA to solve SSOA. Sensitivity analysis is presented for sourcing strategy, penalty threshold and penalty factor. The developed model was successfully deployed in a large international sourcing conference with multiple bidding rounds, which helped in more than 10% procurement cost reductions to the manufacturing company.

Research on the scheduling scheme of resource storage locations in deep-sea oil and gas exploitation

Crucial components of the exploration and exploitation of deep-sea oil and gas resources include the identification of pre-disaster emergency resource storage locations and the appropriate scheduling of emergency resources. Frequently, integer linear programming or integer nonlinear programming is used to investigate them. Both techniques may result in optimization, but it is difficult to determine the global optimal solution. Consequently, this study presents a two-stage optimization model of emergency resource storage location-scheduling that not only surpasses the limitations of independent research but also applies an intelligent optimization algorithm to discover the global optimal solution. In the first phase of the model, the objective of optimization is to decrease the emergency response time. Uncertainty and unpredictability are incorporated as marine environmental components in the goal function. Using the analytic hierarchy method, the effect of resource storage and location is evaluated, and the genetic algorithm (GA) and immune algorithm (IA) are used to determine the goal model's optimal solution. The objective of the second stage is to optimize resource scheduling satisfaction, and the resource storage locations determined in the first stage are assigned using a fuzzy trigonometric function formula and mathematical programming algorithm. The two-stage optimization methodology is shown using the deep-sea fire explosion incidence as an example. The results suggest that the transit time of resources from the resource storage site selection points to the operation points calculated by GA is 50% less than that obtained by IA, and the 4 time of IA is at least 5 times that of GA. The overall resource scheduling time is lowered by 41.1% compared to conventional shore-based terminals, the economic cost of an accident is minimized, and the life safety of on-site operators is improved. Throughout 1000 different seasons, the objective ideal value and average value of GA and IA are compared. GA has a slower convergence rate than IA, but its convergence quality is much higher. The quantity of emergency supplies given by each resource storage site may meet the resource need of the operational point. We believe that the model proposed in this study can guarantee the accuracy of prediction results in situations of small sample sizes, and its validity and applicability have been validated.

Resiliency Improvement of Distribution Network Considering the Charge/Discharge Management of Electric Vehicles in Parking Lots through a Bilevel Optimization Approach

Due to the growing use of Plug-in Electric vehicles (PEVs) in transportation networks, the charge/discharge scheduling of PEVs in Electric Vehicles Parking Lots (EVPLs) can be effective on the distribution network’s (DN) resiliency. This paper presents a bilevel optimization model to improve the resiliency of the DN taking into account the interaction between the DN islanding problem and the charge/discharge scheduling of PEVs in the energized EVPLs. In the Upper-Level (UL) problem, regarding the electrical loads and managing the charge/discharge of PEVs, the islands’ boundaries are determined with the aim of maximizing the amount of restored load. Knowing the islands’ boundaries and the energized EVPLs from the UL problem, the changes in travels characteristic including destination EVPLs are determined in the Lower-Level (LL) problem to identify the nearest energized EVPL to the out-of-service destination EVPL. The number of PEV drivers that change their deenergized destination depends on the distance between the nearest energized EVPL to the destination. A combination of mathematical programming and evolutionary algorithm is applied to reach the final solution. The proposed model is implemented by applying several concurrent faults to the 118-bus active DN, which is coupled with a 25-node traffic network. The results confirm the efficiency of the proposed model for improving the resiliency of DNs with managing the charge/discharge of PEVs in the restored EVPLs.

Topology optimization of coated structures with layer-wise graded lattice infill for maximizing the fundamental eigenfrequency

Combining the advantages of lattice infill and coating, coated structures with lattice infill are widely used in engineering to achieve light-weight structural characteristic or certain functionalities. This paper presents a novel concurrent multiscale topology optimization (TO) framework to maximize the fundamental eigenfrequency of structures with a uniform outer coating and layer-wise graded lattice infill microstructures. The macroscale topology optimization is conducted by using the velocity field-based level set method, which inherits the implicit geometrical representation and signed distance property of the conventional level set method (smooth and clear boundaries and well-maintenance of the uniform thickness of the coating). Besides, the employment of general mathematical programming algorithms enables the velocity field-based level set method to handle multiple constraints in an easier way. At microscale, the popular density-based method is used to design layer-wise graded lattice structures. The effective material properties of microstructures are computed by using the asymptotic homogenization method, which bridges macroscale and microscale designs. With higher design flexibility, it is found that coated structures with layer-wise graded lattice infill have higher eigenfrequencies than those with periodic and uniform lattice infill microstructures. The influence of layers of lattice infill and coating thickness on the concurrent optimization of macrostructures and microstructures are carefully studied by showcasing several numerical examples, and the effectiveness of the proposed method is also confirmed, as well as the manufacturability of optimization results.

Teaching Quality of College Students’ Mental Health Based on Mathematical Programming Algorithm

During the evolution of the twenty-first century, the increase in people’s material life level has also brought an increase in mental stress. For college students, not only need to bear heavy academic pressure, but also face the market competition after entering the society. Therefore, the psychological fitness instruction for undergraduate students has become an inseparable part of college education. However, in the current stage of mental health education, the quality of teaching is often difficult to guarantee. For the purpose of promoting the in-depth implementation of mental health education in colleges and universities and improving teaching effectiveness, one needs to analyze the quality of teaching in great details and understand the factors affecting the quality of teaching. In this paper, the mathematical programming algorithm is used to analyze the quality of college students’ Psychological Wellness Instruction. It deeply studies the development status of psychological wellness training and the basic composition and algorithm principle of mathematical programming algorithm. It integrates it into the practice of teaching quality analysis on the basis of linear regression algorithm theory. The experimental results show that the highest confidence interval of teachers’ teaching organization, cognitive level, and students’ participation level in the mental health course has reached more than 80.00%. This shows the importance of these three factors to the improvement of teaching quality. In order to enhance the quality of college students’ psychological wellness training, it is necessary to innovate the form of classroom organization and the degree of interaction between students and the classroom.

Deep preference learning for multiple criteria decision analysis

We propose preference learning algorithms for inferring the parameters of a threshold-based sorting model from large sets of assignment examples. The introduced framework is adjusted to different scores originally used in Multiple Criteria Decision Analysis (MCDA). They include Ordered Weighted Average, an additive value function, the Choquet integral, a distance from the ideal and anti-ideal alternatives, and Net Flow Scores built on the results of outranking-based pairwise comparisons. As a concrete application of these models, we use Artificial Neural Networks with up to five hidden layers. Their components and architecture are designed to ensure high interpretability, which supports the models’ acceptance by domain experts. To learn the most favorable values of all parameters at once, we use a variant of a gradient descent optimization algorithm called AdamW. In this way, we make the MCDA methods suitable for handling vast, inconsistent information. The extensive experiments on various benchmark problems indicate that the introduced algorithms are competitive in predictive accuracy quantified in terms of Area Under Curve and the 0/1 loss. In this regard, some approaches outperform the state-of-the-art algorithms, including generalizations of logistic regression, mathematical programming, rule ensemble and tree induction algorithms, or dedicated heuristics.

A Generalized Projetion Gradient Algorithm for Mathematical Programs with Complementary Constraints

Against the shortcomings that many existing algorithms for solving the standard smoothing nonlinear programming would fail if they were used directly to solve the mathematical programs with complementary constraints( MPCC). By using a complementarity function and the idea of smoothing approximation method, the MPCC problem was transformed into a smoothing nonlinear programming. Combined with the supermemory gradient idea, a generalized projection gradient algorithm is proposed and its global convergence is obtained.

A nested algorithm of truss topology optimization for maximum plastic shakedown loading capacity

Abstract This paper proposes a nested algorithm for truss topology optimization under plastic shakedown theory, which aims at maximizing the shakedown loading capacity. The nested algorithm consists of shakedown analysis and sensitivity-based optimization. Analytical sensitivity of shakedown load with respect to the design variables is derived in a concise form for the first time in conjunction with the adjoint variable scheme. A primal-dual shakedown algorithm is implemented for the determination of the shakedown load limit of structures and adjoint variables needed in the sensitivity analysis. The ground structure approach is applied to formulate the optimization problem for determining the optimized topology and cross-sections of the truss structure. Based on the analytical sensitivity above, the nested algorithm of truss structure topology optimization can be done efficiently by a gradient-based mathematical programming algorithm. Through independent shakedown analysis and optimization processes, the proposed approach facilitates the computation scale and efficiency for large-scale structure optimization design. Several numerical examples involving two- and three-dimensional truss illustrate the effectiveness of the proposed approach.

Analysis of Overall Assignment and Sorting of Tasks in Heterogeneous Computing Systems Based on Mathematical Programming Algorithms

Analysis of Overall Assignment and Sorting of Tasks in Heterogeneous Computing Systems Based on Mathematical Programming Algorithms

Real-time optimal energy management of microgrid with uncertainties based on deep reinforcement learning

Microgrid (MG) is an effective way to integrate renewable energy into power system at the consumer side. In the MG, the energy management system (EMS) is necessary to be deployed to realize efficient utilization and stable operation. To help the EMS make optimal schedule decisions, we proposed a real-time dynamic optimal energy management (OEM) based on deep reinforcement learning (DRL) algorithm. Traditionally, the OEM problem is solved by mathematical programming (MP) or heuristic algorithms, which may lead to low computation accuracy or efficiency. While for the proposed DRL algorithm, the MG-OEM is formulated as a Markov decision process (MDP) considering environment uncertainties, and then solved by the PPO algorithm. The PPO is a novel policy-based DRL algorithm with continuous state and action spaces, which includes two phases: offline training and online operation. In the training process, the PPO can learn from historical data to capture the uncertainty characteristic of renewable energy generation and load consumption. Finally, the case study demonstrates the effectiveness and the computation efficiency of the proposed method.

Optimized Application of Sustainable Development Strategy in International Engineering Project Management

The aim of this paper is to establish an international framework for sustainable project management in engineering, to make up the lack of research in this field, and to propose a scientific theoretical basis for the establishment of a new project management system. The article adopts literature review, mathematical programming algorithm and case study as the research method. The literature review applied the visual clustering research method and analyzed the results of 21-year research in this field. As a result, the project management system was found to have defects and deficiencies. A mathematical model was established to analyze the composition and elements of the optimized international project management system. The case study research selected large bridges for analysis and verified the superiority and practicability of the theoretical system. Thus, the goal of sustainable development of bridges was achieved. The value of this re-search lies in establishing a comprehensive international project management system model; truly integrating sustainable development with project management; providing new research frames and management models to promote the sustainable development of the construction industry.

Multi-material topology optimization of piezoelectric composite structures for energy harvesting

Energy harvesting is an essential technology for enabling low-power, maintenance-free electronic devices, and thus has attracted much attention in recent years. In this paper, we propose a multi-material topology optimization approach for the design of energy harvesting piezoelectric composite structures. The energy conversion efficiency of piezoelectric composite structure is maximized by optimally distributing elastic, piezoelectric and void materials. To this end, a multi-material interpolation model is particularly established. In order to improve gradient-based mathematical programming algorithms, analytical sensitivities of topological design variables are derived using the adjoint method. An additional constraint on structural compliance is considered in design to maintain the load-carrying capability and improve the convergence. A variety of numerical experiments are performed to test our approach on a benchmark composite beam with piezoelectric layers. The proposed approach has been shown effective in increasing the energy conversion efficiency by the simultaneous distribution of the piezoelectric and non-piezoelectric materials. The performance calibration of the optimized design and the reconstructed topologies based on computer-aided design demonstrate the effectiveness of the proposed method under both static and harmonic load conditions.