Optimal Solution Procedure Research Articles

Low-carbon economic operation of energy hub integrated with linearization model and nodal energy-carbon price

Energy hub has positive significance in absorbing renewable energy, improving energy utilization efficiency and reducing carbon emissions. Considering both linearization energy hub model and nodal integrated energy-carbon price, a low-carbon economic operation model of energy hub is constructed by taking advantage of the bi-level optimization structure. First, in order to simplify the modeling procedures and improve the solving efficiency, reversibility judgment criteria and linearization processes in energy hub modeling are improved. Then, a nodal integrated energy-carbon pricing strategy is proposed and calculated according to flow tracing method and carbon emission flow method. Additionally, the bi-level optimization model and solution procedure are presented to obtain the optimal operating states of energy hubs. At last, for the simulation results, the characteristics and the influence of nodal price on energy consumption behaviors of energy hubs are analyzed, the proposed model is effective to reduce the carbon emissions and operating costs.

Incorporating transportation costs into the single and multiple items newsvendor problems.

The efficiency and responsiveness of supply chains are vitally dependent on inventory replenishment and transportation decisions. In this paper, we study a supply chain consisting of a single retailer ordering seasonal products within the newsvendor framework. The primary objective of the paper is to investigate the retailer's decision-making process, aimed at determining the optimal replenishment quantities and selecting the appropriate mix and size of the truck fleet. Initially, we formulate a mathematical model where the retailer exclusively manages a limited fleet of its own trucks for inbound transportation of a single seasonal product. In this context, we determine a lower breakeven point for the fixed transportation cost than what has been previously proposed in the literature. Subsequently, we examine a commonly encountered transportation scenario where the retailer has the opportunity to expand its fleet size by leasing trucks from the external market. The outcomes of the numerical example indicates that the flexibility resulting from the utilization of different types of trucks can lead to reduced overall costs. We also address the practical transportation problem of efficiently shipping various seasonal products solely with the retailer's own trucks. For this complex problem, we propose an optimal solution procedure based on Lagrangian method. We show that the joint replenishment of multiple products results in cost savings and enhances utilization of the trucks' capacities.

A multi‐priority hierarchical optimization method for double‐layer model predictive control

AbstractConsidering the demand for the sequential regulation of manipulated variables in actual industrial process control, the conventional solution of double‐layer model predictive control faces the problem that the weight coefficients are difficult to tune. This paper proposes an improved hierarchical optimization method for manipulated variables in the steady‐state optimization layer of double‐layer model predictive control. The proposed method can adjust the manipulated variables sequentially without an accurate weight coefficient to avoid difficulty in tuning the weight coefficients. The relation between the optimal solution and the feasible region of the steady‐state optimization layer is analysed to describe the reoptimization of the key manipulated variables. The impact of the economic cost coefficient on the optimal solution with the sensitivity analysis method is studied, and the complexity of using the weight coefficient to solve the priority optimization problem of the manipulated variables is assessed. The steady‐state optimization solution procedure is improved based on the theory of the multiobjective complete hierarchical method. The hierarchical and sequential optimization of the manipulated variables results in expanding the space and freedom of the key manipulated variables, increasing efficiency, reducing consumption, and improving economic performance. The improved hierarchical optimization method is direct and simple in achieving optimization sequentially and satisfies the need for adjusting the manipulated variables according to human intentions.

The Backhaul Profit Maximization Problem: Optimization Models and Solution Procedures

We present a compact mixed integer program (MIP) for the backhaul profit maximization problem in which a freight carrier seeks to generate profit from an empty delivery vehicle’s backhaul trip from its last scheduled delivery to its depot by allowing it to deviate from the least expensive (or fastest) route to accept pickup-and-delivery requests between various points on the route as allowed by its capacity and required return time. The MIP is inspired by a novel representation of multicommodity flow that significantly reduces the size of the constraint matrix compared with a formulation based on the classical node-arc representation. This, in turn, leads to faster solution times when using a state-of-the-art MIP solver. In an empirical study of both formulations, problem instances with 10 potential pickup/drop-off locations and up to 72 pickup-and-delivery requests were solved an average 1.44 times faster in real time with our formulation, whereas instances with 20 locations and up to 332 pickup-and-delivery requests were solved an average of 11.88 times faster. The largest instances in the comparative study had 60 locations and up to 3,267 pickup-and-delivery requests; these instances required an average of more than 54 hours of real time to solve with the node-arc–based formulation but were solved in an average of under two hours of real time using our compact formulation. We also present a heuristic algorithm based on our compact formulation that finds near optimal solutions to each of the 60-location instances within 22 minutes of real time and near optimal solutions to instances with up to 80 locations within four and a half hours of real time.

N ways to simulate short-range particle systems: Automated algorithm selection with the node-level library AutoPas

AutoPas is an open-source C++ library delivering optimal node-level performance by providing the ideal algorithmic configuration for an arbitrary scenario in a given short-range particle simulation. It acts as a black-box container, internally implementing an extensive set of algorithms, parallelization strategies, and optimizations that are combined dynamically according to the state of the simulation via auto-tuning. This paper gives an overview of the high-level user perspective, as well as the internal view, covering the implemented techniques and features. The library is showcased by incorporating it into the codes LAMMPS and ls1 mardyn, and by investigating various applications. We further outline node-level shared-memory performance and scalability of our auto-tuning software which is comparable to LAMMPS. Program summaryProgram Title: AutoPasCPC Library link to program files:https://doi.org/10.17632/9kdb2p76hv.1Developer's repository link:https://github.com/AutoPas/AutoPasCode Ocean capsule:https://codeocean.com/capsule/0391732Licensing provisions: BSD 2-clauseProgramming language: C++17, CMake 3.14Nature of problem: The evaluation of the short-range pairwise interactions in an N-Body simulation can be achieved using many different algorithms and parallelization techniques. Depending on the nature of the scenario, its current state, and the forces of interest, the optimal algorithm configuration can differ greatly. Choosing this optimum is a non-trivial task even for experts. Furthermore, this optimum can change over the course of a simulation. Typically, a particle simulation software only implements one algorithm for force computation and is thus specialized for a certain type of simulation. It is up to the user to choose the program suitable for his needs.Solution method: The AutoPas library implements a range of state of the art algorithms to find the relevant neighbors for the N-Body pairwise force calculation. It provides multiple shared-memory parallelization strategies using OpenMP and further algorithm optimization parameters that can all be set at run-time. A big burden for users persists in requiring the expert knowledge to pick the optimal solution procedure for a simulation. AutoPas removes this burden by tuning all aforementioned options automatically and dynamically. This way, simulation programs that make use of AutoPas give every domain scientist the possibility to make use of the most suitable algorithm configuration for arbitrary scenarios.

Scheduling with lot streaming in a two-machine re-entrant flow shop

Lot streaming is splitting a job-lot of identical items into several sublots (portions of a lot) that can be moved to the next machines upon completion so that operations on successive machines can be overlapped; hence, the overall performance of a multi-stage manufacturing environment can be improved. In this study, we consider a scheduling problem with lot streaming in a two-machine re-entrant flow shop in which each job-lot is processed first on Machine 1, then goes to Machine 2 for its second operation before it returns to the primary machine (either Machine 1 or Machine 2) for the third operation. For the two cases of the primary machine, both single-job and multi-job cases are studied independently. Optimal and near-optimal solution procedures are developed. Our objective is to minimize the makespan, which is the maximum completion time of the sublots and job lots in the single-job and multi-job cases, respectively. We prove that the single-job problem is optimally solved in polynomial-time regardless of whether the third operation is performed on Machine 1 or Machine 2. The multi-job problem is also optimally solvable in polynomial time when the third operation is performed on Machine 2. However, we prove that the multi-job problem is NP-hard when the third operation is performed on Machine 1. A global lower bound on the makespan and a simple heuristic algorithm are developed. Our computational experiment results reveal that our proposed heuristic algorithm provides optimal or near-optimal solutions in a very short time.

Real option valuation of timber harvesting contracts

AbstractA primary challenge for forestry businesses is valuing timber harvesting contracts. This article presents an empirical application of determining the optimal harvest volumes under stochastic prices to determine the economic value of timber harvesting contracts and manage business risk using real options theory. We illustrate a dynamic optimization solution procedure and the choice between a single long‐term versus two short‐term timber harvesting contracts from a risk management perspective. A case study of timber harvesting contracts sold in British Columbia is used to demonstrate specification of the many details and adaptations that are required in such valuation problems. Our article offers some interesting results. The highest timber harvesting contract values occur with optimal harvest quantities rather than an equal annual allowable cut (AAC). The difference in values can be substantial (two to three‐fold). Consequently, forestry businesses can benefit by timing their harvest to nonequal quantities in later years of a timber harvesting contract. Depending on the quality of timber, the maximum stumpage value for the second short‐term timber harvesting contract ranges from $12 to $17.8 per cubic meter, resulting in lower profit margins for equal AAC. In contrast, with optimal harvesting, the maximum stumpage value ranges from $2 to $8.5 per cubic meter and higher profit margins. These bounds for stumpage price and profit margins would be useful for forest businesses to better manage business risks when bidding for timber harvesting contracts.

Minimum-lap-time optimisation and simulation

The paper begins with a survey of advances in state-of-the-art minimum-time simulation for road vehicles. The techniques covered include both quasi-steady-state and transient vehicle models, which are combined with trajectories that are either pre-assigned or free to be optimised. The fundamentals of nonlinear optimal control are summarised. These fundamentals are the basis of most of the vehicular optimal control methodologies and solution procedures reported in the literature. The key features of three-dimensional road modelling, vehicle positioning and vehicle modelling are also summarised with a focus on recent developments. Both cars and motorcycles are considered.

A New Traffic Flow Control Method for Terminal Control Area Using Dioid Algebra

In this article, the system model of the terminal control area is built considering the constraints between different departure routes. The balance for the departure routes in the terminal control area is achieved and the optimal control inputs for the departure flights are also acquired. In particular, the dioid algebra is employed to describe all kinds of concurrent events in the terminal control area and define the interactions between different flight trajectories. In this way, the new optimization model and solution procedure is introduced in order to improve the operation effect of air traffic flow. Finally, different scenarios such as deterministic and stochastic cases are given to demonstrate the performance of the system model. The essence of the system model is allocating optimal time slots to flights coming from different airports.

Discriminative subspace matrix factorization for multiview data clustering

In a real-world scenario, an object is easily considered as features combined by multiple views in reality. Thus, multiview features can be encoded into a unified and discriminative framework to achieve satisfactory clustering performance. An increasing number of algorithms have been proposed for multiview data clustering. However, existing multiview methods have several drawbacks. First, most multiview algorithms focus only on origin data in high dimension directly without the intrinsic structure in the relative low-dimensional subspace. Spectral and manifold-based methods ignore pseudo-information that can be extracted from the optimization process. Thus, we design an unsupervised nonnegative matrix factorization (NMF)-based method called discriminative multiview subspace matrix factorization (DMSMF) for clustering. We provide the following contributions. (1) We extend linear discriminant analysis and NMF to a multiview version and connect them to a unified framework to learn in the discriminant subspace. (2) We propose a multiview manifold regularization term and discriminant multiview manifold regularization term that instruct the regularization term to discriminate different classes and obtain the geometry st ructure from the low-dimensional subspace. (3) We design an effective optimization algorithm with proven convergence to obtain an optimal solution procedure for the complex model. Adequate experiments are conducted on multiple benchmark datasets. Finally, we demonstrate that our model is superior to other comparable multiview data clustering algorithms.

Using NSGA-II to solve multi-objective competitive location problem with cooperative coverage for distance-based attractiveness

Multi-objective competitive location problem with cooperative coverage for distance-based attractiveness is introduced in this paper. The potential facilities compete to be selected to serve all demand points which are determined by maximizing total collective attractiveness of all demand points from assigned facilities and minimizing the fixed and distance costs between all demand points and selected facilities. Facility attractiveness is represented as a coverage of the facility with full, partial and none coverage corresponding to maximum full and partial coverage radii. Cooperative coverage, which the demand point is covered by at least one facility, is also considered. The problem is formulated as a multi-objective optimization model and solution procedure based on elitist non-dominated sorting genetic algorithms (NSGA-II) is developed. Experimental example demonstrates the best non-dominated solution sets obtained by developed solution procedure. Contributions of this paper include introducing competitive location problem with facility attractiveness as a distance-based coverage of the facility, re-categorizing facility coverage classification and developing solution procedure base upon NSGA-II.

Discrete material selection and structural topology optimization of composite frames for maximum fundamental frequency with manufacturing constraints

This paper proposes a methodology for simultaneous optimization of composite frame topology and its material design considering specific manufacturing constraints for the maximum fundamental frequency with a bound formulation. The discrete material optimization (DMO) approach is employed to couple two geometrical scales: frame structural topology scale and microscopic composite material parameter scale. The simultaneous optimization of macroscopic size or topology of the frame and microscopic composite material design can be implemented within the DMO framework. Six types of manufacturing constraints are explicitly included in the optimization model as a series of linear inequality or equality constraints. Sensitivity analysis with respect to variables of the two geometrical scales is performed using the semi-analytical sensitivity analysis method. Corresponding optimization formulation and solution procedures are also developed and validated through numerical examples. Numerical study shows that the proposed simultaneous optimization model can effectively enhance the frame fundamental frequency while including specific manufacturing constraints that reduce the risk of local failure of the laminated composite. The proposed multi-scale optimization model for the maximum fundamental frequency is expected to provide a new choice for the design of composite frames in engineering applications.

Inflation and time value of money in a vendor–buyer inventory system with transportation cost and ordering cost reduction

The article presents a single-vendor and a single-buyer integrated production inventory system with inflation and the time value of money. The main focus is on the effect of ordering cost reduction dependent on lead time and lead time reduction. Two integrated continuous review models are developed. For both cases, our objective is to minimise the total integrated system cost by simultaneously optimising the order quantity, safety factor, lead time and number of shipments. We take the transportation cost as a function of the shipment lot size and it is taken to be in an all unit-discount cost format. Thus we incorporate transportation cost explicitly into the model and develop optimal solution procedure for solving the proposed inventory system. An efficient algorithm for finding the optimal solution is developed and numerical examples are given to illustrate the model.

Neutrosophic Optimization Model and Computational Algorithm for Optimal Shale Gas Water Management under Uncertainty

Shale gas energy is the most prominent and dominating source of power across the globe. The processes for the extraction of shale gas from shale rocks are very complex. In this study, a multiobjective optimization framework is presented for an overall water management system that includes the allocation of freshwater for hydraulic fracturing and optimal management of the resulting wastewater with different techniques. The generated wastewater from the shale fracking process contains highly toxic chemicals. The optimal control of a massive amount of contaminated water is quite a challenging task. Therefore, an on-site treatment plant, underground disposal facility, and treatment plant with expansion capacity were designed to overcome environmental issues. A multiobjective trade-off between socio-economic and environmental concerns was established under a set of conflicting constraints. A solution method—the neutrosophic goal programming approach—is suggested, inspired by independent, neutral/indeterminacy thoughts of the decision-maker(s). A theoretical computational study is presented to show the validity and applicability of the proposed multiobjective shale gas water management optimization model and solution procedure. The obtained results and conclusions, along with the significant contributions, are discussed in the context of shale gas supply chain planning policies over different time horizons.

An Inverse Dynamics Optimization Formulation With Recursive B-Spline Derivatives and Partition of Unity Contacts: Demonstration Using Two-Dimensional Musculoskeletal Arm and Gait.

In this study, an inverse dynamics optimization formulation and solution procedure is developed for musculoskeletal simulations. The proposed method has three main features: high order recursive B-spline interpolation, partition of unity, and inverse dynamics formulation. First, joint angle and muscle force profiles are represented by recursive B-splines. The formula for high order recursive B-spline derivatives is derived for state variables calculation. Second, partition of unity is used to handle the multicontact indeterminacy between human and environment during the motion. The global forces and moments are distributed to each contacting point through the corresponding partition ratio. Third, joint torques are inversely calculated from equations of motion (EOM) based on state variables and contacts to avoid numerical integration of EOM. Therefore, the design variables for the optimization problem are joint angle control points, muscle force control points, knot vector, and partition ratios for contacting points. The sum of muscle stress/activity squared is minimized as the cost function. The constraints are imposed for human physical constraints and task-based constraints. The proposed formulation is demonstrated by simulating a trajectory planning problem of a planar musculoskeletal arm with six muscles. In addition, the gait motion of a two-dimensional musculoskeletal model with sixteen muscles is also optimized by using the approach developed in this paper. The gait optimal solution is obtained in about 1 min central processing unit (CPU) time. The predicted kinematics, kinetics, and muscle forces have general trends that are similar to those reported in the literature.

Power-flow-tracing-based congestion management in hydro-thermal optimal power flow algorithm

This paper presents a method for managing congestion constraints in a hydro-thermal optimal power flow solution procedure. The congestion constraint is handled in this paper as an active power generation constraint. To achieve this solution, a power flow tracing technique is used to detect the generators contributing to line congestion to penalize them by reducing their outputs. The congestion is then removed by setting the maximum power of the affected generators to the penalized value. The proposed algorithm is implemented using MATLAB software. Finally, the performance of the proposed algorithm is tested and the results for the 5-bus, 30-bus, and 34-bus Nigerian power networks are presented.

Portfolio Optimization with Nonparametric Value at Risk: A Block Coordinate Descent Method

In this paper, we investigate a portfolio optimization methodology using nonparametric value at risk (VaR). In particular, we adopt kernel VaR and quadratic VaR as risk measures. As the resulting models are nonconvex and nonsmooth optimization problems, albeit with some special structures, we propose some specially devised block coordinate descent (BCD) methods for finding approximate or local optimal solutions. Computational results show that the BCD methods are efficient for finding local solutions with good quality and they compare favorably with the branch-and-bound method-based global optimal solution procedures. From the simulation test and empirical analysis that we carry out, we are able to conclude that the mean-VaR models using kernel VaR and quadratic VaR are more robust compared to those using historical VaR or parametric VaR under the normal distribution assumption, especially when the information of the return distribution is limited. The online supplement is available at https://doi.org/10.1287/ijoc.2017.0793 .

Optimal design of rotational inertial double tuned mass dampers under random excitation

The rotational inertial double tuned mass damper (RIDTMD) is a type of passive mass damper which includes a physical mass as well as a rotational mass. This rotational mass is produced by an inerter which is capable of providing large effective mass utilizing very little physical mass. By selecting the proper design parameters, the RIDTMD show promise at more effective response reduction of underlying primary systems in comparison to conventional tuned mass dampers (TMDs). However, when the primary system is subjected to random loads, the previously considered optimum design values for harmonic excitation are not effective. This motivates an investigation to determine the exact analytical optimum solution for selecting the stiffness and damping design values of RIDTMD when the primary structure is subjected to random force and base excitation. In this paper, an exact optimization solution procedure is presented with the goal of finding the optimum design values of the RIDTMD when mitigating the response of a structure subjected to random force and base excitation. Utilizing the obtained optimum design values, the effectiveness of the RIDTMD is also studied in comparison to conventional TMDs. The results of this study show that the RIDTMD with optimized stiffness and damping values outperforms the optimized conventional TMD; however, the degree of its increased effectiveness in reducing the main mass response is reliant upon the selection of appropriate pairs of secondary and rotational mass.

Simulation-based model for the optimization of machining parameters in a metal-cutting operation

To achieve a certain measurable performance in cutting machines, the machine parameters need to be optimized. Several constraints determine the possible values that these parameters can take. Although parameters are usually assumed to be deterministic, in practice, it is common to find variations on the characteristics of the products or the processes. Modeling machining parameters as stochastic factors provides a more realistic representation of cutting operations. Moreover, multiple operational objectives are of interest, in many real situations, these multiple objectives are conflicting. Consequently, the problem of setting the parameters becomes a trade-off situation. This paper presents a novel Simulation-based Multi-Objective Optimization (SimMOpt) solution procedure. The procedure is divided into two phases: (1) finding initial solutions and, (2) using a simulated annealing-based method for finding neighboring solutions. In the first phase, non-linear goal programming is used for finding high quality initial solutions. The second phase incorporates Pareto Archive Evolution Strategy (PAES) and hypotheses testing for searching near-optimal solutions for a set of stochastic parameters (i.e., cutting speed, feed rate, and depth of cut) in metal cutting operations. Three objectives are optimized (i.e., operation time, operation cost, and quality of the product). The results from implementing this procedure are analyzed and compared to a baseline methodology based on the Multi-Objective Simulated Annealing (MOSA) algorithm. The analysis demonstrates that the proposed method outperforms the Genetic Algorithm (GA), which was the benchmark algorithm, in terms of the solution quality of all the objectives. More importantly, the solutions from using the SimMOpt procedure outperform those obtained from using an enhanced MOSA-based approach (i.e., 4.71% improvement in the hypervolume approximation).

A two-echelon supply chain inventory model with shortage backlogging, inspection errors and uniform demand under imperfect quality items

Actually, some production and inspection processes do not work perfectly, thereby producing a certain number of defective items and inspection errors. Previous imperfect-quality integrated inventory studies have mostly focused on developing models that do not consider two-way imperfect inspection under stochastic demand. Thus, this paper proposes a cost-minimising integrated vendor-buyer production-inventory model that incorporates imperfect production quality, stochastic demand, and imperfect inspection processes. The imperfect inspection processes are Type I inspection error of classifying a non-defective item as defective and Type II inspection error of classifying a defective item as non-defective. Meanwhile, the demand is assumed uniformly distributed. The objective of this research is to determine the optimal order quantity and reorder point such that the expected integrated total annual cost is minimised. In order to solve the integrated model, an optimal solution procedure is developed. A numerical example is provided to illustrate the application of the model. Besides, a sensitivity analysis is also given to investigate the effects of six important parameters (the transportation cost, the buyer's holding cost, the vendor's holding cost, the percentage of defective items, Type I error, and Type II error) on the optimal solution.