Commercial Optimization Research Articles

Multi-Objective Optimization for Order Assignment in Food Delivery Industry with Human Factor Considerations

The order assignment in the food delivery industry is of high complexity due to the uneven distribution of order requirements and the large-scale optimization of workforce resources. The delivery performance of employees varies in different conditions, which further exacerbates the difficulty of order assignment optimization. In this research, a non-linear multi-objective optimization model is proposed with human factor considerations in terms of both deteriorating effect and learning effect, in order to acquire the optimal solutions in practice. The objectives comprised the minimization of the operational cost in multiple periods and the workload balancing among multiple employees. The proposed model is further transformed to a standardized mixed-integer linear model by the exploitation of linearization procedures and normalization operations. Numerical experiments show that the proposed model can be easily solved using commercial optimization softwares. The results indicate that the variance of employee performance can affect the entire delivery performance, and significant improvement of workload balancing can be achieved at the price of slight increase of the operational cost. The proposed model can facilitate the decision-making process of order assignment and workforce scheduling in the food delivery industry. Moreover, it can provide managerial insights for other labor-intensive service-oriented industries.

A multi-objective bi-level location problem for heterogeneous sensor networks with hub-spoke topology

An heterogeneous sensor network (hSN) consists of different types of sensor nodes with varying coverage capability, range, and sensing quality. hSNs are used by military and other defense organizations for a number of purposes such as monitoring critical facilities, surveilling an area of interest, tracking enemies, or protecting borders. Therefore, the deployment problem of such networks to form an effective coverage and surveillance is of high importance. In this study, we consider the problem of locating an hSN along a two-dimensional belt-shaped border region which includes a number of critical facilities that need protection against intruders. Assuming a hub-spoke location topology, we allow the use of cooperative and gradual covering, multiple types of sensors, critical facilities and intruders. We developed two competing multi-objective mixed integer non-linear program formulations as well as their equivalent mixed integer linear program (MILP) reformulations which adopt a goal programming approach. The MILP formulations are then solved by a commercial optimizer for a set of problem instances using the branch-and-cut (B&C) procedure with various branching and node selection strategies as well as different user defined optimality gap and goal settings. Our results indicate that the performance of formulations are significantly affected by the B&C variable selection strategy as well as the goal levels determined by the decision-makers. We also observe that, using proper settings, the majority of the problem instances can be solved within a maximum of 10% optimality gap in reasonable computing times.

Multi-Stage Transmission Network Planning Considering Transmission Congestion in the Power Market

The uncertainty of generation and load increases in the transmission network in the power market. Considering the transmission congestion risk caused by various uncertainties of the transmission network, the optimal operation strategies of the transmission network under various operational scenarios are decided, aiming for the maximum of social benefit for the evaluation of the degree of scenario congestion. Then, a screening method for major congestion scenario is proposed based on the shadow price theory. With the goal of maximizing the difference between the social benefits and the investment and maintenance costs of transmission lines under major congestion scenarios, a multi-stage transmission network planning model based on major congestion scenarios is proposed to determine the configuration of transmission lines in each planning stage. In this paper, the multi-stage transmission network planning is a mixed integer linear programming problem. The DC power flow model and the commercial optimization software CPLEX are applied to solve the problem to obtain the planning scheme. The improved six-node Garver power system and the simplified 25-node power system of Zhejiang Province, China are used to verify the effectiveness of the proposed multi-stage planning model.

EAGO.jl: easy advanced global optimization in Julia

An extensible open-source deterministic global optimizer (EAGO) programmed entirely in the Julia language is presented. EAGO was developed to serve the need for supporting higher-complexity user-defined functions (e.g. functions defined implicitly via algorithms) within optimization models. EAGO embeds a first-of-its-kind implementation of McCormick arithmetic in an Evaluator structure allowing for the construction of convex/concave relaxations using a combination of source code transformation, multiple dispatch, and context-specific approaches. Utilities are included to parse user-defined functions into a directed acyclic graph representation and perform symbolic transformations enabling dramatically improved solution speed. EAGO is compatible with a wide variety of local optimizers, the most exhaustive library of transcendental functions, and allows for easy accessibility through the JuMP modelling language. Together with Julia's minimalist syntax and competitive speed, these powerful features make EAGO a versatile research platform enabling easy construction of novel meta-solvers, incorporation and utilization of new relaxations, and extension to advanced problem formulations encountered in engineering and operations research (e.g. multilevel problems, user-defined functions). The applicability and flexibility of this novel software is demonstrated on a diverse set of examples. Lastly, EAGO is demonstrated to perform comparably to state-of-the-art commercial optimizers on a benchmarking test set.

Robust Stochastic Optimization Made Easy with RSOME

We present a new distributionally robust optimization model called robust stochastic optimization (RSO), which unifies both scenario-tree-based stochastic linear optimization and distributionally robust optimization in a practicable framework that can be solved using the state-of-the-art commercial optimization solvers. We also develop a new algebraic modeling package, Robust Stochastic Optimization Made Easy (RSOME), to facilitate the implementation of RSO models. The model of uncertainty incorporates both discrete and continuous random variables, typically assumed in scenario-tree-based stochastic linear optimization and distributionally robust optimization, respectively. To address the nonanticipativity of recourse decisions, we introduce the event-wise recourse adaptations, which integrate the scenario-tree adaptation originating from stochastic linear optimization and the affine adaptation popularized in distributionally robust optimization. Our proposed event-wise ambiguity set is rich enough to capture traditional statistic-based ambiguity sets with convex generalized moments, mixture distribution, φ-divergence, Wasserstein (Kantorovich-Rubinstein) metric, and also inspire machine-learning-based ones using techniques such as K-means clustering and classification and regression trees. Several interesting RSO models, including optimizing over the Hurwicz criterion and two-stage problems over Wasserstein ambiguity sets, are provided. This paper was accepted by David Simchi-Levi, optimization.

Axial compressor optimization method

In the presented work, an algorithm was developed for finding the optimal configuration of the blades of multi-stage axial compressors using 3D CFD modeling as the main tool and using commercial optimization programs. When developing the algorithm, special attention was paid to the development of a method for parameterizing the shape of the blade and a program based on it, which allow you to automatically change the shape of the blade of the axial compressor. They were used by the authors during optimization as a tool that converts variable parameters into the “new” blade geometry. The created algorithm can be used to improve the basic parameters of the compressor (efficiency, pressure ratio, mass flow rate, etc.) due to the correction of the shape of the blade profiles and their position relative to each other. In this case, the algorithm considers the possible presence of various constraints.

Modular transit: Using autonomy and modularity to improve performance in public transportation

In this paper we investigate a new form of automated public transportation, named ‘modular transit’, configured to overcome the shortcomings of the traditional bus, including the first- and last-mile problem, low occupancy, and low levels of comfort, accessibility, and flexibility. The modular transit system consists of a set of trailer modules who can travel locally to serve demand and connect travelers to main modules for long-distance trips. We mathematically model this system on a time-expanded network, thereby reducing the size of the optimization problem and rendering the problem amenable to being solved with commercial optimization engines. We conduct extensive numerical experiments and sensitivity analyses to study the performance of modular buses under various configurations. Finally, we compare the modular transit service with a door-to-door shuttle service as benchmark to showcase the benefits of modular transit.

Using a Hybrid Evolutionary Algorithm for Solving Signal Transmission Station Location and Allocation Problem with Different Regional Communication Quality Restriction

This study aims to investigate the signal transmission station location-allocation problems with the various restricted regional constraints. In each constraint, the types of signal transmission stations and the corresponding numbers and locations are to be decided at the same time. Inappropriate set up of stations is not only causing the unnecessary cost but also making the poor service quality. In this study, we proposed a hybrid evolutionary approach integrating the immune algorithm with particle swarm optimization (IAPSO) to solve this problem where each of the regions is with different maximum failure rate restrictions. We compared the performance of the proposed method with commercial optimization software LINGO®. According to the experimental results, solutions obtained by our IAPSO are better than or as well as the best solutions obtained by LINGO®. It is expected that our research can provide the telecommunication enterprise the optimal/near-optimal strategies for the setup of signal transmission stations.

Failure Mitigation and Restoration in Interdependent Networks via Mixed-Integer Optimization

We propose a new optimization model for determining optimal mitigation and restoration strategies for coupled interdependent networks in the context of preserving and/or restoring the maximum flow through the entire networked system, subject to cascading node failures that may be caused by disruptions of a subset of “seed nodes” at an initial time step. Previous related studies mainly focused on “static” strategies to mitigate cascading failures. However, our model allows one to identify “dynamic” strategies for step-by-step failure propagation, given initial seed node disruptions. Moreover, the proposed model accounts for backup arc capacity and node fortification to mitigate the impact of further failure cascades on network performance. The objective is to restore network performance during a finite recovery planning horizon at total minimal cost. We formulate this problem by mixed-integer optimization, and derive valid inequalities using the substructure of the problem. We report a summary of computational experiments to demonstrate the strength and effectiveness of the inequalities when compared to solving the problem with a commercial optimization solver.

The Time-dependent Electric Vehicle Routing Problem: Model and solution

We study a new problem named the Time-dependent Electric Vehicle Routing Problem (TDEVRP) which involves routing a fleet of electric vehicles to serve a set of customers and determining the vehicle’s speed and departure time at each arc of the routes with the purpose of minimizing a cost function. We propose an integer linear programming (ILP) model to formulate the TDEVRP and show that the state-of-the-art commercial optimizer (CPLEX) can only solve instances of very limited sizes (with no more than 15 customers). We thus propose an iterated variable neighbourhood search (IVNS) algorithm to find near-optimal solutions for larger instances. The key ingredients of IVNS include a fast evaluation method that allows local search moves to be evaluated in constant time O(1), a variable neighbourhood descent (VND) procedure to optimize the node sequences, and a departure time and speed optimization procedure(DSOP) to optimize the speed and departure time on each arc of the routes. The proposed algorithm demonstrates excellent performances on a set of newly created instances. In particular, it can achieve optimal or near-optimal solutions for all small-size instances (with no more than 15 customers) and is robust for large-size instances where the gap between the average and the best solution value is consistently lower than 2.38%. Additional experimental results on 40 benchmark instances of the closely related Time-Dependent Pollution Routing Problem indicate that the proposed IVNS algorithm also performs very well and even discovers 39 new best-known solutions (improved upper bounds).

Determinación del amortiguamiento independiente de la frecuencia en estructuras civiles incluso en la situación de modos de vibración muy próximos aplicando técnicas de optimización

Specific computer programs for identification in modal analysis of structures are not economical, and they may not always be available. This paper presents a technique for simple optimization, getting fast and quality results, in the estimation of the damping ratios for each separate mode, and that can be resolved with a demo version (downloadable for free from the internet) of commercial optimization software. It is suitable for low levels of structural damping (or non-frequency-dependent damping), which are those that appear in large structures. Likewise, it is not necessary for the modes to be separate, or even that the magnitude of the near modes be less than that of those with which we are working; within the algorithm movable residual complements optimize their position according to the frequency and vertical axes (the response magnitude), to take into account the influence of the modes outside the considered range. In addition, it is not very sensitive to the presence of noise in the signal.

A Critical Review and Assessment of Different Thermoviscoplastic Material Models for Simultaneous Hot/Cold Forging Analysis

The simultaneous hot/cold forging is an innovative production process, taking advantage of the high accuracy for cold forming and low forces for hot forming. However, the choice of a suitable material model for such a large temperature range is a difficult issue and insufficiently regarded. Hence, the aim of this contribution is a critical review and assessment of the prediction capability and accuracy of three already existing thermo-viscoplasticity models. Therefore, the simulation results of the Bammann, Chiesa and Johnson (BCJ) model, the Evolving Microstructural M odel of I nelasticity (EMMI) and a recently proposed user defined constitutive model by Bröcker and Matzenmiller, based on an enhanced concept of rheological elements, are compared to test data considering a large range from room temperature up to approximately 1400 K (1127 ∘C). All three material models may represent the thermo-viscoplastic characteristics of metals, whereby each investigated material model comprises different approaches for the temperature dependency of the initial yield stress, nonlinear isotropic hardening, and strain rate sensitivity. All material parameters are identified with the test data of the low alloy steel 50CrV4/51CrV4, the case hardening steel 16MnCr5, the low carbon steel C15 and the aluminium alloy AlMgSi1 by using the commercial optimisation software LS-OPT. The prediction capability and accuracy of each model is evaluated on the basis of the mean squared error by means of a comparsion of real and predicted stress-strain curves for the four different metals. Finally, an industrial oriented hot/cold forging process for the production of a gear shaft made of the low alloy steel 51CrV4 is simulated with LS-DYNA using the three material models and, subsequently, their performance is discussed. As achievement of this model assessment, suitable as well as inappropriate temperature dependent approaches are identified for this large temperature range providing new insights into suitable material models for the analysis of a simultaneous hot/cold forging process.

Predicting solutions of large-scale optimization problems via machine learning: A case study in blood supply chain management

Practical constrained optimization models are often large, and solving them in a reasonable time is a challenge in many applications. Further, many industries have limited access to professional commercial optimization solvers or computational power for use in their day-to-day operational decisions. In this paper, we propose a novel approach to deal with the issue of solving large operational stochastic optimization problems (SOPs) by using machine learning models. We assume that decision makers have access to facilities to optimally solve their large-scale optimization model for some initial and limited period and for some test instances. This might be through a collaborative project with research institutes or through short-term use of high-performance computing facilities. We propose that longer term support can be provided by utilizing the solutions (i.e., the optimal value of the actionable decision variables) of the stochastic optimization model from this initial period to train a machine learning model to learn optimal operational decisions in the future. In this study, the proposed approach is employed to make decisions on transshipment of blood units in a network of hospitals. We compare the decisions learned by several machine learning models with the optimal results obtained if the hospitals had access to commercial optimization solvers and computational power, and with the hospital network’s current empirical heuristic policy. The results show that using a trained neural network model reduces the average daily cost by about 29% compared with current policy, while the exact optimal policy reduces the average daily cost by 37%. Although optimization models cannot be fully replaced by machine learning, our proposed approach while not guaranteed to be optimal can improve operational decisions when optimization models are computationally expensive and infeasible for daily operational decisions in organizations such as not-for-profit and small and medium-sized enterprises.

Optimized dispatching based on wind-photovoltaic-hydropower-thermal-bundled strategy

The rapid development of wind power and photovoltaic is conducive to optimizing the energy structure and resolving fossil energy crisis, in response to the strategic direction of energy saving and emission reduction in China. However, the intermittence and fluctuation of wind, photovoltaic and other renewable energy sources pose greater challenges to the secure and stable operation of the power grid. Therefore, it is of theoretical significance and practical value to study the optimal dispatching of power system with wind and photovoltaic large-scale connected to grid. This work proposes an optimal scheduling strategy based on wind-photovoltaic-hydropower-thermal bundled according to the energy sources reasonable allocation proportion. The strategy gives full play to the complementary characteristics of energy, and realizes the comprehensive optimization of system peak shaving, economic cost and environmental benefit. The bundled power configuration layer defines the bundled fitness index, which takes into account the comprehensive influences of conventional unit utilization rate, load tracking degree and wind power abandonment. Based on the commercial optimization software CPLEX, the output of conventional hydropower units and the combination of thermal power units are solved. Finally, the feasibility of the model is verified by a case study.

Optimization Model of Key Equipment Maintenance Scheduling for an AC/DC Hybrid Transmission Network Based on Mixed Integer Linear Programming

The unbalanced distribution of resource and consuming centers in China has prompted the AC/DC hybrid transmission technology. The maintenance scheduling of an AC/DC hybrid transmission network is the key technology to ensure its safety and reliability. In this study, the mutual influence mechanism of an AC/DC system in a maintenance period was analyzed in detail. The overhead transmission line and transformer are key equipment within an AC/DC hybrid transmission network, and an optimization model of the key equipment maintenance scheduling was established. The objective of the model was to improve the system reliability during the maintenance scheduling. By considering the constraints of maintenance cost, maintenance resources, and maintenance workload, the maintenance scheduling of overhead transmission lines and transformer branches was obtained. The over-limit situation of power flow and the weakness of the system during the maintenance period was evaluated. The “double-layer substitution method” was adopted to convert the nonlinear constraints into its bilinear formulation such that it could then be solved. The random number sampling method was used to quantify the system reliability, and the commercial optimization software was used to solve the optimized scheduling. Based on the improved IEEE RTS-79 system and the Hubei Province electrical system, the simulation results showed the effectiveness of the proposed method.

A deterministic model for the transshipment problem of a fast fashion retailer under capacity constraints

In this paper we present a novel transshipment problem for a large apparel retailer that operates an extensive retail network. Our problem is inspired by the logistics operations of a very large fast fashion retailer in Turkey, LC Waikiki, with over 475 retail branches and thousands of products. The purpose of transshipments is to rebalance stocks across the retail network to better match supply with demand. We formulate this problem as a large mixed integer linear program and develop a Lagrangian relaxation with a primal–dual approach to find upper bounds and a simulated annealing based metaheuristic to find promising solutions, both of which have proven to be quite effective. While our metaheuristic does not always produce better solutions than a commercial optimizer, it has consistently produced solutions with optimality gaps lower than 7% while the commercial optimizer may produce very poor solutions with optimality gaps as high as almost 300%. We have also conducted a set of numerical experiments to uncover implications of various operational practices of LC Waikiki on its system’s performance and important managerial insights.

Solving the facility location and fixed charge solid transportation problem

In this paper, a new variant of the Solid Transportation Problem (STP) that incorporates both facility location and Fixed Charge Solid Transportation Problem (FCSTP) is presented with significant applications in logistics. It integrates decisions of diverse planning horizons: operational, tactical and strategic. The problem is termed Fixed Charge Solid Location and Transportation Problem (FCSLTP). Benchmark data obtained from the literature was extended for experimentation purposes. Solution to the FCSLTP was obtained using CPLEX commercial optimization solver. A Lagrange Relaxation Heuristic (LRH) was developed as an alternative solution for users not possibly having access to CPLEX. We further defined an equivalent FCSLTP in the main paper and termed this as FCSTP-EQ. The FCSTP-EQ was compared to our FCSLTP to investigate possible cost savings with both formulations. Results obtained showed CPLEX outperforming the Lagrange relaxation heuristic developed both in the upper bound and lower bound generation for the problem sizes considered. Additionally, the cost savings obtained using the FCSLTP was consistently better than the FCSTP-EQ. The upper bound generation capability of Lagrange relaxation could possibly be improved by using better search methods such as metaheuristics. Under certain conditions, the FCSTP could feasibly be used as a starting solution to solve the FCSLTP.

A Mixed Integer Linear Programming Model for Rolling Stock Deadhead Routing before the Operation Period in an Urban Rail Transit Line

In an urban rail transit line, train services are performed by the rolling stocks that are initially stored at depots. Before the start of the operation period, rolling stocks consecutively leave the depots and run without passengers (deadhead routing) to the origin station of their corresponding first departure train service in an operation day (first train service) using either direct or indirect routes. This paper investigates the rolling stock deadhead routing problem in an urban transit line with multiple circulation plans, depots, and rolling stock types. Given the rolling stock circulation plans, the problem is to identify a deadhead route for the rolling stock required by the train services to cover the initial operation. By pregenerating all direct and indirect candidate deadhead routes in a polynomial manner, the problem is then nicely formulated as a mixed integer linear programming (MILP) model to minimize the total deadhead mileages. A real-world case from the urban rail transit line 3 of Chongqing in China is adopted to test the proposed method. Computational results demonstrate that the problems of large-scale instances can be quickly solved to optimality by commercial optimization solvers on a personal computer. In addition, our optimization method is better than the empirical practices in terms of the solution quality. Meanwhile, alternative measures can further decrease the total deadhead mileages according to the proposed model, e.g., opening idle switch stations and prolonging the time that is used for the rolling stock departure. Finally, the model is further extended to consider operating costs, and more computation cases are tested for better adapting to the practical operating conditions.

An Optimal Generation Scheduling Approach Based on Linear Relaxation and Mixed Integer Programming

This paper proposes an optimal generation scheduling approach based on linear relaxation and mixed integer programming, which is used to solve the generation dispatch problem. The quadratic transmission loss constraint of each transmission line is converted into linear constraints by using the linear relaxation and mixed integer programming technique. Consequently, the original optimal generation scheduling problem is formulated as a quadratic programming or mixed integer quadratic programming problem that can be solved by commercial optimization solver. In order to improve the efficiency of algorithm, this paper further analyses the generation scheduling model and deletes the redundant variables and constraints. Three test systems, including IEEE 30-node system, IEEE 118-node system, and Polish 2746-node system, are employed to examine the effectiveness of the proposed method. The comparative results obtained by the proposed method, quadratically constrained quadratic programming method (QCQP), and solving constraint integer programs solver (SCIP) verify the effectiveness of the proposed method in solving the optimal generation scheduling problem.

A High-speed Train Timetable Rescheduling Approach in case of Disturbances

This paper from a macroscopic viewpoint develops a train timetable rescheduling approach on a single high-speed railway line under disturbances, i.e. inevitable train delays in the duration of the train operation. A mixed-integer linear programming model is formulated to minimize the arrival delay and the departure delay altogether. The commercial optimization software CPLEX is adopted in an effort to seek the optimal solution in an acceptably short time required in the real-time rescheduling process. The proposed approach is further tested on a real-world case study and the numerical results show that compared with the results obtain by the traditional genetic algorithm, using CPLEX to solve the model can yield better solutions and consume the desired computation time, thereby demonstrating its effectiveness and efficiency.