Exact Solution Procedure Research Articles

A hybrid deep-learning-metaheuristic framework for bi-level network design problems

This study proposes a hybrid deep-learning-metaheuristic framework with a bi-level architecture for road network design problems (NDPs). We train a graph neural network (GNN) to approximate the solution of the user equilibrium (UE) traffic assignment problem and use inferences made by the trained model to calculate fitness function evaluations of a genetic algorithm (GA) to approximate solutions for NDPs. Using three test networks, two NDP variants and an exact solver as benchmark, we show that on average, our proposed framework can provide solutions within 1.5 % gap of the best results in less than 0.5 % of the time used by the exact solution procedure. Our framework can be utilized within an expert system for infrastructure planning to determine the best infrastructure planning and management decisions under different scenarios. Given the flexibility of the framework, it can easily be adapted to many other decision problems that can be modeled as bi-level problems on graphs. Moreover, we foreseen interesting future research directions, thus we also put forward a brief research agenda for this topic. The key observation from our research that can shape future research is that the fitness function evaluation time using the inferences made by the GNN model was in the order of milliseconds, which points to an opportunity and a need for novel heuristics that 1) can cope well with noisy fitness function values provided by deep learning models, and 2) can use the significantly enlarged efficiency of the evaluation step to explore the search space effectively (rather than efficiently). This opens a new avenue for a modern class of metaheuristics that are crafted for use with AI-powered predictors.

A genetic algorithm for the personnel task rescheduling problem with time preemption

In this paper, we study the personnel task rescheduling problem with time preemption. We assume a baseline task schedule has been composed some time in advance that has been rendered infeasible due to operational uncertainty. When restoring the schedule feasibility, the personnel planner takes several considerations into account encompassing the provided service level, resource stability, and task adherence. The latter stems from the possibility that in the problem under study tasks can be interrupted and resumed later, better known as time preemption. We propose a genetic algorithm complemented with local search techniques to compose an operational schedule in an effective manner. The genetic algorithm operates on a dedicated decoding mechanism to compose high-quality duties for individual workers efficiently. Computational experiments are conducted to benchmark the performance of the proposed procedure with other exact and (meta-)heuristic solution procedures, and to demonstrate the value of the algorithm design choices. Furthermore, the impact of preempting tasks in time is assessed by changing the objective function structure and the proportion of non-preemptive tasks.

Shipment planning and safety stock placement in maritime supply chains with stochastic demand and transportation times

This paper introduces and studies shipment planning and safety stock placement in bulk and semi-bulk maritime supply chains. This problem jointly optimizes the assignment of destinations to origins, shipment quantities of multiple products by determining the share of the contract by sea transport options, sailing speed, and multi-echelon safety stocks with the objective to minimize the expected total transportation and inventory cost. In the case of a serial system supplying a single product, we analytically characterize the effect of sailing speed and different time and cost parameters on optimal safety stock placement. For the general case, the integrated problem can be solved in four different ways. We present a mixed integer nonlinear program (MINLP) and the superior reformulation of the mixed integer conic quadratic integer program (MICQP) that can be solved using state-of-the-art solvers. Then, we propose two exact solution procedures that iteratively approximate the nonlinear terms in the objective function and constraints. Our numerical experiments illustrate the interdependence between safety stock placement, assignment decisions, and sailing speed. Results also show that it is important to adopt multi-stage inventory optimization and there is an added value in integrating shipment planning and safety stock placement. Furthermore, computational experiments demonstrate that all the solution approaches are alternatives to solving small instance sizes. For medium and large instances, the solvers are unable to provide quality solutions within one hour while the iterative procedures find optimal or near-optimal solutions in reasonable CPU times.

R-SALSA: A branch, bound, and remember algorithm for the workload smoothing problem on simple assembly lines

We consider a simple assembly line balancing problem with given cycle time and number of stations. A quadratic objective function based on a so-called smoothness index SX levels the workloads of the stations. For this problem, called SALBP-SX, only a few solution procedures have been proposed in literature so far. In this paper, we extend and improve the branch-and-bound procedure SALSA (Simple Assembly Line Smoothing Algorithm) of Walter et al. (2021) to a bidirectional branch, bound, and remember algorithm called R-SALSA (R for remember). Like SALSA, it is based on a dynamic programming scheme which pre-determines potential workloads of the stations and provides a construction plan for possible station loads. This scheme is extended by the new concept of supporters and preventers which significantly enhances branching, bounding, and logical tests. Furthermore, a tailored heuristic that searches for improved initial solutions, a bidirectional branching scheme and additional dominance rules are integrated. In extensive computational experiments, we find out that our new procedure clearly outperforms all former exact solution procedures on benchmark data sets with up to 1000 tasks.

Adaptive local search algorithm for solving car sequencing problem

The global competitive environment leads companies to consider how to produce high-quality products at a lower cost. Mixed-model assembly lines (MMAL) are often designed such that average station work satisfies the time allocated to each station, but some models with work-intensive options require more than the allocated time. Sequencing varying models in a mixed-model assembly line is the short-term decision problem that has the objective of preventing line stoppage resulting from a station work overload. Accordingly, a good allocation of models is necessary to avoid work overload. The car sequencing problem (CSP) is a specific version of the mixed-model sequencing problem that minimizes the work overload by controlling the sequence of models. In order to do that, CSP restricts the number of work-intensive options by applying capacity rules. Consequently, the objective is to find the sequence with the minimum number of capacity rule violations. In this study, we show that exact solution procedures are insufficient for application in industry. however, we provide five improved lower bounds for CSPLib instances by solving problems optimally with a subset of options. Additionally, we present four local search metaheuristics that are commonly used to solve CSP. The local search algorithms are compared over CSP benchmark instances, including CSPLib and ROADEF Challenge 2005. The computational experiments show that an Adaptive Local Search (ALS) provides a significant advantage by not requiring tuning on the operator weights due to its adaptive control mechanism. Moreover, results show that the algorithmic effort should focus on randomly exploring more non-deteriorated solutions instead of systematic search or spending time visiting deteriorated solutions to escape local optima.

On 3D exact free torsional-bending vibration and buckling of biaxially loaded isotropic and anisotropic Timoshenko beams with complex cross-section

This research reports on Three Dimensional (3D) exact free torsional-bending vibrations and buckling of Timoshenko beams possessing homogeneous and nonhomogeneous properties and complex cross-section. The proposed exact solution is derived from 3D elasticity equations. The Hamilton’s integral equation is initially employed to establish the 3D exact governing Partial Differential Equations (PDEs) of motion and buckling, taking into account the effect of biaxial load applied to Timoshenko beams possessing complex cross-section. The PDEs are then solved using integral transform and trigonometric series differentiation procedure. The current solution procedure does not require characteristic deformation function to be predetermined and has fast convergence. A root finding algorithm is proposed to screen and filter the discontinuity and breakdown points as well as imaginary roots of the determinant function associated with bending eigenfrequency and eigenbuckling matrices. Two algorithms are further developed to capture the 3D dynamic and buckling mode shapes of biaxially loaded Timoshenko beams without any restriction imposed on the complexity of cross-section and degree of material anisotropy. The accuracy and convergence of the proposed 3D exact solution are first investigated by results comparison with the experimental and theoretical results in the published literature for a particular case in which bending natural frequencies response and modes shapes of a free-free isotropic Timoshenko beam with rectangular cross-section are sought. Finally, the effect of material isotropy/anisotropy, cross-section complexity, and biaxial load on torsional-bending natural frequencies, critical buckling loads, and 3D vibration and buckling mode shapes are thoroughly explored using the proposed exact solution procedure and validated by Abaqus finite element package.

Approximations for many-visits multiple traveling salesman problems

A fundamental variant of the classical traveling salesman problem (TSP) is the so-called multiple TSP (mTSP), where a set of m salesmen jointly visit all cities from a set of n cities. The mTSP models many important real-life applications, in particular for vehicle routing problems. An extensive survey by Bektas (Omega34(3), 2006) lists a variety of heuristic and exact solution procedures for the mTSP that solve particular problem instances. In this work we consider a further generalization of mTSP, the many-visits mTSP, where each city v has a request r(v) of how many times it should be visited by the salesmen. This problem opens up new real-life applications such as aircraft sequencing, while at the same time it poses several computational challenges. We provide polynomial-time algorithms for several variants of the many-visits mTSP that compute constant-factor approximate solutions.

A constructive branch-and-bound algorithm for the project duration problem with partially renewable resources and general temporal constraints

This paper deals with the resource-constrained project scheduling problem with partially renewable resources and general temporal constraints with the objective to minimize the project duration. The consideration of partially renewable resources allows to integrate the decision about the availability of a resource for a specific time period into the scheduling process. Together with general temporal constraints, which permit to establish minimum and maximum time lags between activities, even more aspects of real-life projects can be taken into account. We present a branch-and-bound algorithm for the stated problem that is based on a serial schedule-generation scheme. For the first time it is shown how a dominance criterion can be applied on the associated generation scheme to reduce the start times in each scheduling step. To improve the performance of the solution procedure, we integrate consistency tests and lower bounds from the literature and devise new pruning techniques. In a comprehensive experimental performance analysis we compare our exact solution procedure with all available branch-and-bound algorithms for partially renewable resources. Additionally, we investigate a directly derived priority rule-based approximation method from our new enumeration scheme. The results of the computational study demonstrate the efficiency of our branch-and-bound algorithm and reveal that the derived approximation method is only suited to solve small- and medium-sized instances.

Benders decomposition for internal truck renewal decision in green ports

ABSTRACT To effectively decrease emissions and pollution emitted by equipment in container ports, many ports began to update equipment using diesel fuels to achieve the aim of green ports. This paper studies an internal truck renewal problem in container ports and proposes a two-stage stochastic programming model to optimally determine internal truck composition optimization adjustment including three renewal modes, i.e. purchasing, retrofitting, and chartering. An exact solution procedure based on Benders decomposition accelerating by Pareto-optimal cuts is developed for the proposed model. Given the problem background of Shanghai Yangshan Deep Water Port, comprehensive computational experiments are carried out to verify the effectiveness of the proposed mathematical model and the performance of the solution approach. According to the numerical experiments, some suggestions for the management of renewing internal trucks in green ports are summarized at the end of the paper.

Gas chromatograph calibration of gas mixtures using a versatile precision volumetric apparatus

A compact, volumetric apparatus was developed for accurate automated preparation of standard gas and gas-liquid mixtures for gas chromatograph detector calibration, with accuracies comparable to those from gravimetric or Coriolis flow methods. The method developed by the principal author is not an adaptation or extension of any other apparatus or technology, and measurements involve only stepper motor steps, temperature, and pressure ratios. Mixture preparation is accomplished via the displacement of gas between chambers in a highly uniform cylinder, separated by a movable piston. Piston movement, with piston end rods of exactly equal diameter, ensures that there is no change in interior volume, and the volume of gas displaced from the bottom into the top compartment is exactly proportional to the piston travel measured to within 10μm. The apparatus, operation, and previously unpublished measurements on common refinery gas mixtures over large concentration ranges are described in detail. These confirmed the accuracy and versatility of the apparatus and also the principle of no pressure change during mixture preparation, from sensitive pressure measurements. Conservative expanded uncertainties in prepared mixture mole fraction ranged from 0.001 to 0.002 over extended composition ranges. Absolute average deviations for the detector response factor for the mixtures ranged from 0.001 to 0.002. An exact new mathematical solution procedure permits the use of impure "pure" gases without loss of accuracy and can be applied to other procedures for standard gas mixture preparation. An exact expression is listed for determining "pure" gas purity.

A multi-method approach to scheduling and efficiency analysis in dual-resource constrained job shops with processing time uncertainty

In dual-resource constrained job shop scheduling, jobs have to be assigned to workers and machines. While the problem is notoriously hard in terms of computational complexity, additional practical difficulties arise from data uncertainty and worker efficiency variation. In this paper, we propose a methodological pipeline combining mathematical optimization, simulation, and data analysis to cope with these aspects over time. Accounting for uncertain worker processing times, we employ an iterative two-stage optimization-simulation approach: A first-stage optimization model determines an assignment of workers to jobs; in the second stage, the scheduling of this assignment is evaluated operationally using sampled realizations of worker processing times. Both stages are executed in an alternating fashion until no further improvement is possible in the average realized makespan. At the end of a work day, realized worker efficiencies are then measured in a slacks-based data envelopment analysis on the operations level. Workers learn about their individual efficiency and are prompted to reduce inefficiencies. The resulting overall methodology not only provides robustified schedules for dual-resource constrained job shops under uncertainty, but also reduces the impact of uncertainty over time by motivating workers to operate on the efficient frontier. Computational results are conducted in several settings with both heuristic and exact solution procedures for the second-stage dual-resource constrained job shop scheduling problem. The results demonstrate the versatility of the outline with respect to addressing uncertainty and worker inefficiency.

A partition-based branch-and-bound algorithm for the project duration problem with partially renewable resources and general temporal constraints

The concept of partially renewable resources provides a general modeling framework that can be used for a wide range of different real-life applications. In this paper, we consider a resource-constrained project duration problem with partially renewable resources, where the temporal constraints between the activities are given by minimum and maximum time lags. We present a new branch-and-bound algorithm for this problem, which is based on a stepwise decomposition of the possible resource consumptions by the activities of the project. It is shown that the new approach results in a polynomially bounded depth of the enumeration tree, which is obtained by kind of a binary search. In a comprehensive experimental performance analysis, we compare our exact solution procedure with all branch-and-bound algorithms and state-of-the-art heuristics from the literature on different benchmark sets. The results of the performance study reveal that our branch-and-bound algorithm clearly outperforms all exact solution procedures. Furthermore, it is shown that our new approach dominates the state-of-the-art heuristics on well known benchmark instances.

Twin-crane scheduling during seaside workload peaks with a dedicated handshake area

To enable the efficient division of labor in container yards, many large ports apply twin cranes, two identical automated stacking cranes each dedicated to one of the transfer zones on the seaside and landside. The use of a handshake area, a bay of containers that separates the dedicated areas of the two cranes, is a simple means to avoid crane interference. Inbound containers arriving in the transfer zone of one crane and dedicated to a stacking position of the other crane’s area are placed intermediately in the handshake area by the first crane and then taken over by the second crane, and vice versa for outbound containers. Existing research only evaluates simple heuristics and rule-based approaches for the coordination of twin cranes interconnected by a handshake area. For this setting, accounting for precedence constraints due to stacking containers in the handshake area, we derive exact solution procedures under a makespan minimization objective. In this way, a comprehensive computational evaluation is enabled, which benchmarks heuristics with optimal solutions and additionally compares alternative crane settings (i.e., without workload sharing and cooperation with flexible handover). We further provide insights into where to position the handshake area. Our results reveal that when planning is too simple (i.e., with a rule-based approach), optimality gaps become large, but with sophisticated optimization, the price of a simplified crane coordination via a handshake area is low.

Crowdshipping by employees of distribution centers: Optimization approaches for matching supply and demand

Seeing the huge success of sharing platforms such as Uber, Lyft, and Airbnb, where owners of under-used assets are connected with users willing to pay for the use of these assets, it is not surprising that retailers aim to transfer the basic idea of the sharing economy to their last-mile deliveries. In crowdshipping, the under-used assets are transport capacities of private drivers and the users are the retailers aiming for additional and cost-efficient delivery capacities for their home deliveries. A major drawback of crowdshipping is that retailers can hardly guarantee their promised delivery services when subcontracting individuals. To avoid this problem, different retailers are establishing crowdshipping platforms offering a reward to the employees of their distribution centers for crowdshipping online orders on their way back from work. We investigate the resulting optimization problem for matching crowdshipping supply and demand in this context. We present an efficient exact solution procedure based on Benders decomposition, which maximizes the number of matched shipments while considering the employees’ minimum expected earnings per time unit. This procedure is shown to solve instances of real-world size before a work shift is over and the shipments have to be loaded into the trunks of the employees’ cars. Furthermore, we show the impact of crowdshipping on all main stakeholders and identify critical success factors.

The Exact Solution Procedure for Resource Constrained Proposal Project Portfolio Problem

The Exact Solution Procedure for Resource Constrained Proposal Project Portfolio Problem

Static and dynamic characteristics of the post-buckling of fluid-conveying porous functionally graded pipes with geometric imperfections

In this study, the static and dynamic responses of functionally graded material (FGM) pipes with porosities and geometric imperfections are investigated. The material properties of the porous FGM pipe are assumed to vary continuously and smoothly along the radial direction based on the modified power-law distribution. The nonlinear equations of motion are derived on the basis of the Euler-Bernoulli beam hypothesis incorporating the effects of von Kármán nonlinearity and initial imperfection. Two general cases of pipes with movable and immovable ends are considered. Closed-form solutions for nonlinear critical buckling velocity and nonlinear stability behavior of system under different boundary conditions are proposed. Subsequently, the free vibration problem around the buckled configuration is solved as a eigenvalue problem, and the natural frequencies are calculated using a new exact solution procedure that considers the gyroscopic effect. The effects of important parameters including the initial imperfection, the power-law index, the porosity volume fraction, and geometric properties on buckling and post-buckling behavior of system are explored in numerical results.

On the p-hub interdiction problem

Hub location models are one of the basic concepts to model design problems for communication and traffic networks. These networks are often exposed to threats such as attacks or natural disasters. However, the literature on extensions of hub location models capable of taking such threats into account is scarce. In this article, we investigate the so-called multiple allocation p-hub r-interdiction problem, where a locator has to choose p hubs, knowing in advance that r<p of them will be interdicted. The objective is to minimize the total routing costs in the network after interdiction. This problem can also be interpreted as a minmax-robust p-hub location problem with an exponentially large uncertainty set containing the worst case for each choice of hubs. We present a new bi-level formulation for the problem and investigate its mathematical structure. Using these structural results, we propose the first exact solution procedure for the problem. We compute the optimal solutions for the well-known CAB-data set and compare them to heuristic results. Moreover, we investigate the complexity of the problem and show that already the interdiction problem for given hubs is NP-hard.

Economic lot-size problem for a cleaner manufacturing system with warm-up period

There are instances that production machines require a warm-up period to reach their anticipated productivity. This study extends an economic manufacturing quantity (EMQ) problem by considering warm-up issue in the model. Warming up the machine decreases production loss, emission, and machine depreciation. Therefore, this study helps industry to enhance the profitability and also to reduce the environmental impact by decreasing waste generation and improving machine efficiency. In this study, we divide our system into three subsystems based on the relationships between production and consumption. Then we provide a mathematical model for each subsystem (three in total). The first two models are single-item EMQ inventory problems and the third one is a multi-item single-machine EMQ problem. In the third model, a machine/facility manufactures some items under a limited manufacturing volume. The purpose of these proposed models is to find the optimum cycle length to minimize the total system cost that consists of manufacturing, inventory and setup costs. Finally, we propose exact solution procedures after proving the convexity of these mathematical models.

Optimizing the changing locations of mobile parcel lockers in last-mile distribution

To reduce congestion, environmental damage, and negative health impact in large urban areas plenty of novel concepts for last-mile distribution have been innovated in the recent years. The concept treated in this paper are mobile parcel lockers that are able to change their locations during the day, either autonomously or moved by a human driver. By relocating lockers their reach towards addressees also varying their whereabouts over the day can be increased. This paper optimizes the changing locations of lockers, such that customers are at some time during the planning horizon within a predefined range of their designated locker. Our aim is to minimize the locker fleet when satisfying all customers. We formulate the resulting mobile locker location problem and provide suited exact solution procedures. To asses the potential whether mobile lockers are a promising last-mile concept, worth the investment required to develop it to a market-ready solution, we benchmark the necessary fleet size of mobile lockers with the required number of their stationary counterparts. Our results show that considerable reductions are possible.

High-density storage with mobile racks: Picker routing and product location

In response to the scarce space in many urban areas, high-density storage has become a widely discussed topic in warehousing research and practice. We investigate a storage setting where mobile racks are mounted on rails, so that a strong engine moves whole blocks of racks aside, opening an aisle and enabling access to a specific rack. Moving the heavy racks takes a considerable amount of time and, consequently, it strongly affects the total pick time. We formalise the resulting operational picker-routing problem, which aims at routing the picker such that as few aisles as possible need to be accessed and the total distance covered is minimal. Moreover, we address the interdependent tactical product-location problem, which deals with deciding on the storage locations of the items to be picked. We present suitable exact and heuristic solution procedures for both problems. In a comprehensive computational study, we apply these algorithms to explore the interdependencies between product location and picker routing, and derive recommendations as to suitable storage policies in a mobile rack warehouse.