Binary Programming Model Research Articles

Optimizing speed of a green truckload pickup and delivery routing problem with outsourcing: Heuristic and exact approaches

Optimizing fuel consumption cost alongside truck speed decisions is crucial for transportation enterprises when making outsourcing decisions. However, existing research on truck fuel consumption optimization is not state-of-the-art, leading to suboptimal outsourcing outcomes. This study addresses a green truckload pickup and delivery problem with outsourcing, focusing on speed optimization and fuel consumption cost. We model the problem as a multi-attribute directed graph and propose an arc-based mixed-integer programming model and a set-partitioning binary programming model. We then analyze the monotonic properties of arc cost, simplify the set-partitioning model, and develop a mixed-integer programming-based heuristic, a branch-and-price algorithm, and a column-generation-based heuristic. To tackle the challenge of speed decisions in fuel consumption optimization, we design specific extension and dominance rules within a labeling algorithm. All algorithms are tested on several sets of instances. Numerical experiments demonstrate the effectiveness of the proposed models and algorithms.

Pre-DNNOff: On-Demand DNN Model Offloading Method for Mobile Edge Computing

Deep Neural Networks (DNNs) are critical for modern intelligent processing but cause significant latency and energy consumption issues on mobile devices due to their high computational demands. Moreover, different tasks have different accuracy demands for DNN inference. To balance latency and accuracy across various tasks, we introduce PreDNNOff, a method that offloads DNNs at a layer granularity within the Mobile Edge Computing (MEC) environment. PreDNNOff utilizes a binary stochastic programming model and Genetic Algorithms (GAs) to optimize the expected latency for multiple exit points based on the distribution of task inference accuracy and layer latency regression models. Compared to the existing method Edgent, PreDNNOff has achieved a reduction of about 10% in the expected total latency, and due to the consideration of different tasks’ varying requirements for accuracy, it has a broader applicability.

Partial reformulation-linearization based optimization models for the Golomb ruler problem

In this paper, we provide a straightforward proof of a conjecture proposed in \cite{Duxbury2021} regarding the optimal solutions of a non-convex mathematical programming model of the Golomb ruler problem. Subsequently, we investigate the computational efficiency of four new binary mixed-integer linear programming models to compute optimal Golomb rulers. These models are derived from a well-known nonlinear integer model proposed in \cite{Kocuk2019}, utilizing the reformulation-linearization technique. \modif{Finally, we provide the correct outputs of the greedy heuristic proposed in \cite{Duxbury2021} and correct some false conclusions stated or implied therein.}

Using Optimization Modeling to Determine Locations for Aerial Firefighting Resources Based on Wildfire Risk Data

The increase of the global mean temperature likely leads to more frequent and prolonged fire weather periods, with hot and dry conditions. This would also lead to increased frequency and magnitude of wildfires, and increased risk of spatial and temporal co-occurrence. A key to control and suppress wildfires during fire weather is a strong initial response, for which aerial firefighting resources can be used. This paper investigates the potential of optimization modeling to support pre-wildfire location planning of aerial firefighting resources, by developing a binary integer programing model and test it on Swedish case data. The model produces useful results given considerably less amount of available input data to determine the locations, compared with the manual planning. With relatively short solution times, it shows potential to support fast relocation of resources during sudden changes of circumstances, and to facilitate implementation of a standard operating procedure, with less expert knowledge dependence.

A robust mixed-integer binary programming model for operating theater scheduling to the patient and the surgeon under uncertainty in an open-heart Surgery Department

In hospitals, the surgical ward is both a cost and revenue center. In this ward, hospitals face challenges such as increasing demand, limited resources, and rising costs. Consequently, the decisions made have an implications effect on the hospital's performance. Therefore, in this paper a robust mixed-integer binary programming model is proposed with three objectives of maximizing the efficiency of available resources, minimizing the patients waiting time, and minimizing surgery costs that are formulated utilizing the augmented epsilon constraint approach. This model allocates the operating room to the patient and the surgeon and then obtains the required bed capacity inside the downstream units for stand-alone cardiac hospitals. This model includes different preferences for hospital, surgeon, and patient: waiting time, patient cancellations, tardiness, uncertainties in surgery durations, the patient operation start times, the overtime per working day, time windows, SICU beds, planning horizon, and the idle times of the surgeons, operating theater, and working day. The proposed model is solved using robust optimization to deal with stochastic. The proposed model is formulated on the stochastic programming method proposed by Bertsimas and Sim. In the proposed model, a rolling horizon method is used to reschedule the program after cancellation. The computational results illustrate that the rolling horizon method reduces waiting time and increases throughput. The results illustrate that the benefit obtained from the introduced model has improvements in reducing the surgery costs, and patient waiting time, and increasing the efficiency of available resources. This study has been performed at Shahid Rajaei Heart Hospital in Iran.

Integrated DANP and binary goal programming model in generating joint-decision making for packaging postponement and supplier selection

Integrated DANP and binary goal programming model in generating joint-decision making for packaging postponement and supplier selection

Column generation for the multi-port berth allocation problem with port cooperation stability

This paper proposes a multi-port berth allocation problem (MPBAP) under a cooperative environment, which aims to determine berthing times and berthing positions for all considered vessels arriving at multiple neighboring ports. The previous studies on the MPBAP (or the BAP with multiple ports) consider that multiple ports have established stable cooperation, while the port cooperation stability problem (PCSP) has not been addressed. This paper investigates the PCSP with the MPBAP, where our MPBAP further integrates the vessel diverting issue that vessels with excessive waiting times can be diverted to neighboring ports. For the PCSP, we investigate how to group multiple neighboring ports into different stable port groups, and then determine optimal port groups. For all possible port groups, we propose a mixed integer programming model for the MPBAP, and a column generation approach is devised to solve it. Based on optimal solutions of the MPBAP for various port groups, cooperative game theory is utilized to obtain stable port groups, and then the PCSP can be formulated as a binary programming model for determining optimal port groups. Numerical experiments are carried out to account for the efficiency and effectiveness of the proposed models and solution method.

Design Optimization of Stacked Pallet Load Units

The article deals with the problem of building stacked pallet load units consisting of at least two stackable pallet load units. Moreover, this article concerns the part of the flow of goods in distribution networks that is prepared at the place of initial assembly in the form of palletized loading units designed for the final receiver. Such a unit does not exceed the limits of permissible weight or height. The article proposes a single-criteria binary programming model in which the goal is to minimize the pallet spaces required to accommodate the constructed units. In addition to the classical parameters of acceptable weight and height of the units, the constraints also take into account the fragility of the goods placed on each unit, filling the top layer of each unit, and its height homogeneity. The model developed was verified on a test dataset, and the savings from the use of optimum construction of the stacked palletized cargo units were demonstrated through the conducted experiments.

An optimization model for solving the route clustering problem

Clustering models and algorithms are important to tackle large-scale transportation and optimization problems. Studies considered various clustering strategies to condense the sizes of highly complex problems as part of heuristic solution approaches. In this study, we develop an optimization model to solve the route clustering problem (RCP). In the RCP, a given route, consisting of a series of nodes to be visited with a particular sequence, is to be partitioned into clusters such that cluster connection node distances are maximized, i.e., connector nodes are desired to be as apart from each other as possible. Meanwhile, the total distance taken in each cluster is also capped. A binary programming model is formulated to solve the RCP, and the source code is available at https://gitlab.com/tcokyasar/rcp. The program takes a set of nodes with a given visiting order, number of clusters desired, and a within-cluster distance threshold. It then returns labels for each node indicating which cluster it is assigned.

Using Geopandas for locating virtual stations in a free-floating bike sharing system

Free-floating bike-sharing systems can have a positive influence on the mobility of urban centers and developing efficient localization strategies is crucial to avoid crowding at peak times and increase service availability. Our study aims to efficiently resolve the location of virtual bike stations in a Latin American city through a geospatial data wrangling methodology that allows us to respond opportunely to the potential demand forecasted for the city. This approach is implemented in Python, and it uses the Geopandas and LocalSolver libraries to determine locations for the virtual bike stations that maximize the system coverage. The decision-making process is supported by a binary integer mathematical programming model, and the instances are built from intercity travel surveys that provide realistic data based on travel demand. The developed decision support system prototype provides a recommendation about where virtual bike stations should be located during peak hours and improve general availability by more than 37%. Moreover, when the system's users participate in the relocation of bicycles, the model can eliminate up to 80% of the CO2 emissions and nearly 50% of the operational costs associated with the relocation process.

Joint planning of electric vehicle battery swapping stations and distribution grid with centralized charging

This paper presents a framework for optimal planning of battery swapping stations (BSS) in centralized charging mode. In this mode, the batteries are charged at a central charging station (CCS). Then they will be distributed among BSSs. Moreover, there is no charging equipment at BSSs, and depleted batteries are returned to the CCS to recharge. In this context, firstly, a probabilistic model is developed to estimate the power consumption profile of the CCS. Then, a planning framework comprised of linear and nonlinear parts is introduced to minimize the total investment and operation costs. In the linear part, a binary integer linear programing (BILP) model is proposed to determine the optimal place and grade of BSSs, considering the investment cost of BSSs as well as the batteries transportation costs. In the nonlinear part, which is solved by genetic algorithm (GA), a model is developed to find out which branches of the distribution network need to be reinforced to minimize the network reinforcement and energy loss costs. The developed models are implemented on the IEEE 69-bus network, and the results are examined under different scenarios. The obtained results verify the efficiency of the developed models.

검색광고 최적화 시스템: 키워드 효율성 분석 및 입찰가 최적화

This paper introduces an optimization system for search engine marketing. The system involves two major deciding factors in search engine marketing, i.e., a keyword configuration and a bidding strategy, with a goal of maximizing various performance indicators such as the number of impressions, clicks, and conversions. To this end, we first present a keyword efficiency analysis model based on the data envelopment analysis. The model draws relative keyword efficiencies for target performance indicators, and it provides a keyword configuration guide to advertisers. Second, we present a multi-objective binary programming model to find an efficient keyword bidding strategy under multiple target performance indicators and a budget. Also, an iterative solution approach is developed to consider its multi-objective and non-linear nature. The developed system is applied to real-world operations, and it is shown that our system provides significant benefits in operational efficiency.

Scheduling method for pairing night-shift and morning-shift duties on metro lines with complex structure

Scheduling the night-shift and morning-shift duties pairing plan (NMDPP) is a common process in Chinese metro crew management. Since metro crews work in a special working environment, sufficient rest is essential for them. NMDPP will affect the rest time of crews on metro lines with multiple depots and handover points. To improve the rest time of crews, this paper proposes a binary programming model to optimise the NMDPP. Moreover, a hybrid algorithm combining General Variable Neighbourhood Search (GVNS) with an Assignment Algorithm is designed to find high-quality solutions for this problem. Finally, computational experiments with both artificial data and real-life data are conducted. The results indicate that the GVNS can obtain high-quality solutions efficiently for various NMDPPs. Besides, the proposed method can effectively increase the rest time of crews compared to the practical method used in metro companies.

A binary fuzzy goal programming model with fuzzy parameters to select the fruits and vegetables market hall location for Istanbul

In urban areas, delivery of the products necessary to survive to the desired points has vital importance, and public distribution centers (PDCs) are one of the most important components of this system. In this paper, we present a hybrid method to analyze the locations of F&VMHs which is one of the PDCs types. Firstly, the alternative numbers have been decreased by interval-valued trapezoidal fuzzy grey relational analysis (IVTFGRA) method. Secondly, we develop a binary fuzzy goal programming (BFGP) model with fuzzy parameters to determine the most appropriate F&VMH locations by taking into consideration costs, arrival times and CO2 emission goals. Then, the BFGP model is converted to standard FGP model. In the last stage, the constraints with fuzzy parameters are transformed to crisp constraints with Peidro et al. (2010)’s methodology. The results show that current F&VMHs need to be moved to the locations that are more cost effective and out of the city center.

Factors affecting the presence of Arctic charr in streams based on a jittered binary genetic programming model

Arctic charr is one of the fish species most sensitive to climate change but studies on their freshwater habitat preferences are limited, especially in the fluvial environment. Machine learning methods offer automatic and objective models for ecohydrological processes based on observed data. However, i) the number of ecological records is often much smaller than hydrological observations, and ii) ecological measurements over the long-term are costly. Consequently, ecohydrological datasets are scarce and imbalanced. To address these problems, we propose jittered binary genetic programming (JBGP) to detect the most dominant ecohydrological parameters affecting the occurrence of Arctic charr across tributaries within the large subarctic Teno River catchment, in northernmost Finland and Norway. We quantitatively assessed the accuracy of the proposed model and compared its performance with that of classic genetic programming (GP), decision tree (DT) and state-of-the-art jittered-DT methods. The JBGP achieves the highest total classification accuracy of 90% and a Heidke skill score of 78%, showing its superiority over its counterparts. Our results showed that the dominant factors contributing to the presence of Arctic charr in Teno River tributaries include i) a higher density of macroinvertebrates, ii) a lower percentage of mires in the catchment and iii) a milder stream channel slope.

Scheduling External Trucks Appointments in Container Terminals to Minimize Cost and Truck Turnaround Times

Background: Scheduling the arrival of external trucks in container terminals is a critical operational decision that faces both terminal managers and trucking companies. This issue is crucial for both stakeholders since the random arrival of trucks causes congestion in the terminals and extended delays for the trucks. The objective of scheduling external truck appointments is not only to control the workload inside the terminal and the costs resulting from the excessive waiting times of trucks but also, to reduce the truck turnaround time. Methods: A binary programming model was proposed to minimize the waiting time cost, demurrage cost, and container delivery cost. Moreover, a sensitivity analysis was performed to compare various scenarios in terms of cost and to study to what extent the workload level is affected. The mathematical model was solved using Gurobi© 8.1.0 software. Results: 30 instances found in the literature were solved and evaluated in terms of the objective function value (i.e., cost) and truck turnaround time before and after controlling the workload inside the container terminal using the new proposed constraint. Conclusions: The obtained results showed a better distribution of the terminal workload, as well as a lower truck turnaround time that reduces the total cost.

A Novel Multi-Objective Nonlinear Discrete Binary Gaining-Sharing Knowledge-Based Optimization Algorithm

GSK algorithm is based on the concept of how humans acquire and share knowledge through their lifespan. Discrete Binary version of GSK named novel binary Gaining Sharing knowledge-based optimization algorithm (DBGSK) depends on mainly two binary stages: binary junior gaining sharing stage and binary senior gaining sharing stage with knowledge factor 1. These two stages enable BGSK for exploring and exploitation of the search space efficiently and effectively to solve problems in binary space. Besides, one of these practical applications is to optimally schedule the flights for residual stranded citizens due to COVID-19. The problem is defined for a decision maker who wants to schedule a multiple stepped trip for a subset of candidate airports to return the maximum number of residuals of stranded citizens remaining in listed airports while comprising the minimization of the total travelled distances for a carrying airplane. A nonlinear binary mathematical programming model for the problem is introduced with a real application case study, the case study is solved using (DBGSK).

Optimum periodic maintenance policy of repairable multi-component system with component reallocation and system overhaul

Motived by cost savings, this paper studies a new periodic maintenance policy for multi-component systems, for which multiple component reallocations and system overhauls are jointly implemented aperiodically at fixed times and components are minimally repaired immediately after failures in a life cycle. Different workloads or conditions of different positions can lead to different degradation processes of components, thus component reallocation can be used to balance the degradation between components at different positions, which has been widely studied. System overhaul can improve the conditions of components by imperfect or perfect repair. Component reallocation and system overhaul are mutually dependent and jointly affect the degradation of components and the maintenance cost of a system. In this paper, the failure rate functions of components are modeled using virtual age, and then a binary mixed integer nonlinear programming model is established to determine the optimal time and assignment for component reallocations, and the optimal time and degree for system overhauls by minimizing the long-run average maintenance cost of the system. Further, the number of system overhauls is proved to be finite, and a decomposition method is proposed. Numerical examples are provided to show the effectiveness of the joint of component reallocations and system overhauls.

Component rearrangement and system replacement for a system with stochastic degradation processes

Consider a system of multiple functionally-interchangeable components. These components degrade following non-homogeneous stochastic processes that are related to different workloads, usage rates, or operating environment. The unbalanced degradation levels of components affect the overall performance of the system. This paper studies a preventive maintenance policy based on component rearrangement, and the goal is to prolong the useful time of a system before its replacement or overhaul. In this model, the optimal component rearrangement is planned to execute at optimal time. The stochastic degradation models and reliability functions that incorporate the component rearrangement are built. Then a mixed binary nonlinear programming model is established to optimize the component rearrangement plan, rearrangement time, and system replacement time. The models are derived for each of the Wiener process, gamma process, and inverse Gaussian process, which are three most widely used stochastic degradation processes. The specified models are derived for k-out-of-n:F, series–parallel, and parallel–series systems. Furthermore, a hybrid approach is proposed that integrates permutation-based heuristic global search for solving a combinatorial subproblem and nonlinear optimization method for solving constrained continuous subproblems. The analytical results and numerical experiments demonstrate the efficiency of the models and solution approach and provide the insights of the component-rearrangement based maintenance policy.

A swarm intelligence graph-based pathfinding algorithm (SIGPA) for multi-objective route planning

Personalized tourist route planning (TRP) and navigation are online or real-time applications whose mathematical modeling leads to complex optimization problems. These problems are usually formulated with mathematical programming and can be described as NP hard problems. Moreover, the state-of-the-art (SOA) path search algorithms do not perform efficiently in solving multi-objective optimization (MO) problems making them inappropriate for real-time processing. To address the above limitations and the need for online processing, a swarm intelligence graph-based pathfinding algorithm (SIGPA) for MO route planning was developed. SIGPA generates a population whose individuals move in a greedy approach based on A∗ algorithm to search the solution space from different directions. It can be used to find an optimal path for every graph-based problem under various objectives. To test SIGPA, a generic MOTRP formulation is proposed. A generic TRP formulation remains a challenge since it has not been studied thoroughly in the literature. To this end, a novel mixed binary quadratic programming model is proposed for generating personalized TRP based on multi-objective criteria and user preferences, supporting, also, electric vehicles or sensitive social groups in outdoor cultural environments. The model targets to optimize the route under various factors that the user can choose, such as travelled distance, smoothness of route without multiple deviations, safety and cultural interest. The proposed model was compared to five SOA models for addressing TRP problems in 120 various scenarios solved with CPLEX solver and SIGPA. SIGPA was also tested in real scenarios with A* algorithm. The results proved the effectiveness of our model in terms of optimality but also the efficiency of SIGPA in terms of computing time. The convergence and the fitness landscape analysis showed that SIGPA achieved quality solutions with stable convergence.