Multi-objective Integer Programming Model Research Articles

A Multi-Objective Optimization Method for Maritime Search and Rescue Resource Allocation: An Application to the South China Sea

To effectively address the increase in maritime accidents and the challenges posed by the trend toward larger ships for maritime safety, it is crucial to rationally allocate the limited maritime search and rescue (MSAR) resources and enhance accident response capabilities. We present a comprehensive method for allocating MSAR resources, aiming to improve the overall efficiency of MSAR operations. First, we use long short-term memory to predict the number of future accidents and employ the K-medoids algorithm to identify the accident black spots in the studied area. Next, we analyze the multi-constraint conditions in the MSAR resource allocation process. A multi-objective integer programming model is constructed to minimize the response time and allocation cost. Finally, we use the non-dominated sorting genetic algorithm II (DNSGA-II) with Deb’s rules to solve the model, and we propose a multi-attribute decision optimization-based method for MSAR resource allocation. We found that the DNSGA-II exhibits better convergence and generates higher-quality solutions compared to the NSGA-II, particle swarm optimization (PSO), and enhanced particle swarm optimization (EPSO) algorithms. Compared with the existing MSAR resource emergency response system, the optimized scheme reduces the response time and allocation cost by 11.32% and 6.15%, respectively. The proposed method can offer decision makers new insights when formulating MSAR resource allocation plans.

Multi-product disassembly line balancing optimization method for high disassembly profit and low energy consumption with noise pollution constraints

Remanufacturing attains much attention from both industrial and academic sectors due to its beneficial roles in energy conservation and environment protection, where disassembly is a crucial part. To reach the comprehensive sustainability and global optimization of disassembling multiple end-of-life products, this paper suggests a multi-objective multi-product disassembly line balancing problem with considering disassembly profit, energy consumption and noise pollution simultaneously. According to the natures of the problem under consideration, a multi-objective integer programming model is constructed. Its goals are to reach maximum disassembly profit and realize minimum energy consumption while observing noise pollution requirements and resource constraints. Accordingly, a multi-objective group teaching optimization algorithm is specially devised. In it, rank and crowding distance methods are employed to partition the population into two groups. Moreover, precedence preserving crossover and mutation methods are severally used on the two groups to realize the teacher phase. Furthermore, to achieve the student phase, an adaptive local search method is applied to refine solutions in an external archive, and thus its exploitation ability is enhanced. By executing contrast experiments between the devised approach and its powerful competitors on a set of real-world test instances, the experimental results validate that it has highly-adaptive and well-superior performance in tackling the problem of concern.

Optimizing the ground intra-city express delivery network: An integrated multiple centrality assessment, multi-criteria decision-making, and multi-objective integer programming model

Optimization of an intra-city express delivery network from three to two levels is of great interest to suppliers and customers for reducing costs and improving service efficiency. One feasible solution is to identify critical nodes in the three-level network and upgrade them as transshipment facilities in the two-level one. However, traditional optimization models seldom combine empirical business data, composite metrics, and objective evaluation rules. We proposed an approach integrating empirical data, multi-criteria decision-making methods based on the real-world application of the SF Express Chengdu branch. We also developed a mathematical optimization model using statistical and operations management techniques combined with logistics expertise for a location decision. First, the appropriateness of each service point as a candidate transshipment facility is evaluated from internal and external perspectives by applying multiple centrality assessment from complex network theory and fuzzy Technique for Order Preference by Similarity to an Ideal Solution, respectively. Second, 16 candidate transshipment facilities are selected by combining these two ways. Then, a multi-objective integer programming model is built to obtain the optimal number, locations of transshipment facilities, and the corresponding service points covered by each transshipment facility. Using this multi-methodologic approach, we show that the optimized two-level network is economically feasible and simply applicable, with the total cost and average delivery time reduced by 18.41% and 6 h, respectively. This article is of practical significance and provides an important reference for optimizing ground express service networks for other large cities.

A Pareto-based discrete particle swarm optimization for parallel casting workshop scheduling problem with fuzzy processing time

The parallel casting workshop scheduling problem is essentially a type of unrelated parallel machine scheduling (UPMS) problem with fuzzy order processing time. In this paper, a tri-objective parallel casting workshop optimization model is investigated to minimize the order advance/delay penalty, makespan, and workload imbalance, and a formula of the solution scale with the number of orders and workshops is derived. In line with the multi-objective integer programming model, a new Pareto-based discrete particle swarm optimization (PDPSO) is proposed. In this algorithm, the particles are encoded with integers. A novel two-phase heuristic is developed for integer-encoded particle updates. The first phase determines the order assignment through a weighting vote, and the second phase sorts the orders according to their dominance in each workshop. Every particle’s update is simultaneously guided by the best compromise solution selected from the personal and global Pareto solution. Meanwhile, the Pareto simulated annealing strategy is introduced in PDPSO to enhance its exploration ability. Multiple simulations under different scales are tested to validate the effectiveness of our proposed model and algorithm. The results show that the proposed PDPSO outperforms the other two multi-objective algorithms and has large advantages in finding the Pareto frontier (PF) with an acceptable solution number and solving speed, especially for small and medium-sized instances.

A Bifactor Approximation Algorithm for Cloudlet Placement in Edge Computing

Emerging applications with low-latency requirements such as real-time analytics, immersive media applications, and intelligent virtual assistants have rendered Edge Computing as a critical computing infrastructure. Existing studies have explored the cloudlet placement problem in a homogeneous scenario with different goals such as latency minimization, load balancing, energy efficiency, and placement cost minimization. However, placing cloudlets in a highly heterogeneous deployment scenario considering the next-generation 5G networks and IoT applications is still an open challenge. The novel requirements of these applications indicate that there is still a gap in ensuring low-latency service guarantees when deploying cloudlets. Furthermore, deploying cloudlets in a cost-effective manner and ensuring full coverage for all users in edge computing are other critical conflicting issues. In this article, we address these issues by designing a bifactor approximation algorithm to solve the heterogeneous cloudlet placement problem to guarantee a bounded latency and placement cost, while fully mapping user applications to appropriate cloudlets. We first formulate the problem as a multi-objective integer programming model and show that it is a computationally NP-hard problem. We then propose a bifactor approximation algorithm, ACP, to tackle its intractability. We investigate the effectiveness of ACP by performing extensive theoretical analysis and experiments on multiple deployment scenarios based on New York City OpenData. We prove that ACP provides a (2,4)-approximation ratio for the latency and the placement cost. The experimental results show that ACP obtains near-optimal results in a polynomial running time making it suitable for both short-term and long-term cloudlet placement in heterogeneous deployment scenarios.

A robust strategy to address the airport gate assignment problem considering operators’ preferences

The airport gate assignment problem (AGAP) has been well studied in the field of airport transportation planning and operations management. For airport operators, it is important to assign flight activities to limited gates economically, and the robustness of the assignment is also a key issue. In this paper, we address the problem of assigning a number of flight activities, including arrival, parking, and departure, to different gates during the operating period. A robust strategy is developed by considering the airport operators’ tow-averse attributes. To solve the problem, firstly, a multi-objective integer programming model is proposed. There are two objectives in the model, one is to maximize the operators’ preferences characterized by scores, and the other is to minimize robustness cost caused by the changes of flight schedule. Secondly, a two-phase Monte Carlo based NSGA-II (TPMC-NSGA II) algorithm is designed, which effectively combines the Monte Carlo characters and the NSGA-II algorithm. Furthermore, a set of computational analyses are conducted. The results show that the proposed model and algorithm are capable of solving the airport gate assignment problem with an economical, robust, and preferred output.

An integrated optimization approach using a collaborative strategy for sustainable cities freight transportation: A Case study

• Logistics collaboration is studied in the planning of sustainable city freight transportation. • An integrated and collaborative approach is proposed for sustainable freight logistics networks. • Three sustainability dimensions are considered. • A case study is conducted to show the applicability of proposed approach and the effects of collaboration on the sustainable development of the society and the environment. In recent years, the increasing freight transportation activities has caused extensive economic, environmental and social impacts on society. Therefore, it becomes necessary for logistics companies to find high-performance strategies to enhance their sustainability. Collaboration between companies appears as one of the promising solution that improves the freight transport efficiency of modern cities. Existing studies on collaborative transport did not sufficiently account for sustainability aspects and they mainly discuss the independent planning of decision-making problems with economic objectives. However, collaboration an integrated decision-making process can significantly ameliorate the effectiveness of urban transportation systems. This study addresses the issue of sustainable freight transportation planning by formulating and solving a collaborative and integrated two-echelon inventory, location and routing problem (2E-CILRP). The 2E-CILRP is formulated as a multi-objective integer programming model that minimizes logistics costs, C O 2 emissions and accident rate. A hybrid heuristic based on machine learning is also introduced to solve the studied problem. The proposed approach combines k -means clustering and genetic algorithms. Comparison of the obtained results with those provided with exact method reveals that the developed approach is more efficient and more practical for designing integrated and collaborative networks with large-sized data. A case study of four agri-food SMEs in France is investigated in order to demonstrate the sustainable benefits of the developed optimization approach. The obtained results suggest that the developed approach can significantly reduce the level of C O 2 emissions, logistics costs and accident rate caused by transportation in cities.

Optimal decision of multiobjective and multiperiod anticipatory shipping under uncertain demand: A data-driven framework

Anticipatory shipping helps to reduce the waiting time of online customers to receive their products. Present studies on anticipatory shipping mainly consider a single period and ignore the waiting time saved for customers. This paper develops a data-driven framework to investigate the multiperiod anticipatory shipping problem with the objectives of minimizing the cost of online retailers and maximizing the saved waiting time of customers. First, we propose a dual-process sales forecasting framework that employs five machine learning algorithms to forecast online retailers’ daily sales using clickstream data and historical sales data. Then, we build a multiperiod and multiobjective integer programming model based on the forecasting sales and forecasting errors to explore the optimal quantity and time of products of anticipatory shipping. Finally, using TOPSIS, Shannon entropy, and LINMAP decision-making methods, the final optimal solution is selected from the Pareto set obtained by the NSGA-II algorithm. The case study results show that anticipatory shipping saves 5.96% cost for the online retailer and 1.69 days of waiting time on average for the customer compared with non-anticipatory shipping. Moreover, performing anticipatory shipping is especially beneficial in the case of high inventory holding cost, large distribution center capacity, and long transportation duration.

A predictive and prescriptive analytical framework for scheduling language medical interpreters.

Although most hospitals in the United States provide medical services in English, a significant percentage of the U.S. population uses languages other than English. Mostly, the interpreting department in a hospital finds interpreters for limited English proficiency (LEP) patients, including inpatients, outpatients, and emergency patients. The department employs full-time and part-time interpreters to cover the demand of LEP patients. Two main challenges are facing an interpreting department: 1) there are many interpreting agencies in the market in which part-time interpreters can be chosen from. Selecting a part-time interpreter with the best service quality and lowest hourly rate makes the scheduling process difficult. 2) the arrival of LEP emergency patients must be predicted to make sure that LEP emergency patients are covered and to avoid any service delay. This paper proposes a framework for scheduling full-time and part-time interpreters for medical centers. Firstly, we develop a prediction model to forecast LEP patient demand in the emergency department (ED). Secondly, we develop a multi-objective integer programming (MOIP) model to assign interpreters to inpatient, outpatient, and emergency LEP patients. The goal is to minimize the total interpreting cost, maximize the quality of the interpreting service, and maximize the utilization of full-time interpreters. Various experiments are conducted to show the robustness and practicality of the proposed framework. The schedules generated by our model are compared with the schedules generated by the interpreting department of a partner hospital. The results show that our model produces better schedules with respect to all three objectives.

Rank-Based Solution Methods and their Applications in Determination of Non-Dominated Points Set For A Multi-Objective Integer Programming Model

For any single-objective mathematical programming model, rank-based optimal solutions are computationally difficult to find compared to an optimal solution to the same single-objective mathematical programming model. In this paper, several methods have been presented to find these rank-based optimal solutions and based on them a new rank-based solution method (RBSM) is outlined to identify non-dominated points set of a multi-objective integer programming model. Each method is illustrated by a numerical example, and for each approach, we have discussed its limitations, advantages and computational complexity.

Two-echelon collaborative multi-depot multi-period vehicle routing problem

Collaboration among logistics operators offers an effective way to improve customer service and freight transportation efficiency. One form of collaboration is the sharing of logistics resources (e.g., delivery vehicles). Existing studies on collaboration and resource sharing have not sufficiently accounted for the time frame within which collaboration happens, and they mostly assume that collaboration among logistics operators occurs in a single time period. This study addresses the issue of collaboration across multiple time periods, in which logistics resources can be shared between different service time periods, by formulating and solving a two-echelon collaborative multi-depot multi-period vehicle routing problem (2E-CMDPVRP). The 2E-CMDPVRP is formulated as a multi-objective integer programming model that minimizes logistics operational costs, service waiting times, and number of vehicles in multiple service periods. A hybrid heuristic algorithm with three-dimensional k-means clustering and improved reference point-based non-dominated sorting genetic algorithm-III (IR-NSGA-III) is proposed to solve the multi-objective optimization model. Comparative analysis results show that the proposed IR-NSGA-III outperforms existing algorithms in terms of the minimization of logistics operational costs, service waiting times, and number of vehicles. The minimum costs remaining saving method and strictly monotonic path selection principle are combined to determine the best profit allocation schemes and the optimal coalition sequences. An empirical case study of a multi-depot multi-period logistics network in Chongqing, China, is used to validate the proposed model and solution algorithm. Results suggest that the proposed collaborative mechanism with multi-depot and multi-period resource sharing can improve the degree of synchronization within a collaborative logistics network, and thus contribute to sustainable development of urban logistics distribution networks.

Considering Section Balance in an Integer Optimization Model for the Curriculum-Based Course Timetabling Problem

University course timetabling is a complex and time-consuming duty that every educational institution faces regularly. It consists of scheduling a set of lectures in predefined time slots so as to avoid student conflicts, meet teacher and room availability, and manage several institution-specific operational rules. In this paper, we schedule courses based on a curriculum, that is, before the students’ registration. Unlike other curriculum-based models, the proposed model considers two practical aspects when managing the conflicts between lectures: (i) it schedules sections of subjects so that each section is evenly likely to be registered by the students, and (ii) it considers the failure rates and periodicity a subject is taught. We present a multi-objective integer programming model that maximizes the use of specific time slots, the symmetry in which the lectures of a course are scheduled during a week, and the flexibility for straggler students to take courses. The model is solved using commercial software, and it is applied to a real course-timetabling problem. We show the advantages of its use by comparing the model’s solution with the actual solution obtained by the manual scheduling.

Integrated framework of system dynamics and meta-heuristic for multi-objective land use planning problem

Land use optimization as a resource allocation problem can be defined as the process of assigning different land uses to a region. Sustainable development also involves the exploitation of environmental resources, investment orientation, technology development, and industrial changes in a coordinated form. This paper studies the multi-objective sustainable land use planning problem and proposes an integrated framework, including simulation, forecasting, and optimization approaches for this problem. Land use optimization, a multifaceted process, requires complex decisions, including selection of land uses, forecasting land use allocation percentage, and assigning locations to land uses. The land use allocation percentage in the selected horizons is simulated and predicted by designing a System Dynamics (SD) model based on socio-economic variables. Furthermore, land use assignment is accomplished with a multi-objective integer programming model that is solved using augmented e-constraint and non-dominated sorting genetic algorithm II (NSGA-II) methods. According to the results of the SD model, land use changes depend on population growth rate and labor productivity variables. Among the possible scenarios, a scenario focusing more on sustainable planning is chosen and the forecasting results of this scenario are used for optimal land use allocation. The computational results show that the augmented e-constraint method cannot solve this problem even for medium sizes. The NSGA-II method not only solves the problem at large sizes over a reasonable time, but also generates good-quality solutions. NSGA-II showed better performance in metrics, including number of non-dominated Pareto solutions (NNPS), mean ideal distance (MID), and dispersion metric (DM). Integrated framework is implemented to allocate four types of land uses consisting of residential, commercial, industrial, and agricultural to a given region with 900 cells.

Shared Bikes Scheduling Under Users’ Travel Uncertainty

With the rise of green concept, shared bikes are booming. The accompanying unbalanced scheduling problem is a scientific problem that needs to be solved urgently. Aiming at the problem of shared bikes scheduling with travel uncertainty, a multi-objective integer programming model is established based on the consideration of static demand of fix time period, station capacity limit, penalty cost and other practical factors. In addition, this paper gives the basic formula to calculate the parameters in the model. An algorithm based on “ant colony algorithm” is then given to solve the model. Taking the massive data provided by the “Mobike” company in 2017 as an example, this paper uses the program analysis data to prove the feasibility and effectiveness of the model and get the initial optimization plan. Finally, the data simulation is carried out to verify the feasibility and accuracy of the optimization scheme and the optimization scheme is adjusted accordingly to obtain the final optimization scheme. The research results show that the final optimization scheme proposed in this paper has certain reference value for the scheduling problem of Shanghai “Mobike”.

Routing optimization of the emergency supplies distribution vehicles using NSGA-II algorithm: a case study

In recent years, emergencies, including natural disasters and other public disasters, have seriously threatened the lives and property security of people all over the world. In order to save more people’s lives and reduce the losses caused by disasters, many researchers have carried out intensive study on the distribution of emergency supplies. This paper first studies Location-Routing Problem(LRP) of alternative logistics centers and material demand points, and constructs a multi-objective integer programming model based on the actual situation. The model consists of two objectives: (1) the minimum total transportation time; (2) the maximum total emergency material satisfaction. Then an algorithm is introduced to solve the above model: NSGA-II. Finally, the emergency materials distribution in Hubei Province is taken as an example to verify the applicability and effectiveness of the above method and the models.

Research on Two-stage Multi-objective Integer Programming Model of Helicopter Distribution Materials in Emergency Logistics

Based on the earthquake disaster, this paper introduces the JIT just-in-time thinking of logistics management, and builds a three-level supply chain network consisting of helicopters, warehouses and material demanders. On this basis, aiming at maximizing the seismic performance, radiation range and optimal helicopter dispatching plan of the material reserve, and establishing the warehouse location and material distribution as the decision variables, a two-stage multi-objective integer programming model is established. The feasibility and effectiveness of the model are verified by specific case analysis, and the efficiency and effect of material distribution in the earthquake disaster reduction system are improved. In addition, according to the actual earthquake disaster area, the model was improved by the ant colony optimization algorithm.

Performance improvement of energy consumption, passenger time and robustness in metro systems: A multi-objective timetable optimization approach

As an effective transport mode to reduce the impact of urban mobility with great capacity and low pollution, metro systems have received rapid development all over the world in recent years. Since a well-designed timetable can improve the service level of passengers, increase the revenue of operating companies, and reduce the environmental pollution, the issue of timetable design/optimization is usually represented as a multi-objective decision problem. This paper develops a multi-objective integer programming model which integrates the energy consumption, the passenger waiting time, and the robustness by optimizing departure and arrival time of trains at each station. A non-dominated sorting genetic algorithm II (NSGA-II) is designed to find the optimal solution. Finally, a case study of Yizhuang line in Beijing metro system is conducted to illustrate the efficiency and effectiveness of the suggested timetable optimization approach.

The integrated optimization of underground stope layout designing and production scheduling incorporating a non-dominated sorting genetic algorithm (NSGA-II)

Stope layout designing and production scheduling are main phases to determine the profitability of an underground mining project. These are mainly related to the output of one phase, which has a significant impact on generating of the next phase. Individual optimization of these two phases results only in a local optimal solution. To date, the integrated optimization of these phases has been carried out to maximize net present value (NPV). In this paper, a multi-objective integer programming model (MOIP) was developed to optimize this integrated problem in a sublevel stoping operation. The non-dominated sorting genetic algorithm (NSGA-II) was incorporated to solve the objective functions. The Pareto front generated by NSGA-II showed good convergence and diversity with the solution time decreasing significantly (from 7-8 days to 6–7 h). The most preferred solution point on the Pareto front increased recovery by 18.55% in exchange for a 0.41% reduction in NPV with respect to the single objective optimization to maximize NPV.

A Multiobjective Integer Linear Programming Model for the Cross-Track Line Planning Problem in the Chinese High-Speed Railway Network

In China, cross-track high-speed trains (CTHSTs) play an important role in railway passenger transportation, with an increasing number of cross-track passengers sourced from the expansion of high-speed railway (HSR) network. The CTHST generally has long travel times, so running CTHSTs is not beneficial for train rescheduling work and plan’s periodicity in the periodic operation context. Thus, the main challenge in cross-track line planning is looking for a symmetry point between passenger transportation and disadvantages of running CTHSTs, which are two conflicting aspects. In this study, we developed a multiobjective integer programming model to produce a balanced cross-track line plan by combining individual-track high-speed trains (ITHSTs) into CTHSTs, which is a discrete optimization problem. This strikes a balance among four goals: the periodicity of the line plan, CTHST quantity, CTHST mileage, and CTHST stops in the context of periodic operation, while satisfying the constraints of passenger demand and the number of available ITHSTs. Numerical experiments are conducted based on a real-world network and optimal solutions were quickly obtained. We analyzed impacts of each goal and parameter on the result and influencing factors of computation. Comparisons with existing methods and real-life plans were also presented to show improvements made by proposed model.

An AIMMS-based decision-making model for optimizing the intelligent stowage of export containers in a single bay

Stowage operations in container terminals are an important part of a port's operational system, as the quality of stowage operations will directly affect the efficiency of port loading and discharge operations, and the scheduling of container shipping liners. The intelligent stowage of containers in container ships was studied in this work. A multi-objective integer programming model was constructed with the minimization of container rehandling, yard crane movements, and the sum of weight differences between stacked container pairs as its objective functions, to address the need for intelligent optimization of single bay export container stowage on a ship's deck. This model also satisfies the stability requirements of preliminary stowage plans drawn by shipping companies, and the operational requirements of container terminals. Linear computational methods were then constructed to transform non-linear constraints into linear ones for better AIMMS solution. Through numerous case analyses and systematic tests, it was shown that our system is able to rapidly solve for stowage planning optimization problems with complex preliminary stowage data, thus proving the applicability and effectiveness of this model. In particular, the application of this model will simultaneously address the safety of ship voyages, the transportation quality of shipping containers and other forms of cargo, and the cost efficiency of ship operations. In addition, this model will also contribute to the optimization of loading and discharge processes in container terminals. Therefore, our model has immense practical value for improving port productivity, as it will contribute to the organization of port operations in a rational, orderly and effective manner.