Multi-objective Integer Nonlinear Programming Research Articles

Multi-objective optimization for through train service integrating train operation plan and type selection

ABSTRACT Providing effective Through Train Services (TTSs) faces challenges due to complex infrastructure conditions, train performances and passenger demands. To enhance TTSs between two different classes of urban rail transit lines with variations in train speed and capacity, we propose a multi-objective Integer Non-Linear Programming (INLP) model. This model maximizes passenger travel time savings and average train load utilization, and develops an integrated approach to simultaneously optimize the frequencies of through express trains and local trains, as well as the operation zones, stopping patterns and type selection of through trains. Additionally, a Non-Dominated Sorting Genetic Algorithm II is designed to solve the INLP model based on a simple test network and a real-world case from the Nanjing Subway. The unique benefits of our proposed method are demonstrated by a comprehensive compared with the Single Line Operation Mode and the all-stop plans under Through Operation Mode.

Fixture layout optimization of large compliant ship part assembly for reducing and straightening butt clearance

Fixture layout is an essential factor in intelligent manufacturing in the shipbuilding industry, affecting assembly quality and efficiency. Its optimization has become an urgent problem in the assembly process of compliant parts. Traditional fixture layout depends on workers’ experience, which leads to butt clearance along the assembly interface. Thus, this article proposes a butt clearance control-oriented fixture layout optimization (BCCFLO) methodology. First, a method for calculating the part dimensional variation under the influence of fixture layout and fixture locating error is developed. Then, a constrained multi-objective integer nonlinear programming (CMINP) model is innovatively formulated to optimize the fixture layout. Furthermore, the non-dominated sorting genetic algorithm-II based on Latin hypercube sampling is designed to address the CMINP model. The case study illustrates and validates that the fixture layout achieved by the proposed method could significantly control the butt clearance for large compliant part assembly in the shipbuilding industry.

A multi-objective nonlinear integer programming model for mixed runway operations within the TMAs

AbstractGlobal air traffic demand has shown rapid growth for the last three decades. This growth led to more delays and congestion within terminal manoeuvring areas (TMAs) around major airports. The efficient use of airport capacities through the careful planning of air traffic flows is imperative to overcome these problems. In this study, a mixed-integer nonlinear programming (MINLP) model with a multi-objective approach was developed to solve the aircraft sequencing and scheduling problem for mixed runway operations within the TMAs. The model contains fuel cost functions based on airspeed, altitude, bank angle, and the aerodynamic characteristics of the aircraft. The optimisation problem was solved by using the $\varepsilon$ -constraint method where total delay and total fuel functions were simultaneously optimised. We tested the model with different scenarios generated based on the real traffic data of Istanbul Sabiha Gökçen Airport. The results revealed that the average total delay and average total fuel were reduced by 26.4% and 6.7%, respectively.

Multiobjective Collaborative Optimization Method for the Urban Rail Multirouting Train Operation Plan

The Train Operation Plan (TOP) of urban rail transit (URT) is a comprehensive plan for the operation of trains, the use of facilities and equipment, and the organization of other operational tasks. The TOP should not only be formulated in terms of time-varying passenger flow periods, but it should also be arranged to consider the substitutability of trains between multiple routes combined with the passenger choice. Based on the principle of “operating by the flow” and the requirement for precise allocation of transport capacity for multiple routes, this article constructs a multiobjective nonlinear integer programming model by taking the minimized generalized travel cost of passengers, total running mileage of trains, fluctuation of trains for each route (as optimization targets), and the combination of requirements of both headways and fully loaded rates as constraints. A multiobjective genetic-based algorithm is designed to simultaneously optimize the TOP and the two-way train stopping time in each period. Finally, the proposed model and algorithm are validated with the real data from the Guangzhou Metro Line 2. The results show that the Pareto optimal TOP and dynamic train stopping time are significantly improved compared to the original values.

Hybrid-integer algorithm for a multi-objective optimal home energy management system

AbstractMost of the energy produced in the world is consumed by commercial and residential buildings. With the growth in the global economy and world demographics, this energy demand has become increasingly important. This has led to higher unit electricity prices, frequent stresses on the main electricity grid and carbon emissions due to inefficient energy management. This paper presents an energy-consumption management system based on time-shifting of loads according to the dynamic day-ahead electricity pricing. This simultaneously reduces the electricity bill and the peaks, while maintaining user comfort in terms of the operating waiting time of appliances. The proposed optimization problem is formulated mathematically in terms of multi-objective integer non-linear programming, which involves constraints and consumer preferences. For optimal scheduling, the management problem is solved using the hybridization of the particle swarm optimization algorithm and the branch-and-bound algorithm. Two techniques are proposed to manage the trade-off between the conflicting objectives. The first technique is the Pareto-optimal solutions classification using supervised learning methods. The second technique is called the lexicographic method. The simulations were performed based on residential building energy consumption, time-of-use pricing (TOU) and critical peak pricing (CPP). The algorithms were implemented in Python. The results of the current work show that the proposed approach is effective and can reduce the electricity bill and the peak-to-average ratio (PAR) by 28% and 49.32%, respectively, for the TOU tariff rate, and 48.91% and 47.87% for the CPP tariff rate by taking into account the consumer’s comfort level.

Bicycle sharing station planning: From free-floating to geo-fencing

Bicycle sharing systems (BSSs) are expanding with unparalleled speed all over the world due to various advantages of cycling such as cost effectiveness, environmentally friendliness, capability to bridge other public transport modes and reduce private vehicle usage. One of the latest trend of BSS mode appears to be free-floating, which offers more flexibility in bike rental and return for cyclists in terms of service locations. However, despite the convenience brought by the free-floating BSS to the users, it also causes a headache for the authorities, largely attributed to its poor enforcement on regulating bad user behaviours, which significantly deteriorates the city scape. In order to preserve the benefits of BSSs and meanwhile solve the problems caused by free-floating BSS, this study develops a multi-objective integer non-linear programming (MOINLP) model to convert an existing free-floating BSS into a geo-fence-based one by determining the geo-fencing stations to be opened, their corresponding parking capacities and deployment of bikes. The three objectives of the developed MOINLP model are minimizing monetary cost, user dissatisfaction as well additional first-/last-mile walking distance of users. The MOINLP model is transformed into an equivalent multi-objective integer linear programming (MOILP) model. The augmented ε-constraint method (AUGMECON2) is customized to solve the MOILP model for exact Pareto optimal solutions while a tailored simulation-based heuristic method is proposed to solve large-scale problems. The numerical experiments have testified the good performance of our proposed solution method and we extend our analysis to Beijing BSS to gain planning insights and policy implications.

Multi-objective optimization of cordon sanitaire considering operation cost and queueing equity

ABSTRACT This paper aims topropose a method to determine the optimal deployment of cordon sanitaire for epidemic control. A bi-level multi-objective programming model is proposed where the lower level is transportation system equilibrium with queueing time to predict link traffic flow, and the upper level is queueing network design, which is a multi-objective integer nonlinear programming model. The primary objective is to minimize the total operation cost of servers with a predetermined waiting time constraint, and the secondary objective is to reach queueing equity. A heuristic algorithm is designed where the method of successive averages is adopted for the lower-level model, and a genetic algorithm is designed for the upper-level model. The computational results show that the methods can find a good heuristic optimal solution. These methods are useful for planners to determine the optimal deployment of cordon sanitaire for disease control and prevention purposes.

Exact Methods for Multi-Objective Integer Nonlinear Programming

Multi-objective integer nonlinear programming (MOINLP) problems are multi-objective integer programming problems with at least one nonlinear objective function or constraint. To date, MOINLP problem has not been exactly solved. Although traditional ε-constraint method can be used to solve MOINLP problem, the obtained solution may not be Pareto-optimal. To overcome this shortcoming, a basic ε-constraint method (BEM) is proposed to solve MOINLP problem exactly. However, the time complexity of BEM is as high as O ( ( p − 1 ) M 2 N ) , where p, M, and N are the numbers of objectives, Pareto-optimal solutions, and feasible solutions, respectively. For this reason, an improved BEM (IBEM) is developed whose time complexity is O ( M 2 N ) . That is, the time complexity of IBEM for solving MOINLP problem is equal to solving the single-objective one. Finally, to avoid using all the feasible solutions (N) in obtaining each Pareto-optimal solution, three methods to eliminate dominated solutions effectively are used before performing IBEM. The test results illustrate that our method can not only solve MOINLP problem exactly but also has high efficiency.

Design of a distribution network for the school lunch program

The national school lunch program (NSLP) is crucial for providing healthy, inexpensive, or free lunches to children, thus benefiting society. Designing a distribution network for the program requires solving a location and routing problem. In this paper, first, we formulate a multi-objective non-linear integer programming formulation of the problem. Next, we develop a two-step approach since the problem is Np-hard. The first stage presents a K-mean clustering method that deals with routing decisions by determining the locations of food processing centers and allocating schools to these centers. The second stage offers a multi-objective mixed-integer linear mathematical model for finding the locations of distribution centers. Besides economic and environmental factors, we optimize travel time in the network as perishable items are involved. A weighted sum approach is presented for different weights of objectives. We provide a real case study in Turkey to demonstrate the applicability of the two-stage approach proposed in this study. The numerical results provide valuable information for decision-makers and authorities to prioritize and prepare action plans.

An incentive mechanism for partner selection from a collaborative network with private information

Partner selection is critical to the success of a Virtual Enterprise. This paper studies the partner selection problem under the virtual organization breeding environment where candidates have private information about their cost to undertake the tasks. A systematic solution is provided to reveal the true value of the private information and then select the optimal partners. This solution mainly comprises two steps: (1) For each possible cost combination, a multi-objective integer nonlinear programming model and an algorithm are designed to obtain the optimal partners. Then, a social choice correspondence, which indicates the optimal partners for any cost combination, is formulated. (2) An incentive mechanism is constructed to implement the social choice correspondence and ensure that candidates will announce their values of cost truthfully. Furthermore, a numerical study is provided to illustrate the effectiveness of the solution and to investigate the relationship between the construction of the collaborative network and the utility to partners. We find that the number of candidates in each period affects the utility of partners as well as the expected surplus of the leading company significantly.

Optimization of Multi-period Three-echelon Citrus Supply Chain Problem

In this paper, a new multi-objective integer non-linear programming model is developed for designing citrus three-echelon supply chain network. Short harvest period, product specifications, high perished rate, and special storing and distributing conditions make the modeling of citrus supply chain more complicated than other ones. The proposed model aims to minimize network costs including waste cost, transportation cost, and inventory holding cost, and to maximize network’s profits. To solve the model, firstly the model is converted to a linear programming model. Then three multi-objective meta-heuristic algorithms are used including MOPSO, MOICA, and NSGA-II for finding efficient solutions. The strengths and weaknesses of MOPSO, MOICA, and NSGA-II for solving the proposed model are discussed. The results of the algorithms have been compared by several criteria consisting of number of Pareto solution, maximum spread, mean ideal distance, and diversification metric.Computational results show that MOPSO algorithm finds competitive solutions in compare with NSGA-II and MOICA.

Multiobjective Sustainable Order Allocation Problem Optimization with Improved Genetic Algorithm Using Priority Encoding

Recently, incorporating carbon emissions into order allocation decisions has attracted considerable attention among scholars and industrialists. Moreover, affected by the random fluctuations of the man, machine, material, method, and environment (4M1E), the production process is usually imperfect with defective products. Reducing product defective rates can effectively improve the quality of the order allocation process. Therefore, considering product defective rate and carbon emission, a multiobjective integer nonlinear programming (INLP) formulation is presented to address this multiproduct, multiperiod, and multi-OEM order allocation problem. Furthermore, exploring the existing literatures, an improved genetic algorithm using priority encoding (IGAUPE) is put forward as a novel optimization technique. Finally, numerical experiments are conducted to validate the correctness of the proposed INLP model as well as the effectiveness of the proposed algorithm. Compared with the genetic algorithm using binary encoding (GAUBE), genetic algorithm using two-layer encoding (GAUTE), and LINGO software, the experiment results show that IGAUPE can improve the efficiency and effectiveness within the predetermined time limit when solving large-scale instances.

Multi-objective optimization of iron ore induration process using optimal neural networks

ABSTRACTInduration in steel industries is the process of pelletizing iron ore particles. It is an important unit operation which produces raw materials for a subsequent chemical reduction in Blast Furnace. Of the enormous amount of energy consumed by Blast Furnace, a large portion is utilized in processing the raw materials. High-quality raw materials, therefore, ensure less consumption of energy in the Blast Furnace. Thus, optimization of induration process is necessary for conservation of a significant amount of energy in steelmaking industries. To realize this, a highly non-linear, industrially validated, 22 dimensional first principles based model for induration is created and a multi-objective optimization problem is designed. However, the physics-based model being computationally expensive, Multi-layered Perceptron Networks (MLPs) are trained to emulate the induration process. Novelty in this work lies with the optimal architecture design of MLPs through a multi-objective integer non-linear programming (MO-INLP) problem and with simultaneous training size estimation through four different Sobol sampling-based algorithms. Successful emulation of induration process resulted in 10-fold speed increment in optimization through surrogate models. To justify the parsimonious behavior of resultant MLPs, five different tests are performed for checking whether they are over-fitted. Comparison with Kriging adds to other highlights.

Negative Total Float to Improve a Multi-Objective Integer Non-Linear Programming for Project Scheduling Compression

This paper presents Multi-Objective Integer Non-Linear Programming (MOINLP) involving Negative Total Float (NTF) for improving the basic model of Multi-Objective Programming (MOP) in case the optimization of the additional cost for Project Scheduling Compression (PSC). Using the basic MOP to solve the more complex problems is a challenging task. We suspect that Negative Total Float (NTF) having an indication to make the basic MOP to solve the more general case, both simple and complex of PSC. The purpose of this research is identifying the conflicting objectives in PSC problem using NTF and improving MOINLP by involving the NTF parameter to solve the PSC problem. The Solver Application, which is an add-in of MS Excel, is used to perform optimization process to the model developed. The results show that NTF has an important role to identify the conflicting objectives in PSC. We define NTF is an automatic maximum value of the activity duration reduction to achieve due date of PSC. Furthermore, the use of NTF as a constraint in MOINLP can solve the more general case for both simple and complex PSC problem. Base on the condition, we state that the basic MOP is still significant to solve the PSC complex problems using MOINLP as a sophisticated MOP technique.

Modelling and optimization of multistream heat exchanger with area targeting

In this work, a new multi-objective mixed integer nonlinear programming (MINLP) model based on Pinch Technology principles is presented. The proposed framework is able to simultaneously maximize the heat recovery, minimize the total heat exchange surface while guaranteeing the heat transfer feasibility. The formulation adopted for the heat integration problem significantly reduces the number of binary variables when dealing with variable temperatures and flowrates, thus enhancing the solution efficiency. The model is then augmented with the introduction of a novel approach for the total area estimation not requiring heavy disjunctions nor complex tailor-made algorithms. A study on the optimization of an air separation unit (ASU) is finally performed to show the potential and effectiveness of the proposed framework.

The Integrated Supply Chain of After-sales Services Model: A Multi-objective Scatter Search Optimization Approach

Abstract: In recent decades, high profits of extended warranty have caused that third-party firms consider it as a lucrative after-sales service. However, customers division in terms of risk aversion and effect of offering extended warranty on manufacturers’ basic warranty should be investigated through adjusting such services. Since risk-averse customers welcome extended warranty, while the customers without taking on risk may remain at the level of basic warranty. In this paper, a multi-objective integer nonlinear programming model is presented for integrating the supply chain of after-sales services. In the suggested model, firstly strategies used by the manufacturers in the basic warranty period and the third party’s policy during the extended warranty period, including the development of a new imperfect maintenance approach, are regulated. Then, the effects of these strategies on the desirability of customers with different levels of risk-taking are analyzed. To optimize the model, the scatter search based approach was introduced for extracting set of non-dominated solutions. The results indicated that increasing level of customers’ risk-taking convinces manufacturers to diminish the basic warranty period and the third party can apply less costly preventive maintenance. Key Words: Warranty, Extended warranty, After-sales services, Customers’ risk-taking, Pareto-set solutions, Multi-objective scatter search

System of Systems Architecting Problems: Definitions, Formulations, and Analysis

The system of systems architecting has many applications in transportation, healthcare, and defense systems design. This study first presents a short review of system of systems definitions. We then focus on capability-based system of systems architecting. In particular, capability-based system of systems architecting problems with various settings, including system flexibility, fund allocation, operational restrictions, and system structures, are presented as Multi-Objective Nonlinear Integer Programming problems. Relevant solution methods to analyze these problems are also discussed.

Multistage assignment optimization for emergency rescue teams in the disaster chain

Human resources and potential secondary disasters are often neglected in the existing emergency resource allocation methods. This paper presents a multistage assignment model for rescue teams to dynamically respond to the disaster chain and develops three priority scheduling strategies defined under the burden-benefit accord principle. A designed NSGA-II, C-METRIC and fuzzy logic methods were developed to solve the above multi-objective integer nonlinear programming model. Finally, the experimental scenarios results indicated that the overall performance of the proposed method was satisfactory in comparison with current method regardless of whether the secondary disasters occurred sooner or later. It was demonstrated that the three proposed priority scheduling strategies outperformed the others; however, which of these three priority strategies is most appropriate for a specific disaster situation depends on the maximum rescue time allowed by the disaster.

Stochastic Multi-Objectives Supply Chain Optimization with Forecasting Partial Backordering Rate: A Novel Hybrid Method of Meta Goal Programming and Evolutionary Algorithms

This study proposes a model for a multi-objective, multi-buyer, multi-vendor, multi-product and multi-constraint supply chain. The buyers’ demand rates are stochastic variables with known probability distribution functions. The classical ([Formula: see text]) inventory control system is used to manage the inventories of all buyers where the lead times are production rate dependent. Shortage is permitted and is partially backordered where the partial back ordering rate is forecasted. The model is considered as a multi-objective integer nonlinear programming problem including cost, service level and lead time objectives and using a novel hybrid method, a hybrid of Meta Goal Programming (MGP) and Firefly Algorithm (FA) are solved. Numerical examples are given to illustrate the proposed method in the study. The results of the study are compared to other hybrid methods of Meta Goal Programming with other evolutionary algorithms such as Bees Algorithms (BA), Particle Swarm Optimization (PSO), Genetic Algorithm (GA) and Simulated Annealing (SA).

Traceability using RFID and its formulation for a kiwifruit supply chain

Traceability is one of the most important requirements in a fruit supply chain. It helps in keeping a track over the quality, perishability and freshness of the fruits which are the foremost concern for maintaining customer satisfaction. In this paper, we consider a case of kiwifruit supply chain and analyze the impact of traceability using Radio Frequency Identification (RFID) tags. A multi-objective integer non-linear programming model (MOINLP) is formulated considering two objective functions which include (i) minimization of the total costs incorporating logistics costs and costs of implementing RFID tags and (ii) minimization of liability costs on occurrence of contamination. To compute this problem, a newly developed approach of Plant Pollinator Optimization Algorithm (PPO) has been implemented and a comparison with the well-known Non-dominated Sorting Genetic Algorithm-II (NSGA-II) is performed. Insights evolving out of this study can help the Supply Chain Managers in minimizing the risks of delivery of perished fruits by tracing it at an earlier stage and thus reducing the liability costs.