Multi-objective Mixed Integer Nonlinear Programming Research Articles

An integrated dynamic facility layout and job shop scheduling problem: A hybrid NSGA-II and local search algorithm

The aim of this research is to study the dynamic facility layout and job-shop scheduling problems, simultaneously. In fact, this paper intends to measure the synergy between these two problems. In this paper, a multi-objective mixed integer nonlinear programming model has been proposed where areas of departments are unequal. Using a new approach, this paper calculates the farness rating scores of departments beside their closeness rating scores. Another feature of this paper is the consideration of input and output points for each department, which is crucial for the establishment of practical facility layouts in the real world. In the scheduling problem, transportation delay between departments and machines' setup time are considered that affect the dynamic facility layout problem. This integrated problem is solved using a hybrid two-phase algorithm. In the first phase, this hybrid algorithm incorporates the non-dominated sorting genetic algorithm. The second phase also applies two local search algorithms. To increase the efficacy of the first phase, we have tuned the parameters of this phase using the Taguchi experimental design method. Then, we have randomly generated 20 instances of different sizes. The numerical results show that the second phase of the hybrid algorithm improves its first phase significantly. The results also demonstrate that the simultaneous optimization of those two problems decreases the mean flow time of jobs by about 10% as compared to their separate optimization.

A Non-Cooperative Framework for Coordinating a Neighborhood of Distributed Prosumers

This paper introduces a scalable framework to coordinate the net load scheduling, sharing, and matching in a neighborhood of residential prosumers connected to the grid. As the prosumers are equipped with smart appliances, photovoltaic panels, and battery energy storage systems, they take advantage of their consumption, generation, and storage flexibilities to exchange energy with neighboring prosumers through negotiating on the amount of energy and its price with an aggregator. The proposed framework comprises two separate multi-objective mixed integer nonlinear programming optimization models for prosumers and the aggregator. Prosumers’ objective is to maximize the comfort level and minimize the electricity cost at each instant of time, while aggregator intends to maximize its profit and minimize the grid burden by matching prosumers’ supply and demand. The evolutionary nondominated sorting genetic algorithm-III (NSGA-III) is employed to generate a set of feasible nondominated solutions to the optimization problem of each individual prosumer and the aggregator. As a bilateral negotiation between each prosumer and the aggregator results in significant computational and communication overhead, a virtual power plant is introduced as an intermediator on behalf of all prosumers to proceed the negotiation with the aggregator in a privacy-preserving noncooperative environment, where no private information is shared. Hence, an automated negotiation approach is embedded in the framework, which enables the negotiators to reactively negotiate on concurrent power and price using private utility functions and preferences. To converge to an acceptable agreement, the negotiation approach follows an alternating-offer production protocol and a reactive utility value concession strategy. The effectiveness of the framework is evaluated by several economic and environmental assessment metrics through a variety of numerical simulations.

Supplier selection and order allocation using two-stage hybrid supply chain model and game-based order price

Achieving an efficient supply chain is impossible without integrating supply chain processes and extending long-term relationships between its members. Evaluating the process, selecting a set of suppliers, and allocating orders are effective parameters in the coordination among supply chain members. In this study, to achieve an organized process, a two-stage hybrid model is presented to choose efficient suppliers, allocate order, and determine price in a supply chain with regard to coordination among members. First, an integrated Multi-Objective Mixed-Integer Nonlinear Programming (MOMINLP) model is provided to minimize costs and evaluate suppliers simultaneously. The proposed model includes a single-buyer multi-vendor coordination model and Data Envelopment Analysis (DEA). Then, the model is simplified and converted into a quadratic programming model. In the second stage, a model is presented to determine the price agreed upon by the buyer and the selected efficient suppliers using the bargaining game and the Nash equilibrium concept. The purpose of this model is to maximize the parties’ utilities considering the order quantity specified in the first stage. At the end of this paper, the data taken and adapted from the previous researches are applied to show the abilities of the proposed models.

Mathematical Formulation and Solving of Green Closed-loop Supply Chain Planning Problem with Production, Distribution and Transportation Reliability

In this paper, developed a new multi-product, multi-period, and multi-level closed-loop green supply chain planning model under uncertain conditions. The formulated model consists of five objective functions, which minimize the cost of the supply chain, minimize the CO2 emission of transportation vehicles, maximize the reliability of manufacturing and distribution centers, maximize the reliability of the transportation system, and maximize the level of service provided. Therefore, the problem of model formulated as a multi-objective mixed integer nonlinear programming. Also, since the proposed model is complex and NP-hard in large size, therefore, for the investigation of the results, we have used a Non-Dominated Sorting Genetic II Algorithm (NSGA-II). In addition, the small of size results of the problem achieved by GAMS software. Therefore, we try to solve these problems by analyzing and comparing them with the help of these algorithm. For this purpose, various size has been considered.

A multi-scenario and multi-objective scheduling optimization model for liquefied light hydrocarbon pipeline system

The mixed transportation mode based pipeline system plays a significant role in the supply chain of liquefied light hydrocarbon. Inefficient scheduling may lead to problems of frequent pump stoppage/restart, high energy consumption, and frequent pressure fluctuation. To avoid these problems, this paper implements the discrete-time representation to develop a multi-scenario and multi-objective mixed integer nonlinear programming model to minimize the pump operation cost and the number of the switching operation. In the model, several factors, such as transportation mode, inventory limits of injection stations, flow rate and pressure limits of pipeline segments, are taken into consideration. Additionally, the uncertainty of the liquefied light hydrocarbon production is described by scenarios. The improved augmented ε-constraint method is implemented to solve this model. Finally, the model is successfully applied to a multi-source single-sink liquefied light hydrocarbon pipeline system in Daqing oilfield in China. The experimental results show that the proposed model outperforms another two available models in profit, safety, and robustness aspects.

Multi-objective open shop scheduling by considering human error and preventive maintenance

This study presents an open shop scheduling model by considering human error and preventive maintenance. The proposed mathematical model takes into account conflicting objective functions including makespan, human error and machine availability. In order to find the optimum scheduling, human error, maintenance and production factors are considered, simultaneously. Human error is measured by Human Error Assessment and Reduction Technique (HEART). Three metaheuristic methods including non-dominated sorting genetic algorithm-II (NSGA-II), multi-objective particle swarm optimization (MOPSO) and strength Pareto evolutionary algorithm II (SPEA-II) are developed to find near-optimal solution. The Taguchi method is applied by adjusting parameters of metaheuristic algorithms. Several illustrative examples and a real case study (auto spare parts manufacturer) are applied to show the applicability of the multi-objective mixed integer nonlinear programming model. The proposed approach of this study may be used for similar open shop problems with minor modifications.

Passenger demand oriented train scheduling and rolling stock circulation planning for an urban rail transit line

We study the integration of train scheduling and rolling stock circulation planning under time-varying passenger demand for an urban rail transit line, where the practical train operation constraints, e.g., the capacity of trains, the number of available rolling stocks, and the entering/exiting depot operations, are considered. Three solution approaches are proposed to solve the resulting multi-objective mixed-integer nonlinear programming (MINLP) problem to deliver both an irregular train schedule (i.e., departure and arrival times of all train services) and a rolling stock circulation plan (including entering/exiting depot operations of rolling stocks and connections between train services) simultaneously. We first present an iterative nonlinear programming (INP) approach, where the solutions of the original MINLP problem are obtained by solving a nonlinear programming problem and a mixed integer linear programming (MILP) problem iteratively. Moreover, an equivalent MILP formulation of the original MINLP model is developed and an approximated MILP approach is proposed to reduce the number of constraints introduced by passenger demand. A case study is conducted based on the practical data of the Beijing Yizhuang line, where the three proposed approaches are compared with a state-of-the-art approach and a practical method used by the traffic planners. This comparison shows the effectiveness and efficiency of the three proposed approaches.

Joint decision model of supplier selection and order allocation for the mass customization of logistics services

This paper formulates a multi-objective mixed-integer nonlinear programming model to simultaneously determine the optimal selection strategy of functional logistics service providers and the order allocation strategy under the mass customization of logistics services. An improved genetic algorithm based on multi-layer coding is designed to solve the model. Numerical experiments show that the supplier selection strategy and the order allocation strategy are mutually influential, therefore, decision makers need to consider both simultaneously to optimize the overall performance of the supply chain. The influence of some important parameters on the model results was observed through a sensitivity analysis.

A comprehensive multi-objective mixed integer nonlinear programming model for an integrated elderly care service districting problem

The integrated care service districting (ICSD) problem is an important logistics decision that the elderly care structures (ECS) face when designing service networks to deliver integrated care to the elderly. The ICSD problem, which aims to prepare enhanced care worker recruitment and training plans for all well-designed service districts, is formulated as a multi-objectives mixed integer nonlinear programming (MOMINLP) model. Several criteria are considered, such as balanced workload of care workers among districts, compactness, indivisibility of elderly locations, and the unknown number of districts to be designed. The model considers three objectives simultaneously, including minimizing the total cost of hiring care workers necessary in all service districts, balancing the workload among districts, and achieving as much compactness of district as possible. Results for analysis were obtained by nondominated sorting genetic algorithm II, a well-known multi-objective evolutionary algorithm for continuous multi-objective optimization, which was modified for our MOMINLP model and tested with actual case. Effects of key parameters, including district- and service-related parameters, on these three objectives were analyzed based on different concerns from decision-makers. Furthermore, different correlations among the deviation of service workload and policies for work encouragement were analyzed for ECS. It informs decision-makers about the performance of key factors of the ICSD problem and improves service quality with proper decisions on related parameters.

A Multiobjective Optimization for Train Routing at the High-Speed Railway Station Based on Tabu Search Algorithm

This paper focuses on the train routing problem at a high-speed railway station to improve the railway station capacity and operational efficiency. We first describe a node-based railway network by defining the turnout node and the arrival-departure line node for the mathematical formulation. Both considering potential collisions of trains and convenience for passengers’ transfer in the station, the train routing problem at a high-speed railway station is formulated as a multiobjective mixed integer nonlinear programming model, which aims to minimize trains’ departure time deviations and total occupation time of all tracks and keep the most balanced utilization of arrival-departure lines. Since massive decision variables for the large-scale real-life train routing problem exist, a fast heuristic algorithm is proposed based on the tabu search to solve it. Two sets of numerical experiments are implemented to demonstrate the rationality and effectiveness of proposed method: the small-scale case confirms the accuracy of the algorithm; the resulting heuristic proved able to obtain excellent solution quality within 254 seconds of computing time on a standard personal computer for the large-scale station involving up to 17 arrival-departure lines and 46 trains.

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.

Sustainable Design and Synthesis of Shale Gas Processing and Chemical Manufacturing Processes

In this work, we propose a superstructure of integrated shale gas processing and chemical manufacturing processes with 51,840 alternative possible process designs. The superstructure consists of eight sections, namely acid gas removal, dehydration, NGLs recovery, NGLs separation, hydrocarbons conversion, light olefins separation, C4 separation, and acid gas disposal. For the steam cracking reactions in the hydrocarbons conversion section, we optimize the product distributions of steam cracking of ethane, propane, n-butane, and i-butane. Extensive process simulations are performed for all the involved processes in the superstructure in order to collect high-fidelity process data and develop detailed process models for the technology/process alternatives in the superstructure. Next, we propose a multiobjective mixed-integer nonlinear programming (MINLP) superstructure optimization model with five groups of constraints, namely superstructure network configuration constraints, mass balance constraints, energy balance constraints, techno-economic evaluation constraints, environmental impact assessment constraints. Three objective functions are maximizing the net present value per GJ of raw shale gas, minimizing the global warming potential per GJ of raw shale gas, and minimizing the water footprint per GJ of raw shale gas, respectively. A tailored global optimization algorithm is applied to efficiently solve the resulting nonconvex MINLP problem. The application of the proposed framework is illustrated through a case study based on a Marcellus shale gas feed.

Multi-objective economic-resource-production optimization of sustainable organic mixed farming systems with nutrient recycling

Abstract This paper addresses the optimal design of mixed crop-livestock farming systems for resource efficiency, economic profitability, and environmental sustainability. The trade-offs among profit, water productivity, and organic matter accumulation are considered. We propose a novel optimization model that accounts for economics, crop cultivation, livestock production, water requirement, soil organic matter, and nitrogen cycling, among other important elements of organic farming systems. The resulting problem is a multi-objective mixed-integer nonlinear fractional programming (MINLFP) problem, which consists of fractional objective function and nonconvex nonlinear constraints. After reformulating the nonconvex constraints into convex ones, we propose a tailored global optimization algorithm to solve the resulting MINLFP problem. We further present a case study on a 100 ha organic mixed crop-livestock farm with 19 types of crops, 22 types of crop products, 3 type of livestock, and 2 types of animal products to illustrate the applicability of the proposed model and solution methods. Computational results suggest that it is more profitable to produce more high value cash crops and milk; it is more water efficient to grow cash crops than fodder; and it generates more soil organic matter accumulation by growing more crops with larger amount of root stubble and enlarging the heard size.

A capacity maximization scheme for intersection management with automated vehicles

With the advent of connected and automated vehicle technology, in this paper, we propose an innovative intersection operation scheme named as MCross: Maximum Capacity inteRsection Operation Scheme with Signals. This new scheme maximizes intersection capacity by utilizing all lanes of a road simultaneously. Lane assignment and green durations are dynamically optimized by solving a multi-objective mixed-integer non-linear programming problem. The demand conditions under which full capacity can be achieved in MCross are derived analytically. Numerical examples show that MCross can almost double the intersection capacity (increase by as high as 99.51% in comparison to that in conventional signal operation scheme).

A multiobjective optimization model and an orthogonal design–based hybrid heuristic algorithm for regional urban mining management problems

ABSTRACTIn this paper, a multiobjective mixed-integer piecewise nonlinear programming model (MOMIPNLP) is built to formulate the management problem of urban mining system, where the decision variables are associated with buy-back pricing, choices of sites, transportation planning, and adjustment of production capacity. Different from the existing approaches, the social negative effect, generated from structural optimization of the recycling system, is minimized in our model, as well as the total recycling profit and utility from environmental improvement are jointly maximized. For solving the problem, the MOMIPNLP model is first transformed into an ordinary mixed-integer nonlinear programming model by variable substitution such that the piecewise feature of the model is removed. Then, based on technique of orthogonal design, a hybrid heuristic algorithm is developed to find an approximate Pareto-optimal solution, where genetic algorithm is used to optimize the structure of search neighborhood, and both local branching algorithm and relaxation-induced neighborhood search algorithm are employed to cut the searching branches and reduce the number of variables in each branch. Numerical experiments indicate that this algorithm spends less CPU (central processing unit) time in solving large-scale regional urban mining management problems, especially in comparison with the similar ones available in literature. By case study and sensitivity analysis, a number of practical managerial implications are revealed from the model.Implications: Since the metal stocks in society are reliable overground mineral sources, urban mining has been paid great attention as emerging strategic resources in an era of resource shortage. By mathematical modeling and development of efficient algorithms, this paper provides decision makers with useful suggestions on the optimal design of recycling system in urban mining. For example, this paper can answer how to encourage enterprises to join the recycling activities by government’s support and subsidies, whether the existing recycling system can meet the developmental requirements or not, and what is a reasonable adjustment of production capacity.

An integrated chance-constrained stochastic model for efficient and sustainable supplier selection and order allocation

Effective allocation of scarce resources across supply chain environments is an emerging issue, as enterprises face shortfalls in raw materials, human labour, budgetary resources, equipment, energy and capacity. We consider these related objectives in designing efficient and sustainable supply networks using a multi-objective mixed-integer non-linear programming (MINLP) model for efficient and sustainable supplier selection and order allocation with stochastic demand. Our approach considers sustainability dimensions including economic, environmental and social responsibility, but also seeks to design the most efficient supply network given constraints of the supply market. Enterprise efficiency is assessed using a bi-objective data envelopment analysis (DEA) whose inputs include raw materials, current expenses and labour force capacity. The resulting model is non-convex because of the presence of bilinear terms in DEA-related constraints, so we introduce a multi-stage solution procedure that first uses piecewise McCormick envelopes (PCM) to linearise the bilinear terms. Next, we introduce a set of valid inequalities in order to improve solution time of the problem whose dimension significantly increases after being linearised. We then exploit chance constrained programming approaches to deal with stochastic demand. Finally, a single aggregated objective function is derived using a fuzzy multi-objective programming approach. A manufacturing case study demonstrates the validity of the proposed approach, and its effectiveness in designing a supply network that addresses the ‘triple bottom line’ of people, profit and planet that comprises many sustainability initiatives in an efficient manner.

A novel multi-objective programming model of relief distribution for sustainable disaster supply chain in large-scale natural disasters

To save lives and reduce suffering of victims, the focus of this paper is to design the strategies of relief distribution regarding beneficiary perspective on sustainability. This problem is formulated as a multi-objective mixed-integer nonlinear programming model to maximize the lowest victims' perceived satisfaction, and minimize respectively the largest deviation on victims’ perceived satisfaction for all demand points and sub-phases. Then, genetic algorithm is proposed to solve this mathematical model. To validate the proposed methodologies, a case study from Wenchuan earthquake is illustrated. Computational results demonstrate genetic algorithm here can achieve the trade-off between solution quality and computation time for relief distribution with the concern of sustainability. Furthermore, it indicates that the methodology provides the tools for decision-makers to optimize the structure of relief distribution network and inventory, as well as alleviate the suffering of victims. Increasingly, this paper expects to not only validate the proposed model and method, but also highlight the importance and urge of considering beneficiary perspective on sustainability into relief distribution problem.

Solving a Multi-Objective Mathematical Model for a Multi-Skilled Project Scheduling Problem by Particle Swarm Optimization and Differential Evolution Algorithms

A Multi-Skilled Project Scheduling Problem (MSPSP) that is an extension of a Multi-Mode Resource-Constrained Project Scheduling Problem (MM-RCPSP) has been generally addressed to schedule a project with staff members as resources. In MSPSP, each activity requires different specialties and each staff member has a known skill level in performing an activity. This causes to encounter a huge number of modes while performing activities of a project. This research focuses on a special type of MSPSP known as Multi-Objective Multi-Skilled Project Scheduling Problem (MOMSPSP) which incorporates some new objectives in the MSPSP and develops a multi-objective mixed-integer nonlinear programming (MINLP) model. The model is exactly solved for small-sized instances using CPLEX solver. To solve such a NP-hard problem for medium and large-sized instances, two efficient meta-heuristic algorithms based on Differential Evolution (DE) and Particle Swarm Optimization (PSO) are proposed. To evaluate the efficiency of the proposed algorithms, the results are compared with each other as well as to the optimal ones obtained by the CPLEX solver for small instances. Finally, the designed DE algorithm is identified as the superior proposed algorithm for solving the propounded MOMSPSP in terms of some performance metrics.

Multi-objective modeling and optimization for scheduling of cracking furnace systems

Cracking furnace is the core device for ethylene production. In practice, multiple ethylene furnaces are usually run in parallel. The scheduling of the entire cracking furnace system has great significance when multiple feeds are simultaneously processed in multiple cracking furnaces with the changing of operating cost and yield of product. In this paper, given the requirements of both profit and energy saving in actual production process, a multi-objective optimization model contains two objectives, maximizing the average benefits and minimizing the average coking amount was proposed. The model can be abstracted as a multi-objective mixed integer nonlinear programming problem. Considering the mixed integer decision variables of this multi-objective problem, an improved hybrid encoding non-dominated sorting genetic algorithm with mixed discrete variables (MDNSGA-II) is used to solve the Pareto optimal front of this model, the algorithm adopted crossover and mutation strategy with multi-operators, which overcomes the deficiency that normal genetic algorithm cannot handle the optimization problem with mixed variables. Finally, using an ethylene plant with multiple cracking furnaces as an example to illustrate the effectiveness of the scheduling results by comparing the optimization results of multi-objective and single objective model.

Optimization-based framework for resin selection strategies in biopharmaceutical purification process development.

This work addresses rapid resin selection for integrated chromatographic separations when conducted as part of a high‐throughput screening exercise during the early stages of purification process development. An optimization‐based decision support framework is proposed to process the data generated from microscale experiments to identify the best resins to maximize key performance metrics for a biopharmaceutical manufacturing process, such as yield and purity. A multiobjective mixed integer nonlinear programming model is developed and solved using the ε‐constraint method. Dinkelbach's algorithm is used to solve the resulting mixed integer linear fractional programming model. The proposed framework is successfully applied to an industrial case study of a process to purify recombinant Fc Fusion protein from low molecular weight and high molecular weight product related impurities, involving two chromatographic steps with eight and three candidate resins for each step, respectively. The computational results show the advantage of the proposed framework in terms of computational efficiency and flexibility. © 2017 The Authors Biotechnology Progress published by Wiley Periodicals, Inc. on behalf of American Institute of Chemical Engineers Biotechnol. Prog., 33:1116–1126, 2017