Mixed Integer Linear Programming Research Articles

THE MODIFIED MEAN ABSOLUTE DEVIATION INTEGER LINEAR PROGRAMMING MODEL FOR GLOBAL PORTFOLIO ASSET ALLOCATION

This study develops a practical yet robust Mean Absolute Deviation (MAD) Mixed-Integer Linear Programming (MILP) model for a global investment portfolio tailored to the constraints faced by Malaysian retail investors, such as transactional fees and foreign currency exchange spreads, to provide more accurate estimations of portfolio returns. The MAD ILP model is modified to address these factors, aiming to enhance utility and efficiency. The study utilizes a Maybank 12-month fixed deposit cash account and ten selected Exchange-Traded Funds (ETFs) from iShares, Vanguard, and State Street Global Advisors for global portfolio construction. Forecasting techniques were utilized to generate expected returns for the ETFs and foreign currency exchange spreads. Based on the MAD model proposed by Konno and Wijayanayake (2001), the study introduces three modifications: incorporating transaction cost elements specific to Malaysian investors, including foreign currency exchange spreads in return calculations, and transforming the model from mixed-integer to pure integer model to accommodate minimum transaction lot constraint. Verification and validation exercises demonstrate the model’s ability to replicate real-world portfolio construction and reliable simulations. The model offers a practical tool for self-ascribed investors aiming to optimize global investment portfolios while considering unique constraints and transaction costs.

Short-term load distribution model for giant cascade serial diversion-type hydropower stations

With the development of complex cascade serial diversion-type hydropower plants (CSDHP) in Southwest China, it has become imperative to study short-term scheduling challenges that are distinctive to this type of hydropower facility. Unlike conventional cascade hydropower stations, which have large reservoirs to regulate the outflow between stations, the CSDHP system consists of several diversion-type hydropower plants connected in series, requiring strict matching of turbine discharge between upstream and downstream facilities. In addition, these plants impose complex operation constraints, such as multiple units sharing one tunnel, which greatly increases the difficulty of short-term scheduling. This paper proposes a short-term optimal scheduling model for CSDHP systems aimed at achieving efficient load distribution among units while minimizing water consumption. The model takes into account the strict matching of turbine discharge and the complex constraints of multiple units sharing one tunnel. Subsequently, the model is transformed into a mixed integer linear programming problem using specified linearization techniques, with complexity further addressed via an iterative resolution method. A case study of a cascade illustrates the model’s efficacy in facilitating effective unit load distribution under complex hydraulic and electrical constraints, which substantially reduces the system’s water consumption by up to 6.1% during the dry season and 1.8% during the flood season, and reducing the number of crossing forbidden zones by 50.0% and 52.0%, respectively. The result shows the models’ potential to enhance day-ahead scheduling for the CSDHP system.

A double-layer Q-learning driven memetic algorithm for integrated scheduling of procurement, production and maintenance with distributed resources

The existing research on integrated production scheduling typically focuses on activities related to both production and post-production (e.g., operation and maintenance), with limited consideration for simultaneously integrating pre-production activities (e.g., raw material procurement). However, achieving the equilibrium between the manufacturer and the demander for intelligent manufacturing systems requires the optimal scheduling solution that integrates both pre-production and post-production activities. Inspired by this, we investigate a novel integrated scheduling problem that concurrently considers raw material procurement, production scheduling and equipment maintenance (abbreviated as SIPPM). A mixed-integer linear programming model is developed to simultaneously minimize the total costs for the manufacturer and the demander. Furthermore, a double-layer Q-learning driven memetic algorithm (DQMA) is proposed to solve the SIPPM. In DQMA, a well-tailored three-layer hybrid encoding method is presented for chromosome representation. The global search of DQMA employs three crossover and three mutation operators. Moreover, a knowledge-based local search operator with six methods, guided by an effective double-layer Q-learning structure, is devised to enhance local exploitation capabilities. The superiority of DQMA is verified through comparison with three popular multi-objective optimization algorithms on 108 newly established benchmark instances. The proposed integrated scheduling mode is proven to be more effective than two separated scheduling modes without considering raw material procurement.

Security constrained unit commitment in smart energy systems: A flexibility-driven approach considering false data injection attacks in electric vehicle parking lots

In this paper, a new structure, the so-called FBSCUCFDIP-P/EV is proposed as flexibility-based security constrained unit commitment (SCUC) in the presence of false data injection (FDI) attack into the communication infrastructure of electric vehicle parking lot (EVPL). Herein, the uncertain EVPLs are integrated into the SCUC problem with the aim of reducing the operation cost. It is notable that growing integration of unspecified EVPLs can introduce novel challenges to the power system, significantly impacting its flexibility. In this study, electric vehicles are leveraged as a means to enhance system flexibility. Meanwhile, the FDI attacks in EVPLs can distort the system’s flexibility and lead to inaccurate assessments of the power system’s ability to adapt to changing conditions. In order to model the FDI attack, a bi-level optimization problem based on mixed integer linear programming is formulated. At the upper level, the impact of EVPLs on the flexibility indices of the SCUC is evaluated, and the false data injected into the EVPL is calculated at the lower level. Since both levels of the proposed FBSCUCFDIP-P/EV include discrete variables, a reformulation and decomposition technique is utilized to achieve the optimal solution. Instead, an extreme gradient boosting (XGBoost)-based machine learning method is considered to detection and correction of FDI attack. The proposed approach is tested on the IEEE 24-bus system. The simulation results initially indicate the improvement of the flexibility of the power system in proposed structure. Further, injecting false data into all available EVPLs causes to increase the system operation cost. Besides, false data leads to distorted charging and discharging scheduling of EVPLs; likewise, scheduling and commitment of power generation units also changes. Subsequently, the application of the XGBoost algorithm effectively mitigates the impact of FDI attacks, achieving a maximum accuracy of 85.41%.

A Mathematical Programming Model for Minimizing Energy Consumption on a Selective Laser Melting Machine

The scheduling problem in additive manufacturing is receiving increasing attention; however, few have considered the effect of scheduling decisions on machine energy consumption. This research focuses on the nesting and scheduling problem of a single selective laser melting (SLM) machine to reduce total energy consumption. Based on an energy consumption model, a nesting and scheduling problem is formulated, and a mixed integer linear programming model is proposed. This model simultaneously determines part-to-batch assignments, part placement in the batch, and the choice of build orientation to reduce the total energy consumption of the SLM machine. The energy-saving potential of the model is validated through numerical experiments. Additionally, the effect of the number of alternative build orientations on energy consumption is explored.

A multiobjective optimizer with a K-means cluster algorithm for a distributed flexible flowshop rescheduling problem

A distributed flexible flowshop problem (DFFSP) has been extensively studied over recent years. It is assumed that all jobs to be processed are exactly known in advance, and machines are able to work continuously. In practice, however, new jobs often arrive suddenly. Machines sometimes break down unexpectedly. These lower the performance of the scheduling generated, even make it infeasible. To address this problem, this paper considers a rescheduling DFFSP (DFFRP) with new job arrivals and machine breakdowns. The objective is to minimize makespan and the robustness metrics at the same time. Firstly, we propose a multi-objective mixed-integer linear programming model and a non-dominated sorting genetic algorithm-II based on K-means clustering algorithm (KNSGA-II). Secondly, the problem-specific knowledge is explored and a speed-up strategy is designed to save the algorithmic computation. Thirdly, an initialization strategy based on K-means clustering algorithm is developed to generate high-quality initial solutions. And a novel crossover and mutation operator is employed to accelerate the convergence of the algorithm. Finally, by comparing with a number of advanced multi-objective algorithms in the literature in comprehensive experiments, the proposed algorithm has been demonstrated to be much more effective for solving the DFFRP under consideration.

Optimising distributed heterogeneous flowshop group scheduling arising from PCB mounting: integrating construction and improvement heuristics

ABSTRACT In real-world manufacturing systems for processing printed circuit boards (PCBs), the workshops integrating various flowline-based cells are common in large-scale enterprises. The scheduling problem within the systems is modelled as the distributed heterogeneous flowshop group scheduling problem (DHFGSP) in this study. Departing from practical requirements and considering the grouping characteristics among PCB components, we account for carryover sequence-dependent setup time (CSDST). Moreover, recognising the critical importance of just-in-time production in semiconductor manufacturing, the total tardiness, a previously unexplored objective within the DHFGSP context, is addressed. To tackle this problem, a mixed-integer linear programming (MILP) model, capable of obtaining optimal solutions for small-scale instances, is proposed. Due to the NP-hard nature of the problem, obtaining high-quality solutions in a reasonable time using the MILP model becomes challenging for large-scale instances. Therefore, a solution algorithm, comprising construction and improvement heuristics, is developed. Capitalising on the problem’s characteristics, the construction heuristic efficiently generates high-quality feasible solutions in a very short time. Built primarily around artificial bee colony (ABC) optimisation, the improvement heuristic can significantly further enhance solutions by integrating the collaborative and restart operators. Comprehensive experiments on instances of varying scales demonstrate the effectiveness of the proposed algorithm for the problem under investigation.

An improved variable neighborhood search algorithm embedded temporal and spatial synchronization for vehicle and drone cooperative routing problem with pre-reconnaissance

Drones are increasingly utilized for transportation reconnaissance due to their expansive field of view, cost-effectiveness, and agility. They can pre-reconnaissance the traveling routes of the ground vehicles carrying valuable goods to ensure the safety of vehicles and their goods. This rises a novel routing problem for the Vehicles and their Pre-Reconnaissance Drones, which is an integrated point and arc routing problem with temporal and spatial synchronization. A mixed integer linear programming model is developed to formulate the problem with complex synchronization constraints. The Variable Neighborhood Search algorithm integrated with the Temporal & Spatial synchronization-based Greedy search and simulated annealing strategy is designed to solve the model. A practical case based on real urban data from Beijing, China, and random instances with different sizes are tested and compared with the proposed algorithm. Computational results indicated that the proposed algorithm can solve the problem efficiently and outperform the simulated annealing algorithm and the greedy algorithm.

Closed-loop supply chain network design with price-greenness-sensitive demand: A distributionally robust chance-constrained optimization approach

In response to the government’s heightened focus on recycling and remanufacturing, as well as the growing awareness among consumers about environmental security, manufacturing companies are currently required to establish efficient closed-loop supply chain networks in order to improve their socialreputation and competitive advantage. This study investigates the optimization of a Closed-Loop Supply Chain (CLSC) network that involves multiple products, multiple periods, and uncertain returns, which also considers the influence of many factors, such as carbon cap-and-trade policy, raw part procurement discounts, and facility capacity constraints, on the supply chain. Simultaneously, customer demand is sensitive to both product pricing and product greenness, and product greenness can be improved by investing in emission reduction technologies. To address the uncertainty in the returns, we propose a two-stage distributionally robust chance-constrained optimization model, which is transformed into a mixed integer linear programming model. To efficiently address the complex problem, we designan improved Benders decomposition (IBD) algorithm. The experimental results confirm that the IBD algorithm has significant advantages when compared to the Benders decomposition algorithm. Additionally, this study conducted a sensitivity analysis on key parameters and proposed operation suggestions of practical importance.

A novel reduced local search algorithm for optimization of digital filter coefficients

Digital Filtering is an important operation in DSP. Most of the DSP applications demand low power implementations. In CMOS digital circuits, switching from logic 0 to logic 1 and vice-versa decides the dynamic power consumption. This paper proposes and develops a novel algorithm based on mixed integer linear programming to minimize the number of ones (filter cost) in filter coefficients, which in turn minimizes the switching factor of CMOS circuits and the number of additional adders needed for hardware implementation. The search space for finding the optimal value of the coefficient is reduced thereby increasing the speed of execution of the algorithm. The average reduction of 18.02 % in the number of transitions is obtained with the proposed algorithm. The suggested technique results in an 18.72 % decrease in the typical price of digital filters. Also the proposed algorithm works faster than the previously proposed algorithm used for finding the optimized coefficients.

Supermarket-chain grocery delivery optimization through crowdshipping

Acknowledging the rising significance of online sales, the grocery business has embraced the challenge of fulfilling the consequently growing consumer expectations for the last-mile delivery efficiency. This paper investigates the grocery delivery optimisation for the supermarket chain based on the crowdshipping mechanism, which can be one of the viable strategies for establishing prompt and affordable delivery service for customers. Considering the deterministic optimisation setting, this study presents a characteristic routing model with crowdsourced couriers named supermarket-chain grocery delivery crowdshipping problem (SCGDCP), which is a variant of the pickup-and-delivery problem, and develops a corresponding mixed integer linear programming (MILP) model. The SCGDCP involves distinctive problem features including individual depots for couriers, multi-trip open routing, and dual time windows of courier operating and order arrival, which pose the computational challenge in problem solving. A bespoke solution procedure based on adaptive variable neighbourhood search (AVNS) strategy is thus designed for tackling the practical-size SCGDCP. The conducted numerical experiments demonstrate the computational efficiency of the proposed MILP model for the small-size instances with no more than 30 grocery orders and the superiority of the developed AVNS procedure for the Grubhub sampling test instances with up to 200 orders.

Optimizing perishable food products across states: A multi objective evolutionary algorithm for surplus to deficit transportation

Ensuring the seamless flow of goods from farmer to stakeholder is paramount especially considering the facts such as demand fluctuations, quantity availability, vehicle capacity, inventory limits and truck preferences. In this paper, we proposed a mixed integer linear programming (MILP) model for distributing perishable food goods from surplus states to surplus and deficit state wholesalers in the Indian subcontinent, with the goal of minimizing total cost (fixed, variable, and operational) and transportation time. To ensure product delivery on time, we looked at various scenarios including a case with real-life constraints. Solving this computationally complex task with conflicting objectives in a reasonable time is difficult. To handle the aforementioned multi-objective problem, we proposed an evolutionary algorithm based modified non-dominated sorting genetic algorithm II (MNSGA-II). Furthermore, the suggested algorithm’s performance is tested against the most extensively used multi-objective algorithm, Non-dominated Sorting Genetic method-II (NSGA-II). According to the findings, the proposed MNSGA-II outperforms practically all instances.

Trolley Optimisation for Loading Printed Circuit Board Components

A trolley is a container for loading printed circuit board (PCB) components, and a trolley optimisation problem (TOP) is an assignment of PCB components to trolleys for use in the production of a set of PCBs in an assembly line. In this paper, we introduce the TOP, a novel operation research application. To formulate the TOP, we derive a novel extension of the bin packing problem. We exploit the problem structure to decompose the TOP into two smaller, identical, and independent problems. Further, we develop a mixed integer linear programming model to solve the TOP and prove that the TOP is an NP-complete problem. A case study of an aerospace manufacturing company is used to illustrate the TOP which successfully automated the manual process in the company and resulted in significant cost reductions and flexibility in the building process.

Customised bus service design considering flexible vehicle size and transfer incentivization

In this study, the flexible vehicle size and transfer incentivization strategies are incorporated to increase the potential of the customised bus system. In detail, the modular vehicle system is adopted for flexible vehicle size design since it can be connected as the assembled bus in response to demand variation. Also, the transfer among buses is considered to group passengers with the same destinations to increase bus utilisation. However, the passengers will not actively transfer as it is viewed as a disutility. Thus, the incentivization is provided and the transfer demand is elastic under incentivization. We jointly optimise passenger-route assignment, vehicle size, and incentivization scheme by transforming the original nonlinear programming model into a mixed integer linear programming model. Then, to solve the larger case study, the modified ant colony system algorithm is also proposed. The experiments validate the superiority of customised bus service considering flexible vehicle size and transfer incentivization.

A topology and sizing optimisation method for lightweight sandwich structures subject to dynamic and static constraints

A static-dynamic topology-sizing optimisation method is presented. The solution is based on a sequential Mixed-Integer Linear Programming solution and aims to minimise the mass of a structure subjected to concurrent constraints on static and dynamic response. It is shown that the classical problem of the dynamics of lightweight sandwich structures may be mitigated through core topology and face sheet thickness combinations, retaining the static load carrying capacity while presenting stringent dynamic properties at a low mass penalty.A numerical example, in the form of a load carrying sandwich beam which is excited at different frequencies, is used to demonstrate the method.

Designing a centralized storage hydrogen supply chain network with multi-period and bi-objective optimization

This study introduces a multi-period centralized storage optimization model aimed at designing an efficient hydrogen supply chain system, considering cost and emissions as dual objectives. It integrates multiple energy sources, production and storage methods, transport combinations, demand scenarios, and carbon capture systems, offering a comprehensive decision-making approach for hydrogen network design. Employing the mixed-integer linear programming methodology, the proposed model resolves these complexities. The research applies this model to a case study in France, generating six unique scenarios for 10 and 15 cities, and compares them against two distinct decentralized models. The findings consistently highlight the centralized storage model’s cost benefits across various demand scenarios, including cases of unrestricted emissions as well as cases with limited emission targets. The cost-effectiveness of this proposed model enhances its feasibility within the current context of decarbonization.

Integrated food delivery problem considering both single-order and multiple order deliveries

The global food delivery market is rapidly growing, and leading companies in Korea have recently introduced a single-order delivery service, wherein a courier picks up customers’ food and delivers it immediately without visiting other places. Although this delivery service is associated with a high delivery fee, it is popular among customers who prefer fresh and fast delivery, unlike multiple-order delivery services, which handle orders from several customers simultaneously. Nevertheless, the coexistence of both delivery services has led couriers to prefer single-order deliveries because they are more profitable, resulting in intensified competition among couriers. Furthermore, there are cases where the courier visits other restaurants or customers without immediately delivering food to customers who use the single-order delivery service, making it a multiple-order delivery service, which leads to customer dissatisfaction. To address these issues, this study proposes a mixed-integer linear programming model for optimizing order assignment and routing in an environment where both single-order and multiple-order deliveries coexist. The tabu search was used to solve medium-sized and large-sized problems, and several food delivery models were configured by referencing the operating methods of the platforms. Through experiments, we demonstrate that the proposed model is more efficient in properly delivering food to customers for both single and multiple orders than other food delivery models. We also analyzed the impact of various variables through a sensitivity analysis, providing insights into the platform.

Optimal Network Design for Municipal Waste Management: Application to the Metropolitan City of Rome

This work is part of the regional research project PIPER—Intelligent Platform for the Optimization of Recycling Operations, which aims to develop a network design model for waste collection in the metropolitan city of Rome, Italy. The goal is to enhance the strategic planning of treatment and disposal facilities by incorporating transshipment locations to improve the efficiency of waste collection. The motivation for this study stems from the stringent targets set by the European Green Deal to achieve near-zero emissions and the critical role of waste management in realizing circular economy practices. Methods: The problem is formulated as a mixed integer linear program (MILP) that includes constraints on vehicle allocation to shifts and driver requirements. An additional feature of the model is its ability to account for vehicle maintenance issues when deployed on consecutive shifts. Results: The model was tested against a real-world case study in Rome and demonstrated significant potential savings, with a reduction in total traveled distance exceeding 10%. The mathematical model was also used for evaluating strategic scenarios in a “what-if” analysis, allowing the municipal collection company to assess location options for depots, waste treatment facilities, and transshipment points, as well as to optimize the fleet composition and driver allocation during work shifts. Conclusions: This study presents a robust tool for strategic planning in waste collection operations, highlighting the benefits of using transshipment locations to improve efficiency. The findings indicate substantial potential for cost savings and operational improvements, making the model a valuable asset for municipal waste management planning.

Stochastic energy planning of a deltoid structure of interconnected multilateral grids by considering hydrogen station and demand response programs

This paper presents triple-objective stochastic energy planning and management of a deltoid structure in which a microgrid, nano-grid, and main grid connect and exchange power simultaneously. In addition, the impact of hydrogen stations due to the growth of hydrogen vehicles and their crucial role in the power system's future to reduce pollution is also discussed. Moreover, the effect of time-based demand response programs (TOU) according to the elasticity matrix (different operators and price-sensitive flexible loads) for the proposed multilateral grid is investigated under diverse scenarios. Stochastic planning is performed to make results more realistic and authentic. The uncertain parameters for stochastic planning include wind pace, solar radiation, fuel rate, and various demands. The assumed triple objective functions for the proposed planning are the microgrid's profit, the nano-grid's cost, and the total multilateral grid's pollution. The problem is modeled as mixed-integer linear programming (MILP) and solved using the GAMS and LP metric approach. The final results show that by implementing the supposed planning, the microgrid's profit increases by about 22.53 $/day (10.8%), and the nano-grid's cost decreases by about 1.31 $/day (9.8%). On the other hand, the total environmental pollution is reduced significantly and reaches 1.06 kg/day.

Learning to Allocate Time-Bound and Dynamic Tasks to Multiple Robots Using Covariant Attention Neural Networks

Abstract In various applications of multi-robotics in disaster response, warehouse management, and manufacturing, tasks that are known a priori and tasks added during run time need to be assigned efficiently and without conflicts to robots in the team. This multi-robot task allocation (MRTA) process presents itself as a combinatorial optimization (CO) problem that is usually challenging to be solved in meaningful timescales using typical (mixed)integer (non)linear programming tools. Building on a growing body of work in using graph reinforcement learning to learn search heuristics for such complex CO problems, this paper presents a new graph neural network architecture called the covariant attention mechanism (CAM). CAM can not only generalize but also scale to larger problems than that encountered in training, and handle dynamic tasks. This architecture combines the concept of covariant compositional networks used here to embed the local structures in task graphs, with a context module that encodes the robots’ states. The encoded information is passed onto a decoder designed using multi-head attention mechanism. When applied to a class of MRTA problems with time deadlines, robot ferry range constraints, and multi-trip settings, CAM surpasses a state-of-the-art graph learning approach based on the attention mechanism, as well as a feasible random-walk baseline across various generalizability and scalability tests. Performance of CAM is also found to be at par with a high-performing non-learning baseline called BiG-MRTA, while noting up to a 70-fold improvement in decision-making efficiency over this baseline.