Design, synthesis and scheduling of multipurpose batch plants via an effective continuous-time formulation

During the last two decades, the problem of short-term scheduling of multiproduct and multipurpose batch plants has gained increasing attention in the academic, research, and manufacturing communities, predominantly because of the challenges and the high economic incentives. In the last 10 years, numerous formulations have been proposed in the literature based on continuous representations of time. The continuous-time formulations have proliferated because of their established advantages over discrete-time representations and in the quest to reduce the integrality gap and the resulting computational complexities. The various continuous-time models can be broadly classified into three distinct categories: slot-based, global event-based, and unit-specific event-based formulations. In this paper, we compare and evaluate the performance of six such models, based on our implementations using several benchmark example problems from the literature. Two different objective functions, maximization of profit and minimization of makespan, are considered, and the models are assessed with respect to different metrics such as the problem size (in terms of the number of binary variables, continuous variables, and constraints), computational times (on the same computer), and number of nodes needed to reach zero integrality gap. Two additional computational studies with resource constraints such as utility requirements are also considered.

The increasing interest in multipurpose batch plants is evident, because of their inherent flexibility to cope with an ever changing market environment. These plants are easily reconfigured for product modifications, to cover a wide range of operating conditions. They are also suitable for producing different products within the same facility. In spite of this advantage, the design, synthesis, and scheduling of multipurpose batch plants can be a challenging task. This paper addresses design, synthesis, and scheduling simultaneously. It is known that the scheduling platform employed has a significant impact on the computational performance of the overall model in the design and synthesis of batch plants. The recent scheduling model that results in better computational efficiencies is extended to incorporate design and synthesis. Computational studies are presented to illustrate the effectiveness of the proposed model. A comparison with earlier formulations showed that better computational times and objective functions were obtained by this work.

Modeling and Optimization for Short-term Scheduling of Multipurpose Batch Plants

While the part 1 focuses on the application of the proposed formulation to scheduling, this paper focuses mainly on the integration of planning and scheduling in multipurpose batch plants. In dealing with this problem, the method presented in part 2 exploits the mathematical structure of the overall plant model. It is discovered that the overall model exhibits a block angular structure that is decomposed by raw material allocation. If raw materials can be allocated optimally to individual plants, solving individual models for each plant can produce the same results as solving an overall model for the site. This discovery leads to a decomposition strategy that consists of two levels. In the first level, only planning decisions are made, and the objective function is the maximization of the overall profit. The results from solving the planning model give optimal raw material allocation to different plants. In the second level, the raw material targets from the first (planning) level are incorporated into the scheduling submodels for each plant, which are solved independently without compromising global optimality. The objective function for each scheduling submodel is the maximization of product throughput. The scheduling level uses the concept of the state sequence network presented in part 1. Solving scheduling submodels for individual plants rather than the overall site model leads to problems with much a smaller number of binary variables and, hence, shorter CPU times. If conflicts arise, i.e., the planning targets are too optimistic to be realized at the scheduling level, the planning model is revisited with more realistic targets. This eventually becomes an iterative procedure that terminates once the planning and scheduling solutions converge within a specified tolerance. In this way, the planning model acts as coordination for scheduling models for individual plants. An industrial case study with three chemical processes is presented to demonstrate the effectiveness of this approach.

Summary of the Basic StepsThe basic steps in the suggested procedure for the optimal design of multi-purposebatch plants can be summarized as follows:1. List the candidate product groups.2. Obtain the super-structure that contains the candidate groups.3. Derive the horizon constraints..4. Examine the horizon constraints. If at least one horizon constraintimplicitly contains all the time periods, complete the merged formulationand solve the MINLP given in Equations (38) to (44) with the correspondinghorizon constraints. Otherwise, go to step 5.5. Select a product(s) that breaks the loop(s) in the super-structure. Treat thechosen product(s) as two or more artificial products.6. Revise the super-structure to include the additional products. Verify thatthe loop is broken. If this condition is met, go to step 7. Otherwise,return to step 5 and modify the products chosen for splitting.7. Derive the multi-period form of the constraints for the product(s) that aresplit into its (their) values for the time periods in which it (they) appear.Formulate the merged representation of the model for the rest of theproducts, including the horizon constraints. At least one horizonconstraint will contain implicitly all the time periods.Example 2The seven product, ten stage example problem of Suhami and Mah (1982) has beensolved to illustrate the design of a large multi-purpose batch plant. From the super-structure of this problem (Figure 4), the horizon constraints shown in Table II arederived.Using these constraints, the example has been solved with the merged formulation.Data for this problem appears in Table III. In addition, the following specificationshave been used: H = 6200 hr, a = 250 SFr, fi = 0.6, 1 < N <, 3, and 250 < V£ 10,000. As seen in Table IV, the MINLP formulation involves 48 variables and 67constraints. MINOS/Augmented (Murtagh and Saunders, 1980) required 16.09 secondsof CPU-time on a DEC-20 computer to solve the relaxed nonlinear program.

Genetic algorithm for non-linear mixed integer programming problems and its applications

In the past years, the issues of energy efficiency and interference are becoming increasingly serious in wireless local area network (WLAN) since lots of access points (AP) are deployed densely to provide high-speed users access. However, current works focus on solving the two issues separately and the influence of each other is rarely considered. To address these problems, we propose a joint optimization scheme of energy efficiency and interference to reduce energy consumption and interference together without sacrificing users’ traffic demands. Firstly, based on energy consumption measurement of AP and network interference analysis, we establish energy efficiency and interference models respectively. Then, the weighting method is introduced to build the joint optimization to quantify the effects of user-AP association, AP switch, AP transmit power and AP channel on energy consumption and interference. Lastly, we formulate the joint optimization as an Mixed Integer Non-Linear Programming (MINLP) problem. Since the MINLP problem is NP-hard, we proposed an Joint Optimization of Energy Efficiency and Interference (JOEI) algorithm based on greedy method to simplify its computational complexity. The evaluation results show that the proposed algorithm can effectively reduce the network energy consumption while improve the capacity of WLANs.

Drone cell (DC) is an emerging technique to offer flexible and cost-effective\nwireless connections to collect Internet-of-things (IoT) data in uncovered\nareas of terrestrial networks. The flying trajectory of DC significantly\nimpacts the data collection performance. However, designing the trajectory is a\nchallenging issue due to the complicated 3D mobility of DC, unique DC-to-ground\n(D2G) channel features, limited DC-to-BS (D2B) backhaul link quality, etc. In\nthis paper, we propose a 3D DC trajectory design for the DC-assisted IoT data\ncollection where multiple DCs periodically fly over IoT devices and relay the\nIoT data to the base stations (BSs). The trajectory design is formulated as a\nmixed integer non-linear programming (MINLP) problem to minimize the average\nuser-to-DC (U2D) pathloss, considering the state-of-the-art practical D2G\nchannel model. We decouple the MINLP problem into multiple quasi-convex or\ninteger linear programming (ILP) sub-problems, which optimizes the user\nassociation, user scheduling, horizontal trajectories and DC flying altitudes\nof DCs, respectively. Then, a 3D multi-DC trajectory design algorithm is\ndeveloped to solve the MINLP problem, in which the sub-problems are optimized\niteratively through the block coordinate descent (BCD) method. Compared with\nthe static DC deployment, the proposed trajectory design can lower the average\nU2D pathloss by 10-15 dB, and reduce the standard deviation of U2D pathloss by\n56%, which indicates the improvements in both link quality and user fairness.\n

Resource allocation for device-to-device (D2D) communications is usually formulated as mixed integer nonlinear programming (MINLP) problems, which are generally NP-hard and difficult to solve. Traditional methods are based on mathematical optimization techniques, which suffer from forbidding computational complexity or unsatisfactory optimality. In this paper, we introduce a machine leaning (ML) technique, imitation learning, to address the resource allocation in D2D communications. The key idea is learning a good prune policy to speed up the widely-used globally optimal algorithm for the MINLP problems, the branch- and-bound (B&B) algorithm. With appropriate feature selection, imitation learning can be converted into a binary classification problem, which can be solved by the classical support vector machine (SVM). Extensive simulation demonstrates that the proposed method can achieve good optimality and reduce computational complexity simultaneously. It only needs hundreds of training samples and has a good generalization ability. Our proposed method can be also applied to the MINLP problems in other wireless communication networks.

The sustainability of water resources is one of the major concerns of the world. Industries are finding ways to minimize water costs and to reduce water pollution through efficient use of supplies. One of effective solutions is the use of water pinch technology or process integration techniques. Property integration emerged as the third trend of process integration technique (aside from energy and mass integration) to solve the problem of water network synthesis by considering physical stream properties such as pH or resistivity. Various techniques have been done to solve this property-based problem. In this paper, mixed integer non-linear programming (MINLP) problems with topological constraints is studied. Nowadays, various evolutionary algorithms are also used to solve such MINLP problems. In this study, particle swarm optimization is used to solve the property integration problem. A comparison is made between this algorithm and commercial genetic algorithm (GA) applications. Particle swarm optimization is observed to perform favorably compared to GA.

In this chapter, the concept of the state sequence network (SSN) representation, which is the cornerstone of the material entailed in this textbook, is presented. This representation is based on states only, eliminating the use of tasks and units. Using this new representation as a basis, a novel continuous time MILP formulation for short-term scheduling of multipurpose batch plants is developed (Majozi and Zhu, 2001, Ind. Eng. Chem. Res., 40(25): 5935–5949). The presented formulation can readily be extended to intermediate due date scenarios. Time points are used to denote the use or production of a particular state. This formulation leads to a small number of binary variables and much better results when compared to other continuous time formulations published in literature. The reduced number of binary variables is a result of considering states only, thereby eliminating binary variables corresponding to tasks and units. This method has been applied to literature examples and industrial problems which show significant improvement in reducing the number of binary variables, hence CPU times. The last section of this chapter introduces the concept of units aggregation in reducing the binary dimension of large-scale problems. This makes it possible for the method to solve large-scale industrial problems. In the forthcoming chapters of this textbook it will be demonstrated how this formulation is applied in the context of batch process integration with the ultimate aim of freshwater and energy optimization.

Federated learning (FL) over wireless networks has become a key enabler for privacy-preserving distributed artificial intelligence (AI). However, high learning latency remains a critical bottleneck due to the presence of stragglers, limited wireless resources, and frequent model uploads. While model quantization can mitigate this issue by reducing communication overhead, its effectiveness is sensitive to device heterogeneity and time-varying channel conditions. To address this issue, we propose <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">FedDamQu</i>, a communication-efficient FL framework with doubly-adaptive model quantization, which dynamically adjusts quantization bit-widths across devices and communication rounds to balance latency and accuracy. Our objective is to maximize the model performance under learning latency constraints. The main contributions are summarized as follows. 1) Convergence Analysis under Unreliable Channels: We derive a novel convergence error upper bound for <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">FedDamQu</i>, which explicitly quantifies the impact of device selection, unreliable transmission, and quantization error on the global model performance, under both fixed and dynamic quantization gain settings. 2) Joint Optimization Framework: Based on the knowledge from the proposed theoretical bound, we formulate a joint mixed integer nonlinear programming (MINLP) problem that integrates device selection, quantization bit-width configuration, and bandwidth allocation to minimize the convergence error under latency constraints. 3) Efficient Solution Design: The MINLP problem is decomposed into three subproblems, where closed-form solutions for quantization bit-width configuration and bandwidth allocation subproblems are derived, and a lightweight yet effective iterative algorithm is developed to obtain a suboptimal solution for the device selection subproblem. Extensive experiment results validate the theoretical analysis and demonstrate that <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">FedDamQu</i> consistently outperforms existing methods in terms of convergence rate and model accuracy, while significantly reducing the overall learning latency.

Various wireless manufacturing sensors facilitate the monitoring and control process in industrial internet of things (IIoT) systems. Control and image data generated by control and vision-based monitoring systems are transmitted over shared wireless network to edge computing devices for further decisions. Due to limited spectrum resources and sensor transmit power, it is challenging to design efficient quality of service (QoS) aware transmission mechanism for heterogeneous data with diverse real-time and system performance requirements. In this paper, in order to guarantee control system performance and image clarity, the time slot allocation and transmission power for heterogeneous sensors are jointly optimized by formulating a mixed integer nonlinear programming (MINLP) problem. The MINLP problem is decomposed into multiple subproblems which are proved to have strong duality and can be solved in dual domain. Then, according to acknowledge (ACK) signals, we propose a priority-aware heuristic algorithm to solve each subproblem. Finally, the simulation results prove that our proposed mechanism can reduce the number of slots and energy consumption for transmission while guaranteeing performance requirements of heterogeneous data.

Effective scheduling of a large-scale paint production system

A novel mathematical formulation for short-term scheduling of multipurpose batch plants in chemical manufacturing