Decarbonization planning for industrial systems, when accounting for operational flexibility, typically gives rise to large, multi-scale mixed-integer optimization problems. Solution strategies often rely on time-series aggregation (TSA) to reduce computational complexity. While the sensitivity of results to hyperparameters used during TSA is well-documented in the power systems literature, we demonstrate that optimal investment and operational decisions in the industrial decarbonization planning problem also remain highly sensitive to the selection of these hyperparameters. In this work, we propose an algorithm that accelerates Benders decomposition for the simultaneous optimization of annual investment decisions and hourly operational decisions and provides bounds on the objective of the full-space problem. We further show that reduced-space formulations obtained via constrained agglomerative hierarchical clustering with mean-based aggregation provide an upper bound on the full decarbonization planning problem. The proposed approach is illustrated through a case study on refinery decarbonization via electrification and carbon capture. By incorporating operational flexibility, our method promotes earlier adoption of electricity-based technologies, such as e-boilers for process heating and proton exchange membrane (PEM) electrolyzers for H2 production supported by H2 storage, ultimately reducing costs compared to a base case without flexibility.

This paper develops an optimization model for long-term expansion planning and short-term operation of reliable power systems using a probabilistic reliability formulation. A state space method is used to represent various operational states by modeling component failures. The impact of additional generators for reliability improvement is taken into account in the probabilistic model. Generalized Disjunctive Programming (GDP), which integrates logical disjunctions and algebraic constraints, is introduced to develop the optimization model for the probabilistic reliability model. Two expansion models, which use traditional reliability approaches, such as the reserve margin model and the N-k reliability model, are also modeled using GDP. The expansion planning model without reliability is also considered. The four different models are compared using a unified evaluation strategy that uses two key reliability criteria: loss of load expectation (LOLE), which represents the expected duration of power disruptions, and expected energy not served (EENS), which quantifies the total power shortage. The effectiveness of the proposed models is verified through two case studies: an illustrative example and a real-world application based on San Diego County. The results indicate that models with rigorous reliability formulations (e.g., probabilistic or N-k reliability) require higher investment and operational costs but achieve greater reliability compared to models using simplified reliability constraints. Computational results are also presented with problems with up to 200 buses.

Deterministic global optimization of nonlinear models is important in many scientific and engineering applications. This framework typically involves repeatedly solving convex relaxations of the nonconvex problem, meaning that the strength of the relaxations and the cost of computing them directly determine overall efficiency and solution quality. In this work, we develop a tailored continuous convexification framework for Kolmogorov-Arnold Networks in which the univariate components are polynomial functions. By exploiting the additive separable structure of this architecture, the relaxation problem reduces to computing tight convex envelopes of univariate polynomials. We propose a continuous variant of the classical Graham Scan that constructs these envelopes exactly by identifying the bitangents of the polynomial convex hull without discretization or factorable reformulations. We establish the correctness of the algorithm and characterize its computational complexity, and show how these envelopes can be combined to construct strong convex relaxations for polynomial KANs. Computational results demonstrate that the proposed relaxations are both strong and robust, often producing bounds that are comparable, or even orders of magnitude tighter than relaxations of state-of-the-art global optimization solvers while remaining computationally efficient.

In this paper, we describe five solution strategies for scheduling CO2 shipments in a carbon capture and storage (CCS) maritime supply chain. Specifically, we consider an RTN-based MILP, a simplified timeslot-based MILP, discrete-event simulation (DES), an integrated DES and optimization approach, and a discrete-time constraint programming (CP) model. A key innovation in our methodology is the introduction of a DES model in a complex logistic problem that cannot be solved in a reasonable CPU time with a rigorous monolithic MILP optimization approach. This unique simulation tool, which is computationally very efficient but with strong limitations in terms of achieving global optimality, allows us to explore its effective integration with more rigorous optimization techniques. The integration of these two techniques involves using the optimization model to predefine major critical decisions that will be sequentially given to the DES model. Another highlight of this paper is applying constraint programming to reformulate the problem with a discrete-time representation, which offers a rigorous and flexible formulation. Using the powerful CP-SAT solver provided by OR-Tools, it is shown that the CP model can find feasible solutions faster than other discrete-time representation models. Several instances based on real data are solved by all five methodologies to compare their computational expense and the solutions obtained.

The optimal design of layout and cable routing is crucial in maximizing the financial returns of wind farms. Traditionally, the Wind Farm Layout Optimization (WFLO) and Wind Farm Cable Routing (WFCR) problems are addressed separately or with extremely simplified wake models. In this paper, we propose a Mixed-Integer Nonlinear Program (MINLP) formulation for the integrated optimization of layout and cable routing, incorporating a nonlinear wake model, to maximize the Net Present Value (NPV) of wind farms. Moreover, we reformulate the original non-convex MINLP as a Mixed-Integer Quadratically Constrained Program (MIQCP) formulation. Compared to solving the MINLP with global MINLP solvers such as BARON, ANTIGONE, or SCIP, solving the reformulated MIQCP with Gurobi significantly reduces solution time while still guaranteeing optimality. Additionally, a bilevel decomposition method is proposed and validated for solving the integrated optimization problem of larger-scale wind farms. Furthermore, computational results demonstrate that the proposed integrated optimization model significantly improves the NPV compared to existing models that ignore wake effects, adopt a simplified linear wake model, or employ a two-stage optimization.

Industrial gas supply chains require highly coordinated production and distribution operations in which transportation assets represent a critical and costly resource. In these systems, fleet sizing decisions strongly influence routing efficiency, customer service levels, and overall operating costs, particularly under Vendor Managed Inventory (VMI) policies and multi-day transportation operations. This paper addresses an integrated Production Routing Problem (PRP) that explicitly incorporates fleet sizing decisions into the optimization framework. The proposed model simultaneously determines production, inventory, routing, delivery scheduling, fleet allocation, and fleet composition decisions, while considering heterogeneous vehicle fleets, transportation lead times, and customer accessibility restrictions. To address the computational complexity associated with large-scale monolithic Mixed-Integer Linear Programming (MILP) formulations, a decomposition-based solution methodology, denoted as the Fleet Sizing Sequential Approach (FSSA), is proposed. The methodology decomposes the original problem into four coordinated optimization stages that progressively reduce the solution space, while preserving solution quality. The proposed strategy first identifies feasible supply structures, constructs optimized customer visitation schedules, determines the fleet configuration, and finally refines operational production and routing decisions once the fleet structure has been fixed. Computational experiments based on illustrative examples and realistic industrial scenarios show that the proposed methodology effectively identifies efficient fleet configurations, while maintaining tractable model sizes. The results demonstrate that coordinating delivery schedules and fleet sizing decisions improves logistics efficiency, and reduces the number of required vehicles compared with alternative solution approaches. High-quality solutions are achieved within reasonable CPU times, supporting the practical applicability of the proposed framework to large-scale industrial problems.

With the development of industry and automation, optimizing crane operations becomes increasingly important for improving productivity and reducing costs in manufacturing systems. In this paper, we address a crane scheduling problem in tankhouse copper processing systems, where operations are tightly integrated with the production process and the resource sharing is frequent. We propose discrete-time mixed-integer linear programming (MILP), continuous-time MILP, and constraint programming (CP) models to tackle this problem. It is found that the CP model has the best performance considering both single- and multi- crane conditions. To efficiently solve real-world problems, we propose a machine-based decomposition strategy with the CP framework, which solves 128 tasks in 34 seconds over 24 iterations. The results demonstrate the effectiveness of the proposed approach in handling large-scale, complex scheduling problems with high computational efficiency.

This paper proposes a general Mixed-Integer Nonlinear Programming (MINLP) formulation for the optimal design of multiphase pipeline networks gathering oil and gas production from wellpads. In contrast to previous approaches, the model explicitly incorporates nonlinear correlations to predict multiphase pressure losses accurately, enabling a more rigorous optimization of the network design and pipeline sizes. Gathering flows according to production start times, wellhead pressures, and gas-to-oil ratios proves essential to secure production, while simultaneously maximizing transportation capacity and minimizing surface facility costs. The model is able to effectively manage flow pressures at junction nodes, compositions after merging, and flexible network topologies. An efficient successive-relaxation approach based on piecewise-constant underestimations of pressure drops is also proposed to obtain solutions within reasonable computation times. Results show that relaxing the limiting assumptions imposed by previous approaches leads to improvements of up to 20% in the net present value (NPV) of illustrative cases comprising ten wellpads. However, the global optimization of real-size problems with more complex topologies remains a significant challenge.

The chemical industry is making significant investments in clean energy technologies, such as green hydrogen, carbon capture and storage, electric heating, and electrochemical processes to reduce carbon emissions. However, uncertainties regarding investments in recent technologies, fluctuating electricity and carbon prices, and the need to balance existing infrastructure with new ones complicate the transition. In this study, we develop a mixed-integer linear programming formulation to determine the most cost-effective transition for the decarbonization of oil refineries, incorporating electrification for steam generation, green hydrogen production, or carbon capture for blue hydrogen production and other emission sources. Two case studies that consider different refinery configurations are presented. Overall, the results of our simulations indicate that (i) natural gas with carbon capture is more economically favorable than electricity-based options, unless there are significant reductions in electricity prices or stricter emission regulations are imposed; (ii) carbon taxes or credits drive earlier adoption of capture technologies but do not promote electrification.

This paper gives an overview of the development of Mixed-Integer Nonlinear Programming (MINLP) and Generalized Disjunctive Programming (GDP) over the past fifty years. We cover key methods, algorithms, and techniques for solving MINLPs and GDPs, focusing on both the modeling framework and solution techniques. We provide historical perspectives, highlight the key features and major challenges, and aim to give an in-depth introduction to the fields. We also discuss some future research directions. The paper is aimed at readers who are familiar with Mixed-Integer Linear Programming but are not experts on MINLP or GDP.

We propose the REORIENT (REnewable resOuRce Investment for the ENergy Transition) model for energy systems planning with the following novelties: (1) integrating capacity expansion, retrofit and abandonment planning, and (2) using multi-horizon stochastic mixed-integer linear programming with multi-timescale uncertainty. We apply the model to the European energy system considering: (a) investment in new hydrogen infrastructures, (b) capacity expansion of the European power system, (c) retrofitting oil and gas infrastructures in the North Sea region for hydrogen production and distribution, and abandoning existing infrastructures, and (d) long-term uncertainty in oil and gas prices and short-term uncertainty in time series parameters. We utilise the structure of multi-horizon stochastic programming and propose a stabilised adaptive Benders decomposition to solve the model efficiently. We first conduct a sensitivity analysis on retrofitting costs of oil and gas infrastructures. We then compare the REORIENT model with a conventional investment planning model regarding costs and investment decisions. Finally, the computational performance of the algorithm is presented. The results show that: (1) when the retrofitting cost is below 20% of the cost of building new ones, retrofitting is economical for most of the existing pipelines, (2) platform clusters keep producing oil due to the massive profit, and the clusters are abandoned in the last investment stage, (3) compared with a traditional investment planning model, the REORIENT model yields 24% lower investment cost in the North Sea region, and (4) the enhanced Benders algorithm is up to 6.8 times faster than the level method stabilised adaptive Benders.

This paper focuses on addressing the Production Routing Problem (PRP) of industrial gas supply chains (SC). The work introduces a Mixed-Integer Linear Programming (MILP) based approach to effectively tackle this challenging problem. The proposed framework aims to increase company profits by optimizing both production and distribution activities simultaneously. For the distribution part, a route generation algorithm is employed to initially generate a set of feasible routes, ensuring that only routes with practical significance are considered. Subsequently, the mathematical model is developed considering only the set of routes generated. The formulation includes decisions associated with plants production levels, plant selection to supply the different consumers, clients to be visited per trip and day, quantity to be delivered and routes to be used. As part of the problem, it is considered that trucks can make several trips per day, as well as trips of several days. To take into account the last feature, the approach accounts for the explicit effect of the lead time on production and distribution decisions. In this way, the work allows for different delivery times for customers included in the same route, according to their inventories and usage levels. The model considers fleet unavailability until they return to the plants after finishing a trip. Finally, two case studies, one motivating and the other industrial size, are presented and solved. The results obtained demonstrate the effectiveness of the proposed approach to solve the case studies in reasonable CPU times.

We propose Conformal Mixed-Integer Constraint Learning (C-MICL), a novel framework that provides probabilistic feasibility guarantees for data-driven constraints in optimization problems. While standard Mixed-Integer Constraint Learning methods often violate the true constraints due to model error or data limitations, our C-MICL approach leverages conformal prediction to ensure feasible solutions are ground-truth feasible with probability at least $1{-}\alpha$, under a conditional independence assumption. The proposed framework supports both regression and classification tasks without requiring access to the true constraint function, while avoiding the scalability issues associated with ensemble-based heuristics. Experiments on real-world applications demonstrate that C-MICL consistently achieves target feasibility rates, maintains competitive objective performance, and significantly reduces computational cost compared to existing methods. Our work bridges mathematical optimization and machine learning, offering a principled approach to incorporate uncertainty-aware constraints into decision-making with rigorous statistical guarantees.

The growing demand for sustainable energy has driven research into renewable methane production to reduce greenhouse gas emissions and fossil fuel dependence. Lignocellulosic dry residues, wet waste, and captured CO2 are promising feedstocks for methane production via gasification, anaerobic digestion, and synthetic processes with renewable hydrogen. This study systematically compares renewable methane production from these sources using a multiscale approach. A techno-economic evaluation identifies key performance indicators (KPI) for facilities and renewable energy sources. A facility location problem (FLP) determines production capacities and optimal plant locations. The decentralised use of lignocellulosic dry and wet waste and CO2 captured from point and diffuse sources is analysed considering material availability and high transportation costs. The problem is formulated as an MILP, optimising waste and CO2 utilisation, plant locations, and renewable energy systems, solar and wind, across Spain. Lignocellulosic dry waste and CO2 from point sources using MEA are preferred. Sensitivity analysis shows methane prices ranging from 13.028 /MWh to 47.216 /MWh between 2022 and 2050, requiring 66 %-410 % of the budget for full self-sufficiency. With carbon taxes, the most competitive price of 10.735 /MWh is projected for 2050, competitive with current natural gas prices.

Optimization of chemical processes is challenging due to nonlinearities arising from chemical principles and discrete design decisions. The optimal synthesis and design of chemical processes can be posed as a Generalized Disjunctive Programming (GDP) problem. While reformulating GDP problems as Mixed-Integer Nonlinear Programming (MINLP) problems is common, specialized algorithms for GDP remain scarce. This study introduces the Logic-Based Discrete-Steepest Descent Algorithm (LD-SDA) as a solution method for GDP problems involving ordered Boolean variables. LD-SDA transforms these variables into external integer decisions and uses a two-level decomposition: the upper-level sets external configurations, and the lower-level solves the remaining variables, efficiently exploiting the GDP structure. In the case studies presented in this work, including batch processing, reactor superstructures, and distillation columns, LD-SDA consistently outperforms conventional GDP and MINLP solvers, especially as the problem size grows. LD-SDA also proves superior when solving challenging problems where other solvers encounter difficulties finding optimal solutions.

The unit commitment problem determines the optimal strategy to meet the electricity demand at minimum cost by committing power generation units at each point of time. Solving the unit commitment problem gives rise to a challenging optimization problem due to its combinatorial complexity and potentially long solution time requirements. Our proposed solution approach utilizes a decomposition method in conjunction with alternative models from the EGRET library. Results of this decomposition approach tested against four benchmarking systems show that significant computational speed ups are achieved.

Large Language Models have demonstrated potential in accelerating scientific discovery, but they face challenges when making inferences in rapidly evolving and niche domains like Process Systems Engineering (PSE). To address this, we propose a Graph-based Retrieval-Augmented Generation (RAG) pipeline specifically designed for PSE papers. Our pipeline includes custom document parsing, knowledge graph construction, and refinement to enhance retrieval accuracy. We evaluate the effectiveness of our approach using an automatically generated benchmark consisting entirely of PSE-related questions. The results show that our pipeline outperforms both non-RAG and vanilla RAG implementations in terms of relevant document retrieval and overall answer quality. Additionally, our implementation is fully customizable, allowing users to select the papers most relevant to their specific tasks. This framework is openly available, providing a flexible solution for those working in PSE or similar domains.

This work introduces a multi-objective model for the Forest Planning Problem (FPP), designed to optimize forest management by determining the best combination of silvicultural treatments, land harvesting proportions, net carbon sequestration, and timber flow. Using Generalized Disjunctive Programming (GDP), the model addresses two conflicting objectives: maximizing net present value and maximizing CO2 sequestration, while accounting for carbon sequestration losses from third parties. The model is reformulated as a mixed-integer linear programming (MILP) problem using both Hull reformulation and Big-M reformulation and validated with data from a forest company in Misiones, Argentina. Results show that increasing forest area reduces reliance on external timber, and that stand characteristics and diverse prescriptions are more effective for improving CO2 sequestration than simply expanding forest area. Additionally, the Hull reformulation proves more robust for complex problems, while Big-M is advantageous for simpler cases.

We present a mixed-integer linear programming (MILP) model for a maritime inventory routing (MIR) problem for carbon capture and storage (CCS). The model is formulated using an extension of the resource-task network (RTN) representation that minimizes sailing costs. The proposed model can accommodate any number of vessels and emitters. The discrete-time model considers accurate task durations relative to the load of CO2. The model can generate an hourly inventory profile and detailed scheduling with accurate results. We show the computational performance of the model on five small-scale examples, and on one large-scale real life instance.