The bounded degree sum-of-squares (BSOS) hierarchy of Lasserre et al. (EURO J Comput Optim 1–31, 2015) constructs lower bounds for a general polynomial optimization problem with compact feasible set, by solving a sequence of semi-definite programming (SDP) problems. Lasserre, Toh, and Yang prove that these lower bounds converge to the optimal value of the original problem, under some assumptions. In this paper, we analyze the BSOS hierarchy and study its numerical performance on a specific class of bilinear programming problems, called pooling problems, that arise in the refinery and chemical process industries.@en

The functioning of infrastructure networks is vital for modern communities. Maintenance should be planned to ensure infrastructure's functionality and safety at the lowest cost. Interconnected infrastructure networks can affect each other's functionality, and maintenance on one network can impact the serviceability of others. Planned intervention grouping across infrastructures reduces set-up costs and service interruption, improving infrastructure availability and serviceability at lower costs. Finding the best grouping strategy is a known NP-hard problem, with several optimization strategies have been proposed, mainly based on nonlinear models which are computationally expensive and do not guarantee scalability. Furthermore, infrastructure intervention planning models mostly focus on grouping of interventions which are considered as given. In this paper, we propose a new efficient optimization model to optimize intervention grouping for interconnected infrastructure networks. We develop a scalable two-step optimization model where we first plan each individual intervention type based on a preventive maintenance policy accounting for the degradation behavior of objects, then group interventions to minimize the net costs, considering dependencies within and accross infrastructure networks. We formulate the grouping problem as an Integer Linear Program, which can be solved exactly with standard solvers. The model accounts for interactions between infrastructure networks and considers the impact on all stakeholders. It also accommodates various intervention types like maintenance, removal, and upgrading. Using a demonstrative application, we show that our model significantly reduces net costs and outperforms alternative nonlinear formulations and related heuristics in terms of both solution quality and computation performance. Additionally, the optimal intervention plan shows repetitive patterns, which suggests that a rolling horizon strategy could be used where the optimization problem is solved for shorter time horizons, leading to significant computational benefits.@en

The functioning of infrastructure networks is vital for modern communities. Maintenance should be planned to ensure infrastructure's functionality and safety at the lowest cost. Interconnected infrastructure networks can affect each other's functionality, and maintenance on one network can impact the serviceability of others. Planned intervention grouping across infrastructures reduces set-up costs and service interruption, improving infrastructure availability and serviceability at lower costs. Finding the best grouping strategy is a known NP-hard problem, with several optimization strategies have been proposed, mainly based on nonlinear models which are computationally expensive and do not guarantee scalability. Furthermore, infrastructure intervention planning models mostly focus on grouping of interventions which are considered as given. In this paper, we propose a new efficient optimization model to optimize intervention grouping for interconnected infrastructure networks. We develop a scalable two-step optimization model where we first plan each individual intervention type based on a preventive maintenance policy accounting for the degradation behavior of objects, then group interventions to minimize the net costs, considering dependencies within and accross infrastructure networks. We formulate the grouping problem as an Integer Linear Program, which can be solved exactly with standard solvers. The model accounts for interactions between infrastructure networks and considers the impact on all stakeholders. It also accommodates various intervention types like maintenance, removal, and upgrading. Using a demonstrative application, we show that our model significantly reduces net costs and outperforms alternative nonlinear formulations and related heuristics in terms of both solution quality and computation performance. Additionally, the optimal intervention plan shows repetitive patterns, which suggests that a rolling horizon strategy could be used where the optimization problem is solved for shorter time horizons, leading to significant computational benefits.@en

The functioning of infrastructure networks is vital for modern communities. Maintenance should be planned to ensure infrastructure's functionality and safety at the lowest cost. Interconnected infrastructure networks can affect each other's functionality, and maintenance on one network can impact the serviceability of others. Planned intervention grouping across infrastructures reduces set-up costs and service interruption, improving infrastructure availability and serviceability at lower costs. Finding the best grouping strategy is a known NP-hard problem, with several optimization strategies have been proposed, mainly based on nonlinear models which are computationally expensive and do not guarantee scalability. Furthermore, infrastructure intervention planning models mostly focus on grouping of interventions which are considered as given. In this paper, we propose a new efficient optimization model to optimize intervention grouping for interconnected infrastructure networks. We develop a scalable two-step optimization model where we first plan each individual intervention type based on a preventive maintenance policy accounting for the degradation behavior of objects, then group interventions to minimize the net costs, considering dependencies within and accross infrastructure networks. We formulate the grouping problem as an Integer Linear Program, which can be solved exactly with standard solvers. The model accounts for interactions between infrastructure networks and considers the impact on all stakeholders. It also accommodates various intervention types like maintenance, removal, and upgrading. Using a demonstrative application, we show that our model significantly reduces net costs and outperforms alternative nonlinear formulations and related heuristics in terms of both solution quality and computation performance. Additionally, the optimal intervention plan shows repetitive patterns, which suggests that a rolling horizon strategy could be used where the optimization problem is solved for shorter time horizons, leading to significant computational benefits.@en

The sparse bounded degree sum-of-squares (sparse-BSOS) hierarchy of Weisser et al. (2017) constructs a sequence of lower bounds for a sparse polynomial optimization problem. Under some assumptions, it is proved by the authors that the sequence converges to the optimal value. In this paper, we modify the hierarchy to deal with problems containing equality constraints directly, without eliminating or replacing them by two inequalities. We also evaluate the sparse-BSOS hierarchy on a well-known bilinear programming problem, called the pooling problem, as well as a discrete-time optimal control problem.@en

This Chapter ranges through a wide variety of production and demand management problems related to energy commodities systems. The Oil and Gas production enhancement is discussed via oil wells optimal placement as well as water and gas optimal injection, namely waterflooding and gas lift. Further is analyzed the optimal schedule and design of commodities generation in energy hubs and combined cooling, heat and power systems, reaching finally the chemical processes where the specification of the products is taken into account, with mixing tanks, pools, and blending points. Overall, each of these problems is qualitatively discussed identifying the typical objective functions, variables and constraints generalizing its structure, the problem typology is identified as well as the most common methods to solve it.@en