Mixed-integer Dynamic Optimization Research Articles

DRL-Based Secure Aggregation and Resource Orchestration in MEC-Enabled Hierarchical Federated Learning

Federated learning (FL) provides a new paradigm for protecting data privacy by enabling model training at devices and model aggregation at servers. However, data information may be leaked to honest-but-curious aggregation servers by updated model parameters. The existing secure methods do not fully exploit the potentiality of data characteristics in enhancing security, which makes it impossible to optimize limited system resources overall to achieve secure, fair and efficient FL systems. In this paper, a DRL-based joint secure aggregation and resource orchestration scheme is proposed to guarantee security and fairness, and improve efficiency for hierarchical FL assisted by untrusted mobile-edge computing (MEC) servers. We formulate a joint optimization problem of data size, payment and resource orchestration, to maximize the long-term social welfare subject to secure aggregation and limited resources. Since the formulated problem is a complex mixed integer dynamic optimization problem with NP-hardness, where multiple mixed integer optimization variables are highly coupled in time-varying constraints and objective function, it is difficult to obtain its optimal solution via traditional optimization methods. Thus, we propose a hierarchical reward function-based DRL algorithm (MATD3) to guide the agents to approach the optimal policy of secure aggregation and resource orchestration. Simulation results show that the proposed algorithm MATD3 can achieve superior performance over comparison algorithms and the MEC-enabled HFL framework outperforms two-layer FL frameworks.

Negative carbon optimal scheduling of integrated energy system using a non-dominant sorting genetic algorithm

An integrated energy system, as a system where multiple energy sources coexist, is important for achieving energy conservation and emission reduction and upgrading the energy structure. In this study, a regional integrated energy system capable of absorbing CO2 emissions is proposed. The system can absorb 38.24% of the CO2 generated in the system by using the alkaline solution produced by electrolysis of water for hydrogen production. At the same time, the system can recover the waste heat generated by electrolysis of water and fuel cells, which can meet 42.42% of the heat demand. In order to better achieve efficient utilization between energy sources of the integrated energy system, a nonlinear mixed integer dynamic scheduling optimization model is constructed with multiple objectives of minimizing economic operating costs, CO2 emissions, and energy consumption. The model is solved using a non-dominated ranking genetic algorithm, and the optimal scheduling scheme is determined by combining compromise schemes. Meanwhile, the system can spontaneously select the most appropriate scheduling strategy based on the proposed scheduling model. The results show that it saves 7.23% of operation cost, 33.04% of CO2 emission, and 9.94% of energy consumption compared with the conventional cooling, heating, and power triple-supply system. The system is not only a stable source of energy such as electricity and hydrogen, but also achieves energy saving and emission reduction.

Simultaneous design & control of a reactive distillation system – A parametric optimization & control approach

We present a detailed dynamic model for a reactive distillation system, based on which we develop design-dependent explicit optimal control strategies. A mixed-integer dynamic optimization formulation is then proposed integrating design, control and operational components, the solution of which allows us to derive explicit closed-loop strategies that maintain stable and operable conditions in the presence of process disturbances. The simultaneous approach is illustrated with the design of a methyl tert-butyl ether reactive distillation system example as a part of the developed model library in the RAPID SYNOPSIS project.

Integrated process design, scheduling, and model predictive control of batch processes with closed‐loop implementation

AbstractSimultaneous evaluation of multiple time scale decisions has been regarded as a promising avenue to increase the process efficiency and profitability through leveraging their synergistic interactions. Feasibility of such an integral approach is essential to establish a guarantee for operability of the derived decisions. In this study, we present a modeling methodology to integrate process design, scheduling, and advanced control decisions with a single mixed‐integer dynamic optimization (MIDO) formulation while providing certificates of operability for the closed‐loop implementation. We use multi‐parametric programming to derive explicit expressions for the model predictive control strategy, which is embedded into the MIDO using the base‐2 numeral system that enhances the computational tractability of the integrated problem by exponentially reducing the required number of binary variables. Moreover, we apply the State Equipment Network representation within the MIDO to systematically evaluate the scheduling decisions. The proposed framework is illustrated with two batch processes with different complexities.

Mixed-integer minimax dynamic optimization for structure identification of glycerol metabolic network

Cell metabolism is a dynamic regulation process, in which its network structure and/or regulatory mechanisms can change constantly over time due to internal and external perturbations. This paper models glycerol metabolism in continuous fermentation as a nonlinear mixed-integer dynamic system by defining the time-varying metabolic network structure as an integer-valued function. To identify the dynamic network structure and kinetic parameters, we establish a mixed-integer minimax dynamic optimization problem with concentration robustness as its objective functional. By direct multiple shooting strategy and a decomposition approach consisting of convexification, relaxation and rounding strategy, the optimization problem is transformed into a large-scale approximate multistage parameter optimization problem. It is then solved using a competitive particle swarm optimization algorithm. We also show that the relaxation problem yields the best lower bound for the optimization problem, and its solution can be arbitrarily approximated by the solution obtained from rounding strategy. Numerical results indicate that the proposed mixed-integer dynamic system can better describe cellular self-regulation and response to intermediate metabolite inhibitions in continuous fermentation of glycerol. These numerical results show that the proposed numerical methods are effective in solving the large-scale mixed-integer dynamic optimization problems.

Mixed-Integer dynamic optimization of conventional and vapor recompressed batch distillation for economic and environmental objectives

In this contribution, a unique multi-objective mixed-integer dynamic optimization problem considering two conflicting objectives, namely, maximization of amount of product per dollar while minimizing CO2 emission is formulated and solved using the elitist non-dominated genetic algorithm for both conventional batch distillation (CBD) and vapor recompressed batch distillation (VRBD) operating at constant reflux mode. Here, selection of an optimal solution from the Pareto-optimal front is performed by 10 Pareto ranking methods along with entropy weighting. A wide boiling separating system (i.e., acetone and water) is adopted for illustrating the proposed multi-objective optimization of batch distillation. Two separate optimization studies for CBD and VRBD are conducted with the target of either improving an existing plant or setting up a new plant. Results obtained show that most of the popular Pareto ranking methods select same optimal solution for each of these problems. Finally, a comparative analysis is performed to find the benefits of vapor recompression over the conventional scheme.

Optimal Scheduling of Active Distribution Networks With Limited Switching Operations Using Mixed-Integer Dynamic Optimization

The optimal scheduling of active distribution networks (ADNs) significantly enhances voltage security and reduces costs, particularly as the numbers of distributed generation sources and energy storage devices increase. Therefore, this paper proposes a mixed-integer dynamic optimization (MIDO) model for the optimal scheduling of ADNs. This model incorporates loads and distributed generation outputs with continuous trajectories and aims to provide optimal continuous-trajectory schemes for ADNs. The optimization is conducted with the objective of minimizing the daily costs of electricity purchased from distribution substations. However, in practice, discrete control devices are required to adopt a limited number of switching operations, which increase the computational complexity of the MIDO model. Hence, a reduced convex relaxation method is utilized to achieve reduced convex transformation and tight relaxation of the MIDO model with respect to integer variables. This converts the MIDO model into a continuous dynamic optimization model, which is then further approximated as a nonlinear programming model using the Radau collocation method. Meanwhile, the absolute-value constraints limiting the number of switching operations are eliminated by an equivalent conversion to a series of linear inequalities. Numerical simulations on IEEE 33-bus, PG&E 69-bus, and real-world 110-bus ADNs demonstrate the effectiveness and efficiency of the proposed methodology.

Hybrid parallel multimethod hyperheuristic for mixed-integer dynamic optimization problems in computational systems biology

This paper describes and assesses a parallel multimethod hyperheuristic for the solution of complex global optimization problems. In a multimethod hyperheuristic, different metaheuristics cooperate to outperform the results obtained by any of them isolated. The results obtained show that the cooperation of individual parallel searches modifies the systemic properties of the hyperheuristic, achieving significant performance improvements versus the sequential and the non-cooperative parallel solutions. Here we present and evaluate a hybrid parallel scheme of the multimethod, using both message-passing (MPI) and shared memory (OpenMP) models. The hybrid parallelization allows to achieve a better trade-off between performance and computational resources, through a compromise between diversity (number of islands) and intensity (number of threads per island). For the performance evaluation, we considered the general problem of reverse engineering nonlinear dynamic models in systems biology, which yields very large mixed-integer dynamic optimization problems. In particular, three very challenging problems from the domain of dynamic modeling of cell signaling were used as case studies. In addition, experiments have been carried out in a local cluster, a large supercomputer and a public cloud, to show the suitability of the proposed solution in different execution platforms.

Multi-objective optimized operation of integrated energy system with hydrogen storage

In this paper, an integrated energy system (IES) consisting of wind turbine unit, photovoltaic cell unit, electrolytic hydrogen unit, fuel cell unit, and hydrogen storage unit is proposed, and the construction of multi objectives for day-ahead power dispatching of the IES considering both operation and environment cost is discussed. By adopting piecewise linearization method, the optimization variables are divided into 24 periods, and the day-ahead power dispatching optimization problem is transformed into a 24-h piecewise optimization problem. On the basis, a complete non-linear mixed integer dynamic scheduling optimization model is established. An improved non-dominated sorting genetic algorithm (NSGA-II) is applied to solving the model. In optimization process, an interactive strategy is adopted to solve the coordination between discretization of variables and restriction of switching times of electrolyzer. Optimization results show that, compared with the single objective of minimizing operating costs, the multi-objective optimization scheme can reduce carbon emissions by 3.5% with 2.8% increase of operating cost. Compared with the single objective of minimizing environmental, the multi-objective optimization scheme can reduce operating cost carbon by 5.12% with 2.6% increase of environmental cost.

Integrated process design, scheduling, and control using multiparametric programming

A unified theory and framework for the integration of process design, control, and scheduling based on a single high fidelity model is presented. The framework features (i) a mixed-integer dynamic optimization (MIDO) formulation with design, scheduling, and control considerations, and (ii) a multiparametric optimization strategy for the derivation of offline/explicit maps of optimal receding horizon policies. Explicit model predictive control schemes are developed as a function of design and scheduling decisions, and similarly design dependent scheduling policies are derived accounting for the closed-loop dynamics. Inherent multi-scale gap issues are addressed by an offline design dependent surrogate model. The proposed framwork is illustrated by two example problems, a system of two continuous stirred tank reactor, and a small residential combined heat and power (CHP) network.

Simultaneous Design and Control of a Ternary Reactive Distillation Column with Inert Material

AbstractProcess integration means significant challenges in operating a chemical process dynamically due to its complexity. One example is the ternary reactive distillation with inert material. Based on the heuristic approach, chemical process design and process control are performed independently one after another. This may lead to infeasible solutions either in process design and control or in both. The application of simultaneous design and control, formulated as mixed‐integer dynamic optimization (MIDO) problems, increased rapidly in the last decade. Simultaneous process design and control, including control structure selection and control parameters, is devised for the challenging benchmark problem of a ternary reactive distillation with inert material. The improved process design and control is obtained by solving the MIDO problem.

An adaptive wavelet method for solving mixed-integer dynamic optimization problems with discontinuous controls and application to alkali–surfactant–polymer flooding

ABSTRACTThis article presents an adaptive rationalized Haar function approximation method to solve dynamic optimization with mixed-integer and discontinuous controls. Three measures are taken to deal with the discontinuity. First, the problem is converted into a multi-stage optimization problem by non-uniform control vector parameterization. Secondly, an adaptive strategy is proposed to regulate the interval division and the order of Haar function vectors. Thirdly, a structure detection method is presented to refine the subintervals, in which adjacent arcs with the same input type are merged into one to modify redundant subintervals. During this approximation solution, the mixed-integer restriction is realized by the integer truncation strategy. Combined with the Hamiltonian function, a validation principle is shown to verify the optimality of the solution. Finally, the proposed method is applied to solve the enhanced oil recovery for alkali–surfactant–polymer flooding. The effectiveness of the method is illustrated through simulation.

Multi-Objective Mixed-Integer Dynamic Optimization Method Applied to Optimal Allocation of Dynamic Var Sources of Power Systems

For large power systems with huge proportions of industrial loads, dynamic var sources (DVSs) such as STATCOMs and generators provide significant protection against short-term voltage instability. Simultaneously optimizing the locations and capacities of STATCOMs and the settings for adjustment coefficients of generator excitation systems is a goal of this paper; thus, we formulate a multi-objective, mixed-integer dynamic optimization (MOMIDO) model subject to short-term voltage security and rotor-angle stability under multiple contingencies. We also present a reduced convex relaxation (RCR) method to handle STATCOM locations (which are integer variables) and to avoid their combinatorial explosion, and convert the MOMIDO model into a multi-objective nonlinear programming problem via Radau collocation. To obtain complete Pareto optimal solutions for the MOMIDO model, we propose a reduced wide normalized normal constraint (RWNNC) method by enlarging the Utopia plane so that the Pareto optimal solutions are covered completely by its vertical projection, while pruning redundant sections on the Utopia plane to reduce the amount of calculations. Moreover, the simulation results on an IEEE standard 39-bus system and a real provincial power system demonstrate that the proposed method can handle integer variables effectively and obtain complete Pareto optimal solutions.

Dynamic Optimization of the PyNP/PNP Phosphorolytic Enzymatic Process Using MOSAICmodeling

AbstractPyrimidine and purine nucleoside phosphorylases catalyze the reversible phosphorolytic cleavage and formation of the glycosidic bond of purine and pyrimidine nucleosides, respectively, and are thus, key catalysts for the synthesis of new compounds. The selection of the best combination of enzyme and reaction conditions is not trivial, as each of the two enzymes can perform the reaction in two directions and thus, also competes with the other one for the reaction intermediates. A generic approach to the solution of this problem based on the formulation of a mixed integer dynamic optimization program using MOSAICmodeling is presented.

A parallel metaheuristic for large mixed-integer dynamic optimization problems, with applications in computational biology.

BackgroundWe consider a general class of global optimization problems dealing with nonlinear dynamic models. Although this class is relevant to many areas of science and engineering, here we are interested in applying this framework to the reverse engineering problem in computational systems biology, which yields very large mixed-integer dynamic optimization (MIDO) problems. In particular, we consider the framework of logic-based ordinary differential equations (ODEs).MethodsWe present saCeSS2, a parallel method for the solution of this class of problems. This method is based on an parallel cooperative scatter search metaheuristic, with new mechanisms of self-adaptation and specific extensions to handle large mixed-integer problems. We have paid special attention to the avoidance of convergence stagnation using adaptive cooperation strategies tailored to this class of problems.ResultsWe illustrate its performance with a set of three very challenging case studies from the domain of dynamic modelling of cell signaling. The simpler case study considers a synthetic signaling pathway and has 84 continuous and 34 binary decision variables. A second case study considers the dynamic modeling of signaling in liver cancer using high-throughput data, and has 135 continuous and 109 binaries decision variables. The third case study is an extremely difficult problem related with breast cancer, involving 690 continuous and 138 binary decision variables. We report computational results obtained in different infrastructures, including a local cluster, a large supercomputer and a public cloud platform. Interestingly, the results show how the cooperation of individual parallel searches modifies the systemic properties of the sequential algorithm, achieving superlinear speedups compared to an individual search (e.g. speedups of 15 with 10 cores), and significantly improving (above a 60%) the performance with respect to a non-cooperative parallel scheme. The scalability of the method is also good (tests were performed using up to 300 cores).ConclusionsThese results demonstrate that saCeSS2 can be used to successfully reverse engineer large dynamic models of complex biological pathways. Further, these results open up new possibilities for other MIDO-based large-scale applications in the life sciences such as metabolic engineering, synthetic biology, drug scheduling.

Process design and control optimization: A simultaneous approach by multi‐parametric programming

We present a framework for the application of design and control optimization via multi‐parametric programming through four case studies. We develop design dependent multi‐parametric model predictive controllers that are able to provide the optimal control actions as functions of the system state and the design of the process at hand, via our recently introduced PAROC framework (Pistikopoulos et al, Chem Eng Sci. 2015;136:115–138). The process and the design dependent explicit controllers undergo a mixed integer dynamic optimization (MIDO) step for the determination of the optimal design. The result of the MIDO is the optimal design of the process under optimal operation. We demonstrate the framework through case studies of a tank, a continuously stirred tank reactor, a binary distillation column and a residential cogeneration unit. © 2017 American Institute of Chemical Engineers AIChE J, 2017

Automated Design Framework for Synthetic Biology Exploiting Pareto Optimality.

In this work we consider Pareto optimality for automated design in synthetic biology. We present a generalized framework based on a mixed-integer dynamic optimization formulation that, given design specifications, allows the computation of Pareto optimal sets of designs, that is, the set of best trade-offs for the metrics of interest. We show how this framework can be used for (i) forward design, that is, finding the Pareto optimal set of synthetic designs for implementation, and (ii) reverse design, that is, analyzing and inferring motifs and/or design principles of gene regulatory networks from the Pareto set of optimal circuits. Finally, we illustrate the capabilities and performance of this framework considering four case studies. In the first problem we consider the forward design of an oscillator. In the remaining problems, we illustrate how to apply the reverse design approach to find motifs for stripe formation, rapid adaption, and fold-change detection, respectively.

Integrated design and control of semicontinuous distillation systems utilizing mixed integer dynamic optimization

Semicontinuous distillation systems are notoriously difficult to design and optimize because the structural parameters, operational parameters, and control system must all be determined simultaneously. In the past 15 years of research into semicontinuous systems, studies of the optimal design of these systems have all been limited in scope to small subsets of the parameters, which yields suboptimal and often unsatisfactory results. In this work, for the first time, the problem of integrated design and control of semicontinuous distillation processes is studied by using a mixed integer dynamic optimization (MIDO) problem formulation to optimize both the structural and control tuning parameters of the system. The public model library (PML) of gPROMS is used to simulate the process and the built-in optimization package of gPROMS is used to solve the MIDO via the deterministic outer approximation method. The optimization results are then compared to the heuristic particle swarm optimization (PSO) method.

Optimal response under partial plant shutdown with discontinuous dynamic models

This work describes mathematical formulations for modeling aspects of partial shutdowns in multiunit plants. The specific type of partial shutdown considered is one that permits the decoupling of affected units from the rest of the plant, thus enabling continued plant operation, albeit in a more limited fashion. Parsimonious and computationally efficient mixed-integer formulations are presented for specific discontinuous phenomena that arise in partial shutdown modeling, such as shutdown thresholds, induced shutdowns, discontinuous costs, and minimum shutdown durations. It is demonstrated that induced shutdowns (secondary shutdowns triggered by the original shutdown) can be correctly penalized in the objective by capturing the shutdown's true discontinuous economic cost. The computed optimal solution is implemented in closed-loop by employing a multitiered model predictive shutdown controller, in which a discrete-time mixed-integer dynamic optimization (MIDO) problem is embedded. Both objectives of maximizing economics and minimizing restoration (shutdown recovery) time are considered.

Towards the integration of process design, control and scheduling: Are we getting closer?

Abstract The integration of design and control, control and scheduling and design, control and scheduling, all have been core PSE challenges. While significant progress has been achieved over the years, it is fair to say that at the moment there is not a generally accepted methodology and/or “protocol” for such an integration – it is also interesting to note that currently, there is not a commercially available software [or even in a prototype form] system to fully support such an activity. Here, we present the foundations for such an integrated framework and especially a software platform that enables such integration based on research developments over the last 25 years. In particular, we describe PAROC, a prototype software system which allows for the representation, modeling and solution of integrated design, scheduling and control problems. Its main features include: (i) a high-fidelity dynamic model representation, also involving global sensitivity analysis, parameter estimation and mixed integer dynamic optimization capabilities; (ii) a suite/toolbox of model approximation methods; (iii) a host of multi-parametric programming solvers for mixed continuous/integer problems; (iv) a state-space modeling representation capability for scheduling and control problems; and (v) an advanced toolkit for multi-parametric/explicit Model Predictive Control and moving horizon reactive scheduling problems. Algorithms that enable the integration capabilities of the systems for design, scheduling and control are presented on a case of a series of cogeneration units.