Industrial scheduling is an important task that involves the allocation of the orders to resources and the sequencing and timing of the operations to meet delivery dates and to improve the performance of the production system. Most of the research in this area addresses static or offline scheduling problems, i.e. solving scheduling problems for a given set of resources, orders, and due dates, and focuses on the efficiency of the solution process. However, in industrial operations each schedule is outdated shortly after it has been computed due to unforeseen events, e.g. new orders or due dates, lack of materials, maintenance, etc. Often the precomputed schedule does not meet the constraints any more or cannot be executed at all because resources are (temporarily) not available. Then in practice manual re-scheduling takes place. In this contribution we discuss how a static scheduling system can be redesigned for use in dynamic situations, i.e. for reactive scheduling.Our approach builds on previous work on production planning using simulation-optimization. It combines a discrete-event simulator with a tailored evolutionary algorithm to implement a dynamic adaptation of the schedules to the available information. The simulation model is continuously updated with the latest information about the state of the plant and of the orders. At the beginning of a cycle the evolutionary algorithm evaluates all schedules of the current population with this model and then improves them. We demonstrate our solution for a pharmaceutical batch plant example with a high combinatorial complexity. Our study demonstrates that the simulation-optimization framework can effectively handle unforeseen events and provides good solutions fast.

In the chemical industry commercial process simulators are widely used for process design due to their extensive library of models of plant equipment and thermodynamic properties and their ease of use. Most of these simulators compute the steady-states of complex flowsheets, but their models are inaccessible and derivatives with respect to their model parameters are not available. Evolutionary algorithms are a suitable approach for the global optimization of such black-box models, but they require the evaluation of many individuals. Applications to industrial-size case-studies suffer from high computational times where the numerical simulations consume the majority of the time. This contribution proposes the use of neural networks as surrogate models to guide the evolutionary search. These models are trained multiple times during the evolutionary search and are used to exclude nonpromising individuals and to generate candidate solutions. We demonstrate the performance improvement due to the use of the surrogate models for a medium-size case-study of a chemical plant consisting of a reactor, a liquid-liquid separation and a distillation column. The results show that the required number of simulations can be reduced by 50%.

The calculation of the thermo-physical phase equilibrium of a multicomponent mixture is employed in chemical process development to model the number and composition of phases in order to predict and to optimize the reaction and separation performance of a chemical process plant. Complex thermodynamic models as equations of state provide reliable predictions of phase equilibria over a broad operating range. But due to the need for iterative calculations, they are hardly applicable in optimization. This work shows how a combination of classification and regression can be used to replace these calculations in the optimization of the process of hydroformylation of 1-dodecene.

Model-based optimization and control is becoming more and more important in the process industries and in general. Modelling almost always involves the estimation of parameters from available data. The parameter estimation problem is usually posed as the minimization of the prediction error or the maximization of the likelihood function. If the uncertainty of the measurements taken from a real process is assumed to be an interval around the measured values, a set of parameter vectors exists that is able to describe the behavior of the systems within these uncertainties. Guaranteed parameter estimation deals with the problem of determining all parameter vectors that are compatible with uncertain observations. The solution of guaranteed parameter estimation problems for nonlinear dynamic models is computationally very demanding. In this contribution we present a memetic algorithm that determines the sets of feasible model parameters efficiently. It is applied to the estimation of kinetic parameters of a model that describes a copolymerization reaction. In the memetic algorithm, the fitness evaluation is based on the distance of the feasible solutions to each other, thus the presented approach is not restricted to a specific type of models.

Optimization problems with uncertainty can be modelled by two-stage stochastic Mixed-Integer Linear Programs (MILP), where a discrete set of scenarios is used to model the uncertainties and the option of recourse decisions that react to the actual evolution of the uncertainties is represented in the model. Solving these problems for realistic instances with a large number of scenarios becomes computationally very hard, hence (semi)heuristic approaches have been proposed to find good solutions in reasonable computation times. In this contribution we present a new method for solving large scale two-stage mixed-integer linear programs under uncertainty by combining a stage decomposition approach with the principles of Ordinal Optimization: “Order is easier than Value” and “Nothing but the best is very costly”. The proposed heuristic replaces the exact MILP solution of the scenario problems by fast non-exact solutions to perform a ranking (with small errors) of different promising first stage solutions.

In this contribution a derivative-free memetic algorithm (MA) for the design optimization of chemical processes is introduced. Design optimization problems are characterized by nonlinear cost functions and highly constrained and multi-modal search spaces. The MA is a combination of an evolution strategy that addresses the global optimization of discrete and continuous design decisions and a derivative-free optimization method (DFO) that performs a local optimization of the continuous sub-problems that remain after fixing the discrete decisions. The MA calls a process simulation software to simulate the design alternatives, i.e. the evaluation of the objective and the constraints is a black box. In this contribution, the focus lies on the selection of a suitable DFO solver for efficiently solving the continuous constrained sub-problems. Based on latin-hypercube samplings of sub-problems of two instances of a real-world case study, surrogate models for the objective and the constraints were generated. A set of DFO methods was tested and compared on the surrogate models. The method that showed the best performance was coupled to the MA which was then applied to the real-world case study.

In the computer-aided design of chemical processes the quality of a process design is highly dependent on the reliability of the process models. Models for the prediction of physical properties of mixtures of substances play a crucial role here. In recent years, models with better prediction accuracy have been developed, but these models contain implicit equations which slow down the evaluation of the plant models considerably. In this work it is demonstrated that the application of neural networks as surrogate models of thermodynamic data can make the use of advanced thermodynamic models within algorithmic design approaches possible.

In the model-based design of complex technical systems, many design data artifacts are generated, such as models in different formalisms and design-related documents, which include specifications, test results, and design decisions. The consistent treatment and integration of these design artifacts is a challenge that is as of yet unsolved in industrial practice. This paper illustrates the industrial applicability of a software-based Design Framework (DF) [1] for the model-based design of an engine control system that was developed recently within the European research project MULTIFORM [2]. The goal of the Design Framework is to reduce the design effort, and thus the cost, while improving the quality of the designed system by consistently integrating the artifacts and tools that arise in model-based design processes. To ensure that design inconsistencies and errors are detected as early as possible (i.e. when it is relatively cheap to correct them), the framework provides structured data and model management as well as automated design consistency checking and design parameter propagation.

This paper introduces new initialization approaches for evolutionary algorithms that solve two-stage stochastic mixed-integer problems. The two-stage stochastic mixed-integer programs are handled by a stage decomposition based hybrid algorithm where an evolutionary algorithm handles the first-stage decisions and mathematical programming handles the second-stage decisions. The population of the evolutionary algorithm is initialized by using solutions which are generated in a preprocessing step of the hybrid algorithm. This paper presents three different initialization approaches in which the two-stage stochastic mixed-integer program is exploited in order to obtain potentially good starting solutions for the evolutionary algorithm. In case of infeasible initializations, the population is driven toward feasibility by a penalty function. Comparisons of an evolutionary algorithm with a classical random initialization and the new initialization approaches for two real-world problems show that the new initialization approaches lead to high quality feasible solutions in significantly shorter computing times.

Design optimization problems in chemical engineering and in many other engineering domains are characterized by the presence of a large number of discrete and continuous decision variables, complex nonlinear models that restrict the search space, nonlinear cost functions, and the presence of many local optima. The classical approach to such problems are mixed integer nonlinear program solvers that work on a superstructure formulation which explicitly represents all design alternatives. The structural decisions lead to a large number of discrete variables and an exponential increase in the computational effort. The mathematical programming (MP) methods which are usually employed to solve the continuous subproblems that arise by fixing the discrete variables provide only one local optimum which depends strongly on the initialization. Thus standard methods may not find the global optimum despite long computation times. In this contribution we introduce a memetic algorithm (MA) for the global optimization of a computational demanding real-world design problem from the chemical engineering domain. The MA overcomes the problem of getting stuck in local optima by the use of an evolution strategy (ES) which addresses the global optimization of the design decisions, whereas a robust MP solver is used to handle complex nonlinear constraints as well as to improve the individuals of the ES by performing a local search in continuous sub-spaces in an integrated fashion. The MA is discussed in detail, the novel decomposition of the problem class at hand is analyzed and the MA is tested for the example of the optimal design of a reactive distillation column with several thousand decision variables. The MA is the only algorithm that finds the global solution in reasonable computation times. The introduction of structural decisions and additional constraints and discontinuous penalty terms lead only to a moderate increase in the computational effort which demonstrates the potential of this class of memetic algorithms in real-world design optimization problems.

Evolutionary algorithms were originally designed for the optimization of unconstrained problems. When applied to constrained real-world problems, for example to the optimization of the operation of pipeless chemical batch plants, the constraints have to be taken into account to generate feasible solutions. This paper examines different approaches of constraint handling within the framework of an evolutionary scheduling algorithm and a heuristic schedule builder. Repair algorithms eliminate most infeasibilities before passing a candidate solution to the schedule builder. This is shown to be more efficient than dealing with the constraints inside the schedule builder or simply rejecting infeasible solutions.

This article describes a hybrid multiple populations based evolutionary approach for disjunctive mathematical programs with uncertainties in the problem data. The problems are formulated as two-stage linear disjunctive programming problems which are solved by a stage decomposition based hybrid algorithm using multiple evolutionary algorithms to handle the disjunctive sets of the here-and-now (first stage) decisions and mathematical programming to handle the recourse (second stage) decisions. By an appropriate representation of the first-stage disjunctive solution space, the overall problem is decomposed into smaller subproblems without disjunctions. The resulting decomposed first-stage subproblems are solved independently by evolutionary algorithms, leading to parallel evolutions based on multiple populations. During the progress of the optimization, the number of subproblems is systematically reduced by comparing the current best global solution (upper bound) to lower bounds for the subproblems. This approach guaranties that the global optimal solution remains in the union of solution spaces of the remaining subproblems. A comparison of a classical evolutionary algorithm and the new multiple populations evolutionary algorithm for a real world batch scheduling problem shows that the new approach leads to a significantly improved coverage of the set of feasible solutions such that high quality feasible solutions can be generated faster.

Engineering optimization often deals with very large search spaces which are highly constrained by nonlinear equations that restrict the values of the continuous variables. In this contribution the development of a memetic algorithm (MA) for global optimization in the solution of a problem in the chemical process engineering domain is described. The combination of an evolutionary strategy and a local solver based on the general reduced gradient method enables the exploitation of a significant reduction in the search space and of the ability of local mathematical programming solvers to efficiently handle large continuous problems containing equality constraints. The global performance of the MA is improved by the exclusion of regions that are defined by approximations of the basins of attraction of the local optima. The MA is compared to the combination of a scatter search based multi-start heuristic using OQNLP and the local solver CONOPT.

In this contribution, we consider decision problems on a moving horizon with significant uncertainties in parameters. The information and decision structure on moving horizons enables recourse actions which correct the here-and-now decisions whenever the horizon is moved a step forward. This situation is reflected by a mixed-integer recourse model with a finite number of uncertainty scenarios in the form of a two-stage stochastic integer program. A stage decomposition-based hybrid evolutionary algorithm for two-stage stochastic integer programs is proposed that employs an evolutionary algorithm to determine the here-and-now decisions and a standard mathematical programming method to optimize the recourse decisions. An empirical investigation of the scale-up behavior of the algorithms with respect to the number of scenarios exhibits that the new hybrid algorithm generates good feasible solutions more quickly than a state of the art exact algorithm for problem instances with a high number of scenarios.

This contribution proposes a link between the specification of supervisory controllers by Sequential Function Charts (SFC) and the verification of embedded systems with hybrid dynamics. The SFC are transformed into modular timed automata using a procedure based on graph grammars. The resulting controller model is composed with a hybrid automaton (with possibly nonlinear continuous dynamics) that models the plant behavior. In order to verify safety properties of the composed system algorithmically, a tool implementing the recently proposed approach of counterexample guided model checking is employed. The procedure is illustrated for a processing system example.

Technical systems that include complex physical dynamics as well as extensive discrete event control, require powerful modeling and simulation techniques. As the most adequate means for modeling hybrid physical systems, we advocate the use of object-oriented modeling languages such as Modelica. However, the discrete event models often require the use of dedicated graphical editors that cannot be defined appropriately using Modelica. The purpose of the DES/M modeling environment [10] is to provide such editors for different discrete event formalisms and to translate discrete event models automatically into Modelica components such that a discrete event controller can be integrated easily into Modelica models and simulated using standard Modelica software tools. This contribution presents the main concepts used for the representation of several discrete event formalisms in the Modelica language and discusses the class of discrete event formalisms that can be supported by the DES/M environment.

This paper discusses important hybrid aspects of chemical processing plants. It is outlined that discrete phenomena occur both on the physical level and in the control of these plants. As the dynamics of the transformations of energy and material are predominantly continuous, large and complex hybrid systems arise. We focus on three different aspects of dealing with such systems: (1) Modeling and simulation of hybrid systems for the design and optimization of plants, controllers and operating strategies. We present powerful simulation environments that have been developed in recent years. (2) Validation of plant instrumentation and discrete controllers. These systems are largely responsible for the safe and economic operation of chemical plants and the protection of the workforce, and the environment. Techniques for the verification of discrete controllers for continuous processes are discussed, which are based on a discrete approximation of the continuous dynamics. (3) Scheduling of batch plants. For plants that are operated in a discontinuous fashion, the timing and sequencing of the operations are very important for the efficient use of the equipment. This leads to large mixed-integer optimization problems. For a typical example, we show how the process and the constraints can be modeled and describe an efficient solution algorithm.

A new concept is presented for the treatment of real-time transmission problems. It basically consists of a modification of the flow of information. The resulting quantity, which we call the forward flow of information, is smaller than the flow of information according to the usual definition except for special cases. We derive various negative coding theorems in which the forward flow of information is used. These bounds are sharper than those previously known for transmission with finite delay.