Multi-objective optimization

Analytic Hierarchy Process and Multilayer Network-Based Method for Assembly Line Balancing

Assembly line balancing improves the efficiency of production systems by the optimal assignment of tasks to operators. The optimisation of this assignment requires models that provide information about the activity times, constraints and costs of the assignments. A multilayer network-based representation of the assembly line-balancing problem is proposed, in which the layers of the network represent the skills of the operators, the tools required for their activities and the precedence constraints of their activities. The activity–operator network layer is designed by a multi-objective optimisation algorithm in which the training and equipment costs as well as the precedence of the activities are also taken into account. As these costs are difficult to evaluate, the analytic hierarchy process (AHP) technique is used to quantify the importance of the criteria. The optimisation problem is solved by a multi-level simulated annealing algorithm (SA) that efficiently handles the precedence constraints. The efficiency of the method is demonstrated by a case study from wire harness manufacturing.

Operating regime model based multi-objective sensor placement for data reconciliation

Although the number of sensors in chemical production plants is increasing thanks to the IoT revolution, it is still a crucial problem what to measure and how to place the sensors as such the resulted sensor network be robust and cost-effectively provide the required information. This problem is especially relevant in flexible multi-purpose, multi-product production plants when there are significant differences among the operating regions. The present work aims the development of a sensor placement methodology that utilizes the advantages of local linear models. Realizing the often conflicting nature of the key objectives of sensor placement, the problem is formulated as a multi-objective optimization task taking into consideration the cost, estimation accuracy, observability and fault detection performance of the designed networks and simultaneously seeking for the optimal solutions under multiple operating regimes. The effectiveness of the Non-dominated Sorting Genetic Algorithm-II (NSGA-II)-based solution of the defined problem is demonstrated through benchmark examples.

Dörgő Gy., Haragovics M., Abonyi J.: "Operating regime model based multi-objective sensor placement for data reconciliation", 29th European Symposium on Computer Aided Process Engineering, Netherlands, Eindhoven, 2019 June 16-19.

P-graph-based multi-objective risk analysis and redundancy allocation in safety-critical energy systems

As most of the energy production and transformation processes are safety-critical, it is vital to develop tools that support the analysis and minimisation of their reliability-related risks. The resultant optimisation problem should reflect the structure of the process which requires the utilisation of flexible and problem-relevant models. This paper highlights that P-graphs extended by logical condition units can be transformed into reliability block diagrams, and based on the cut and path sets of the graph a polynomial risk model can be extracted which opens up new opportunities for the definition optimisation problems related to reliability redundancy allocation. A novel multi-objective optimisation based method has been developed to evaluate the criticality of the units and subsystems. The applicability of the proposed method is demonstrated using a real-life case study related to a reforming reaction system. The results highlight that P-graphs can serve as an interface between process flow diagrams and polynomial risk models and the developed tool can improve the reliability of energy systems in retrofitting projects.

Hierarchical Representation Based Constrained Multi-objective Evolutionary Optimisation of Molecular Structures

We propose an efficient algorithm to generate Pareto optimal set of reliable molecular structures represented by group contribution methods. To effectively handle structural constraints we introduce goal oriented genetic operators to the multi-objective Non-dominated Sorting Genetic Algorithm-II (NSGA-II). The constraints are defined based on the hierarchical categorisation of the molecular fragments. The efficiency of the approach is tested on several benchmark problems. The proposed approach is highly efficient to solve the molecular design problems, as proven by the presented benchmark and refrigerant design problems.

Group Contribution Method-based Multi-objective Evolutionary Molecular Design

The search for compounds exhibiting desired physical and chemical properties is an essential, yet complex problem in the chemical, petrochemical, and pharmaceutical industries. During the formulation of this optimization-based design problem two tasks must be taken into consideration: the automated generation of feasible molecular structures and the estimation of macroscopic properties based on the resultant structures. For this structural characteristic-based property prediction task numerous methods are available. However, the inverse problem, the design of a chemical compound exhibiting a set of desired properties from a given set of fragments is not so well studied. Since in general design problems molecular structures exhibiting several and sometimes conflicting properties should be optimized, we proposed a methodology based on the modification of the multi-objective Non-dominated Sorting Genetic Algorithm-II (NSGA-II). The originally huge chemical search space is conveniently described by the Joback estimation method. The efficiency of the algorithm was enhanced by soft and hard structural constraints, which expedite the search for feasible molecules. These constraints are related to the number of available groups (fragments), the octet rule and the validity of the branches in the molecule. These constraints are also used to introduce a special genetic operator that improves the individuals of the populations to ensure the estimation of the properties is based on only reliable structures. The applicability of the proposed method is tested on several benchmark problems.

Multiobjective optimization for efficient energy utilization in batch biodiesel production

Achieving environmental sustainability requires minimizing energy consumption and waste generation. Batch chemical industries are prompted to increase productivity and utilize energy more efficiently. However, in contrast to continuous processes, batch process operations are intrinsically time dependent and the multiscale nature of batch operation posts complications in implementing classical effective waste- and energy-minimization strategies. Given the complex nature of batch plants, a systematic way of identifying and evaluating suitable operating strategies is essential. In this work, we present a multiobjective optimization-based approach that integrates a detailed model of the batch process and techniques of experimental design and evolutionary optimization. The proposed concept is applied to the batch production of fatty acid methyl esters (biodiesel). The optimization of the temperature control of this process takes into account objective functions related to purity of the product, batch time, energy usage and profit. The Pareto-fronts generated by full factorial experiment and by a multiobjective evolutionary algorithm (NSGA-II) show how the objectives are correlating or conflicting. The visualization of these fronts and the optimal temperature trajectories supports the engineers and the operators to find the best trade-off among the non-dominated solutions.

Multi- and conflicting- objective process optimization problems can be effectively solved by interactive optimization

Process optimization problems often lead to multi-objective problems where optimization goals are non-commensurable and they are in conflict with each other. In such cases, the common approach, namely the application of a quantitative cost-function, may be very difficult or pointless. For these problems, we developed a method that handles these problems by introducing a human user into the evaluation procedure. Namely, the poposed method uses the expert knowledge directly in the optimization procedure. This approach has been applied successfully in computer graphics and engineering construction design, but it has not been used for chemical process engineering problems so far. During the development of the algorithm, we adopted this approach to typical process engineering problems. The results illustrate that the proposed tool offers a more flexible way to make a compromise among different goals than the conventional optimization methods do. The practical usefulness of the framework was demonstrated through two application examples: tuning of a multi-input multi-output controller and optimization of a fermentation process.

J. Madár, J. Abonyi, F. Szeifert, Interactive evolutionary computation in process engineering, Computers & Chemical Engineering, Volume 29, Issue 7, 15 June 2005, Pages 1591-1597, IF: 1.678 A MATLAB toolbox has been developed based on the proposed concept of Interactive Evolutionary Computation (example 1 and 2) , and it has more than 1500 users at the webpage of the MATLAB central file exchange (

Interactive Evolutionary Computing


In some real-life optimization problems the objectives are often non-commensurable and are explicitly/mathematically not available. Interactive Evolutionary Computation (IEC) can effectively handle these problems.

Tamas Varga, Andras Kiraly, Janos Abonyi, Improvement of PSO algorithm by memory based gradient search - application in inventory management, Swarm Intelligence and Bio-inspired Computation, Elsevier, Xin-She Yang, Zhihua Cui, Renbin Xiao, Amir Hossein Gandomi, Mehmet Karamanoglu, pp.403-422

Webpage of the algorithm and the related papers