Treed Gaussian Process Regression for Solving Offline Data-Driven Continuous Multiobjective Optimization Problems

Abstract For offline data-driven multiobjective optimization problems (MOPs), no new data is available during the optimization process. Approximation models (or surrogates) are first built using the provided offline data and an optimizer, e.g. a multiobjective evolutionary algorithm, can then be utilized to find Pareto optimal solutions to the problem with surrogates as objective functions. In contrast to online data-driven MOPs, these surrogates cannot be updated with new data and, hence, the approximation accuracy cannot be improved by considering new data during the optimization process. Gaussian process regression (GPR) models are widely used as surrogates because of their ability to pr…

An Interactive Framework for Offline Data-Driven Multiobjective Optimization

We propose a framework for solving offline data-driven multiobjective optimization problems in an interactive manner. No new data becomes available when solving offline problems. We fit surrogate models to the data to enable optimization, which introduces uncertainty. The framework incorporates preference information from a decision maker in two aspects to direct the solution process. Firstly, the decision maker can guide the optimization by providing preferences for objectives. Secondly, the framework features a novel technique for the decision maker to also express preferences related to maximum acceptable uncertainty in the solutions as preferred ranges of uncertainty. In this way, the d…

Wastewater treatment plant design and operation under multiple conflicting objective functions

Wastewater treatment plant design and operation involve multiple objective functions, which are often in conflict with each other. Traditional optimization tools convert all objective functions to a single objective optimization problem (usually minimization of a total cost function by using weights for the objective functions), hiding the interdependencies between different objective functions. We present an interactive approach that is able to handle multiple objective functions simultaneously. As an illustration of our approach, we consider a case study of plant-wide operational optimization where we apply an interactive optimization tool. In this tool, a commercial wastewater treatment …

On Constraint Handling in Surrogate-Assisted Evolutionary Many-Objective Optimization

Surrogate-assisted evolutionary multiobjective optimization algorithms are often used to solve computationally expensive problems. But their efficacy on handling constrained optimization problems having more than three objectives has not been widely studied. Particularly the issue of how feasible and infeasible solutions are handled in generating a data set for training a surrogate has not received much attention. In this paper, we use a recently proposed Kriging-assisted evolutionary algorithm for many-objective optimization and investigate the effect of infeasible solutions on the performance of the surrogates. We assume that constraint functions are computationally inexpensive and consid…

Potential of interactive multiobjective optimization in supporting the design of a groundwater biodenitrification process

The design of water treatment plants requires simultaneous analysis of technical, economic and environmental aspects, identified by multiple conflicting objectives. We demonstrated the advantages of an interactive multiobjective optimization (MOO) method over a posteriori methods in an unexplored field, namely the design of a biological treatment plant for drinking water production, that tackles the process drawbacks, contrarily to what happens in a traditional volumetric-load-driven design procedure. Specifically, we consider a groundwater denitrification biofilter, simulated by the Activated Sludge Model modified with two-stage denitrification kinetics. Three objectives were defined (nitr…

A survey on handling computationally expensive multiobjective optimization problems with evolutionary algorithms

Evolutionary algorithms are widely used for solving multiobjective optimization problems but are often criticized because of a large number of function evaluations needed. Approximations, especially function approximations, also referred to as surrogates or metamodels are commonly used in the literature to reduce the computation time. This paper presents a survey of 45 different recent algorithms proposed in the literature between 2008 and 2016 to handle computationally expensive multiobjective optimization problems. Several algorithms are discussed based on what kind of an approximation such as problem, function or fitness approximation they use. Most emphasis is given to function approxim…

Sima – an Open-source Simulation Framework for Realistic Large-scale Individual-level Data Generation

We propose a framework for realistic data generation and the simulation of complex systems and demonstrate its capabilities in a health domain example. The main use cases of the framework are predicting the development of variables of interest, evaluating the impact of interventions and policy decisions, and supporting statistical method development. We present the fundamentals of the framework by using rigorous mathematical definitions. The framework supports calibration to a real population as well as various manipulations and data collection processes. The freely available open-source implementation in R embraces efficient data structures, parallel computing, and fast random number gener…

Genetic programming through bi-objective genetic algorithms with a study of a simulated moving bed process involving multiple objectives

A new bi-objective genetic programming (BioGP) technique has been developed for meta-modeling and applied in a chromatographic separation process using a simulated moving bed (SMB) process. The BioGP technique initially minimizes training error through a single objective optimization procedure and then a trade-off between complexity and accuracy is worked out through a genetic algorithm based bi-objective optimization strategy. A benefit of the BioGP approach is that an expert user or a decision maker (DM) can flexibly select the mathematical operations involved to construct a meta-model of desired complexity or accuracy. It is also designed to combat bloat - a perennial problem in genetic …

Register data in sample allocations for small-area estimation

The inadequate control of sample sizes in surveys using stratified sampling and area estimation may occur when the overall sample size is small or auxiliary information is insufficiently used. Very small sample sizes are possible for some areas. The proposed allocation based on multi-objective optimization uses a small-area model and estimation method and semi-collected empirical data annually collected empirical data. The assessment of its performance at the area and at the population levels is based on design-based sample simulations. Five previously developed allocations serve as references. The model-based estimator is more accurate than the design-based Horvitz–Thompson estimator and t…

APROS-NIMBUS: Dynamic Process Simulator and Interactive Multiobjective Optimization in Plant Automation

Abstract Virtual commissioning of chemical plants often involves a dynamic simulator and an optimization method. This paper demonstrates the integration of APROS, a dynamic process simulator and IND-NIMBUS, an interactive multiobjective optimization software. We implement a multiobjective concentration control problem in APROS involving conflicting objectives and employ a decision maker to interact with IND-NIMBUS and express his preference information to finally obtain his most preferred solution. The results of this study show that APROS and IND-NIMBUS can be integrated and an interactive multiobjective optimization method can help the decision maker in exploring trade-offs among conflict…

On Constraint Handling in Surrogate-Assisted Evolutionary Many-Objective Optimization

Surrogate-assisted evolutionary multiobjective optimization algorithms are often used to solve computationally expensive problems. But their efficacy on handling constrained optimization problems having more than three objectives has not been widely studied. Particularly the issue of how feasible and infeasible solutions are handled in generating a data set for training a surrogate has not received much attention. In this paper, we use a recently proposed Kriging-assisted evolutionary algorithm for many-objective optimization and investigate the effect of infeasible solutions on the performance of the surrogates. We assume that constraint functions are computationally inexpensive and consid…

Interactivized : Visual Interaction for Better Decisions with Interactive Multiobjective Optimization

In today’s data-driven world, decision makers are facing many conflicting objectives. Since there is usually no solution that optimizes all objectives simultaneously, the aim is to identify a solution with acceptable trade-offs. Interactive multiobjective optimization methods are iterative processes in which a human decision maker repeatedly provides one’s preferences to request computing new solutions and compares them. With these methods, the decision maker can learn about the problem and its limitations. However, advanced optimization software usually offer simple visualization tools that can be significantly improved. On the other hand, current approaches for multiobjective optimization…

Surrogate-assisted multicriteria optimization: Complexities, prospective solutions, and business case

Complexity in solving real-world multicriteria optimization problems often stems from the fact that complex, expensive, and/or time-consuming simulation tools or physical experiments are used to evaluate solutions to a problem. In such settings, it is common to use efficient computational models, often known as surrogates or metamodels, to approximate the outcome (objective or constraint function value) of a simulation or physical experiment. The presence of multiple objective functions poses an additional layer of complexity for surrogate-assisted optimization. For example, complexities may relate to the appropriate selection of metamodels for the individual objective functions, extensive …

Probabilistic Selection Approaches in Decomposition-based Evolutionary Algorithms for Offline Data-Driven Multiobjective Optimization

In offline data-driven multiobjective optimization, no new data is available during the optimization process. Approximation models, also known as surrogates, are built using the provided offline data. A multiobjective evolutionary algorithm can be utilized to find solutions by using these surrogates. The accuracy of the approximated solutions depends on the surrogates and approximations typically involve uncertainties. In this paper, we propose probabilistic selection approaches that utilize the uncertainty information of the Kriging models (as surrogates) to improve the solution process in offline data-driven multiobjective optimization. These approaches are designed for decomposition-base…

On potential of interactive multiobjective optimization in chemical process design

Interaktiivinen monitavoiteoptimointi soveltuu hyvin teollisen kemian prosessisuunnitteluun. Jussi Hakanen esittelee väitöskirjassaan menetelmään pohjautuvan uuden työkalun, jollaista ei aiemmin ole ollut tarjolla. Hakanen on soveltanut työkalua onnistuneesti useiden kemiallisten prosessien suunnitteluun huomioimalla uudella tavalla enemmän kuin kaksi prosessin käyttäytymiseen vaikuttavaa tavoitetta.Aikaisemmin kemian prosessien suunnittelussa on otettu huomioon enintään kaksi prosessin toimintaan vaikuttavaa ristiriitaista tavoitetta. Hakasen esittelemä lähestymistapa ei rajoita huomioitavien tavoitteiden määrää, mikä mahdollistaa prosessien aiempaa realistisemman suunnittelun. Väitöstyöss…

On Using Decision Maker Preferences with ParEGO

In this paper, an interactive version of the ParEGO algorithm is introduced for identifying most preferred solutions for computationally expensive multiobjective optimization problems. It enables a decision maker to guide the search with her preferences and change them in case new insight is gained about the feasibility of the preferences. At each interaction, the decision maker is shown a subset of non-dominated solutions and she is assumed to provide her preferences in the form of preferred ranges for each objective. Internally, the algorithm samples reference points within the hyperbox defined by the preferred ranges in the objective space and uses a DACE model to approximate an achievem…

Interactive Multiobjective Optimization of Superstructure SMB Processes

We consider multiobjective optimization problems arising from superstructure formulation of Simulated Moving Bed (SMB) processes. SMBs are widely used in many industrial separations of chemical products and they are challenging from the optimization point of view. We employ efficient interactive multiobjec-tive optimization which enables considering several conflicting objectives simultaneously without unnecessary simplifications as have been done in previous studies. The interactive IND-NIMBUS software combined with the IPOPT optimizer is used to solve multiobjective SMB design problems. The promising results of solving a superstructure SMB optimization problem with four objectives demonst…

A New Paradigm in Interactive Evolutionary Multiobjective Optimization

Over the years, scalarization functions have been used to solve multiobjective optimization problems by converting them to one or more single objective optimization problem(s). This study proposes a novel idea of solving multiobjective optimization problems in an interactive manner by using multiple scalarization functions to map vectors in the objective space to a new, so-called preference incorporated space (PIS). In this way, the original problem is converted into a new multiobjective optimization problem with typically fewer objectives in the PIS. This mapping enables a modular incorporation of decision maker’s preferences to convert any evolutionary algorithm to an interactive one, whe…

Data-Driven Interactive Multiobjective Optimization Using a Cluster-Based Surrogate in a Discrete Decision Space

In this paper, a clustering based surrogate is proposed to be used in offline data-driven multiobjective optimization to reduce the size of the optimization problem in the decision space. The surrogate is combined with an interactive multiobjective optimization approach and it is applied to forest management planning with promising results. peerReviewed

An integrated multiobjective design tool for process design

An integrated multiobjective design tool has been developed for chemical process design. This tool combines the rigorous process calculations of the BALAS process simulator and the interactive multiobjective optimization method NIMBUS. With this design tool, the designer can consider several conflicting performance criteria simultaneously. The interactive nature of this tool allows the designer to learn about the behavior of the problem. To illustrate the possibilities of this design tool, two case studies are considered. One of them is related to paper making while the other one is related to power plants.

Coupling dynamic simulation and interactive multiobjective optimization for complex problems: An APROS-NIMBUS case study

Dynamic process simulators for plant-wide process simulation and multiobjective optimization tools can be used by industries as a means to cut costs and enhance profitability. Specifically, dynamic process simulators are useful in the process plant design phase, as they provide several benefits such as savings in time and costs. On the other hand, multiobjective optimization tools are useful in obtaining the best possible process designs when multiple conflicting objectives are to be optimized simultaneously. Here we concentrate on interactive multiobjective optimization. When multiobjective optimization methods are used in process design, they need an access to dynamic process simulators, …

Interactive Nonlinear Multiobjective Optimization Methods

An overview of interactive methods for solving nonlinear multiobjective optimization problems is given. In interactive methods, the decision maker progressively provides preference information so that the most satisfactory Pareto optimal solution can be found for her or his. The basic features of several methods are introduced and some theoretical results are provided. In addition, references to modifications and applications as well as to other methods are indicated. As the role of the decision maker is very important in interactive methods, methods presented are classified according to the type of preference information that the decision maker is assumed to provide. peerReviewed

A Surrogate-assisted Reference Vector Guided Evolutionary Algorithm for Computationally Expensive Many-objective Optimization

We propose a surrogate-assisted reference vector guided evolutionary algorithm for computationally expensive optimization problems with more than three objectives. The proposed algorithm is based on a recently developed evolutionary algorithm for many-objective optimization that relies on a set of adaptive reference vectors for selection. The proposed surrogateassisted evolutionary algorithm uses Kriging to approximate each objective function to reduce the computational cost. In managing the Kriging models, the algorithm focuses on the balance of diversity and convergence by making use of the uncertainty information in the approximated objective values given by the Kriging models, the distr…

A survey on handling computationally expensive multiobjective optimization problems using surrogates: non-nature inspired methods

Computationally expensive multiobjective optimization problems arise, e.g. in many engineering applications, where several conflicting objectives are to be optimized simultaneously while satisfying constraints. In many cases, the lack of explicit mathematical formulas of the objectives and constraints may necessitate conducting computationally expensive and time-consuming experiments and/or simulations. As another challenge, these problems may have either convex or nonconvex or even disconnected Pareto frontier consisting of Pareto optimal solutions. Because of the existence of many such solutions, typically, a decision maker is required to select the most preferred one. In order to deal wi…

Multiobjective optimization and decision making in engineering sciences

AbstractReal-world decision making problems in various fields including engineering sciences are becoming ever more challenging to address. The consideration of various competing criteria related to, for example, business, technical, workforce, safety and environmental aspects increases the complexity of decision making and leads to problems that feature multiple competing criteria. A key challenge in such problems is the identification of the most preferred trade-off solution(s) with respect to the competing criteria. Therefore, the effective combination of data, skills, and advanced engineering and management technologies is becoming a key asset to a company urging the need to rethink how…

Value of information in multiple criteria decision making: an application to forest conservation

Abstract Developing environmental conservation plans involves assessing trade-offs between the benefits and costs of conservation. The benefits of conservation can be established with ecological inventories or estimated based on previously collected information. Conducting ecological inventories can be costly, and the additional information may not justify these costs. To clarify the value of these inventories, we investigate the multiple criteria value of information associated with the acquisition of improved ecological data. This information can be useful when informing the decision maker to acquire better information. We extend the concept of the value of information to a multiple crite…

Connections of reference vectors and different types of preference information in interactive multiobjective evolutionary algorithms

We study how different types of preference information coming from a human decision maker can be utilized in an interactive multiobjective evolutionary optimization algorithm (MOEA). The idea is to convert different types of preference information into a unified format which can then be utilized in an interactive MOEA to guide the search towards the most preferred solution(s). The format chosen here is a set of reference vectors which is used within the interactive version of the reference vector guided evolutionary algorithm (RVEA). The proposed interactive RVEA is then applied to the multiple-disk clutch brake design problem with five objectives to demonstrate the potential of the idea in…

Interactive Inverse Modeling Based Multiobjective Evolutionary Algorithm

An interactive version of the inverse modeling based multiobjective evolutionary algorithm is presented. Instead of generating a representation of the whole Pareto optimal front, the algorithm aims at producing solutions in the regions where the decision maker is interested in. This is facilitated through an interactive solution process where the decision maker iteratively evaluates a set of solutions shown to her/him and the preference information obtained is used to adapt the search process of the algorithm. peerReviewed

An Interactive Simple Indicator-Based Evolutionary Algorithm (I-SIBEA) for Multiobjective Optimization Problems

This paper presents a new preference based interactive evolutionary algorithm (I-SIBEA) for solving multiobjective optimization problems using weighted hypervolume. Here the decision maker iteratively provides her/his preference information in the form of identifying preferred and/or non-preferred solutions from a set of nondominated solutions. This preference information provided by the decision maker is used to assign weights of the weighted hypervolume calculation to solutions in subsequent generations. In any generation, the weighted hypervolume is calculated and solutions are selected to the next generation based on their contribution to the weighted hypervolume. The algorithm is compa…

An interactive surrogate-based method for computationally expensive multiobjective optimisation

Many disciplines involve computationally expensive multiobjective optimisation problems. Surrogate-based methods are commonly used in the literature to alleviate the computational cost. In this paper, we develop an interactive surrogate-based method called SURROGATE-ASF to solve computationally expensive multiobjective optimisation problems. This method employs preference information of a decision-maker. Numerical results demonstrate that SURROGATE-ASF efficiently provides preferred solutions for a decision-maker. It can handle different types of problems involving for example multimodal objective functions and nonconvex and/or disconnected Pareto frontiers. peerReviewed

Why Use Interactive Multi-Objective Optimization in Chemical Process Design?

Problems in chemical engineering, like most real-world optimization problems, typically, have several conflicting performance criteria or objectives and they often are computationally demanding, which sets special requirements on the optimization methods used. In this chapter, we point out some shortcomings of some widely used basic methods of multi-objective optimization. As an alternative, we suggest using interactive approaches where the role of a decision maker or a designer is emphasized. Interactive multi-objective optimization has been shown to suit well for chemical process design problems because it takes the preferences of the decision maker into account in an iterative manner tha…

On Combining Explainable Artificial Intelligence and Interactive Multiobjective Optimization in Data-Driven Decision Support

Simulation Framework for Realistic Large-scale Individual-level Data Generation with an Application in the Health Domain

We propose a framework for realistic data generation and simulation of complex systems and demonstrate its capabilities in the health domain. The main use cases of the framework are predicting the development of risk factors and disease occurrence, evaluating the impact of interventions and policy decisions, and statistical method development. We present the fundamentals of the framework using rigorous mathematical definitions. The framework supports calibration to a real population as well as various manipulations and data collection processes. The freely available open-source implementation in R embraces efficient data structures, parallel computing and fast random number generation which…

Wastewater treatment: New insight provided by interactive multiobjective optimization

In this paper, we describe a new interactive tool developed for wastewater treatment plant design. The tool is aimed at supporting the designer in designing new wastewater treatment plants as well as optimizing the performance of already available plants. The idea is to utilize interactive multiobjective optimization which enables the designer to consider the design with respect to several conflicting evaluation criteria simultaneously. This is more important than ever because the requirements for wastewater treatment plants are getting tighter and tighter from both environmental and economical reasons. By combining a process simulator to simulate wastewater treatment and an interactive mul…

On interactive multiobjective optimization with NIMBUS® in chemical process design

We study multiobjective optimization problems arising from chemical process simulation. The interactive multiobjective optimization method NIMBUS®, developed at the University of Jyvaskyla, is combined with the BALAS® process simulator, developed at the VTT Technical Research Center of Finland, in order to provide a new interactive tool for designing chemical processes. Continuous interaction between the method and the designer provides a new efficient approach to explore Pareto optimal solutions and helps the designer to learn about the behaviour of the process. As an example of how the new tool can be used, we report the results of applying it in a heat recovery system design problem rela…

Surrogate assisted interactive multiobjective optimization in energy system design of buildings

In this paper, we develop a novel evolutionary interactive method called interactive K-RVEA, which is suitable for computationally expensive problems. We use surrogate models to replace the original expensive objective functions to reduce the computation time. Typically, in interactive methods, a decision maker provides some preferences iteratively and the optimization algorithm narrows the search according to those preferences. However, working with surrogate model swill introduce some inaccuracy to the preferences, and therefore, it would be desirable that the decision maker can work with the solutions that are evaluated with the original objective functions. Therefore, we propose a novel…

Task-based visual analytics for interactive multiobjective optimization

We study how visual interaction techniques considered in visual analytics can be utilized when implementing interactive multiobjective optimization methods, where a decision maker iteratively participates in the solution process. We want to benefit from previous research and avoid re-inventing ideas. Our aim is to widen awareness and increase the applicability of interactive methods for solving real-world problems. As a concrete approach, we introduce seven high-level tasks that are relevant for interactive methods. These high-level tasks are based on low-level tasks proposed in the visual analytics literature. In addition, we give an example on how the high-level tasks can be implemented a…

The value and costs of information for conservation decisions – a comparison of inventory strategies using imperfect and perfect information

Conservation decisions should be made considering the information available. The quality of information can vary, depending on how the data is collected. High quality (expensive) information could be obtained from detailed field inventories, or lower quality (inexpensive / free) information could be obtained from remotely sensed information or previously acquired information. From a Bayesian statistics perspective, the value of collecting better information can be evaluated. The remotely sensed or previously acquired information could serve as prior information while the detailed field inventories could be the posterior information. For a simple one stand decision, the value of information …