Interactive Multiobjective Optimization Method Research Articles

Interactive multiobjective optimization of an extremely computationally expensive pump design problem

ABSTRACT The hydraulic design of a pump is a challenging optimization problem. It has multiple conflicting objective functions based on computationally very expensive (16–20 hours) numerical simulations, and simulation failures, meaning that simulation calls can be unsuccessful. In this article, a surrogate-assisted evolutionary interactive multiobjective optimization method is applied to designing a pump stator. A decision maker's preferences are iteratively incorporated into the solution process and the advantages of an interactive method are demonstrated in two areas: (1) reducing the computation time; and (2) finding a preferred solution that reflects the decision maker's preferences with a low cognitive load. The decision maker was satisfied with the interactive solution process and the final solution reflected his preferences well. Additionally, because he was familiar with the domain of the problem, the preferences he provided guided the search in directions where no failed simulations were encountered. Importantly, the applied method could save days of computation time.

Automatically evolving preference-based dispatching rules for multi-objective job shop scheduling

Dispatching rules represent a simple heuristic for finding good solutions for job shop scheduling problems. Due to their fast applicability and easy handling, they are often used in manufacturing companies to create appropriate production schedules. It has been shown that dispatching rules that are specifically designed for the requirements of a particular environment improve the performance of schedules. Hyper-heuristics based on genetic programming can be used for the automated generation of such dispatching rules. Evolutionary algorithms search the space of dispatching rule components for the most effective priority function to optimize the performance of the resulting schedule. Various studies have highlighted the advantages in the single-objective case, which made it possible to derive a large number of new dispatching rules that exceeded previous benchmark rules. Because it is usually necessary to consider more than one objective simultaneously to ensure effective creation of schedules, the need for a multi-objective optimization method arises. In this paper, we propose an interactive multi-objective optimization method, namely the reference point method, implemented in a hyper-heuristic genetic programming framework. A decision support system has also been developed and implemented in a web-based application to facilitate interaction with the user. Incorporating preferences into the solution process aims to efficiently evolve a dispatching rule that meets the expectations of a decision-maker. A fictitious experiment was carried out in a benchmark job shop environment. The results show that the final solution selected by the decision-maker can produce schedules achieving a desired compromise between the makespan, total tardiness, and total waiting time. Testing the evolved dispatching rule on an independent set of instances and comparing its performance with other benchmark dispatching rules revealed that the proposed method successfully finds dispatching rules that meet the decision-maker’s expectations and are capable of reproducing similar compromise schedules for unseen problems in the same environment.

Interactive multiobjective optimization for finding the most preferred exercise therapy modality in knee osteoarthritis

Background There are no explicit guidelines or tools available to support clinicians in selecting exercise therapy modalities according to the characteristics of individual patients despite the apparent need. Objective This study develops a methodology based on a novel multiobjective optimization model and examines its feasibility as a decision support tool to support healthcare professionals in comparing different modalities and identifying the most preferred one based on a patient’s needs. Methods Thirty-one exercise therapy modalities were considered from 21 randomized controlled trials. A novel interactive multiobjective optimization model was designed to characterize the efficacy of an exercise therapy modality based on five objectives: minimizing cost, maximizing pain reduction, maximizing disability improvement, minimizing the number of supervised sessions, and minimizing the length of the treatment period. An interactive model incorporates clinicians’ preferences in finding the most preferred exercise therapy modality for each need. Multiobjective optimization methods are mathematical algorithms designed to identify the optimal balance between multiple conflicting objectives among available solutions/alternatives. They explicitly evaluate the conflicting objectives and support decision-makers in identifying the best balance. An experienced research-oriented physiotherapist was involved as a decision-maker in the interactive solution process testing the proposed decision support tool. Results The proposed methodology design and interactive process of the tool, including preference information, graphs, and exercise suggestions following the preferences, can help clinicians to find the most preferred exercise therapy modality based on a patient’s needs and health status; paving the way to individualize recommendations. Conclusions We examined the feasibility of our decision support tool using an interactive multiobjective optimization method designed to help clinicians balance between conflicting objectives to find the most preferred exercise therapy modality for patients with knee osteoarthritis. The proposed methodology is generic enough to be applied in any field of medical and healthcare settings, where several alternative treatment options exist. KEY MESSAGES We demonstrate the potential of applying Interactive multiobjective optimization methods in a decision support tool to help clinicians compare different exercise therapy modalities and identify the most preferred one based on a patient’s needs. The usability of the proposed decision support tool is tested and demonstrated in prescribing exercise therapy modalities to treat knee osteoarthritis patients.

Planning the Schedule for the Disposal of the Spent Nuclear Fuel with Interactive Multiobjective Optimization

Several countries utilize nuclear power and face the problem of what to do with the spent nuclear fuel. One possibility, which is under the scope in this paper, is to dispose of the fuel assemblies in the disposal facility. Before the assemblies can be disposed of, they must cool down their decay heat power in the interim storage. Next, they are loaded into canisters in the encapsulation facility, and finally, the canisters are placed in the disposal facility. In this paper, we model this process as a nonsmooth multiobjective mixed-integer nonlinear optimization problem with the minimization of nine objectives: the maximum number of assemblies in the storage, maximum storage time, average storage time, total number of canisters, end time of the encapsulation, operation time of the encapsulation facility, the lengths of disposal and central tunnels, and total costs. As a result, we obtain the disposal schedule i.e., amount of canisters disposed of periodically. We introduce the interactive multiobjective optimization method using the two-slope parameterized achievement scalarizing functions which enables us to obtain systematically several different Pareto optimal solutions from the same preference information. Finally, a case study adapting the disposal in Finland is given. The results obtained are analyzed in terms of the objective values and disposal schedules.

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 (nitrate removal efficiency, drawbacks on produced water, investment and management costs) and the interactive method NIMBUS applied to identify the best-suited design without any a priori evaluation, as for volumetric-load-driven design procedures. When compared to an evolutionary MOO algorithm, the interactive solution process was faster, more understandable and user-friendly and supported the decision maker well in identifying the most preferred solution (main design/operating parameters) to be implemented. Approach strength has been proved through both sensitivity analysis and positive experimental validation through a pilot scale biofilter operated for three months. In synthesis, without any “a priori” evaluation based on practical experience, the MOO design approach allowed obtaining a preferred Pareto optimal design, characterized by volumetric loading in the range 0.85–2.54 kgN m−3 d−1 (EBCTs: 5–15 min), a carbon dosage of 0.5–0.8 gC,dos/gC,stoich, with SRTs in the range 4–27 d.

Interactive Nonconvex Pareto Navigator for multiobjective optimization

We introduce a new interactive multiobjective optimization method operating in the objective space called Nonconvex Pareto Navigator. It extends the Pareto Navigator method for nonconvex problems. An approximation of the Pareto optimal front in the objective space is first generated with the PAINT method using a relatively small set of Pareto optimal outcomes that is assumed to be given or computed prior to the interaction with the decision maker. The decision maker can then navigate on the approximation and direct the search for interesting regions in the objective space. In this way, the decision maker can conveniently learn about the interdependencies between the conflicting objectives and possibly adjust one’s preferences. To facilitate the navigation, we introduce special cones that enable extrapolation beyond the given Pareto optimal outcomes. Besides handling nonconvexity, the new method contains new options for directing the navigation that have been inspired by the classification-based interactive NIMBUS method. The Nonconvex Pareto Navigatormethod is especially well-suited for computationally expensive problems, because the navigation on the approximation is computationally inexpensive. We demonstrate the method with an example. Besides proposing the new method, we characterize interactive navigation based methods in general and discuss desirable properties of navigation methods overall and in particular with respect to Nonconvex Pareto Navigator.

Decision making in multiobjective optimization problems under uncertainty: balancing between robustness and quality

As an emerging research field, multiobjective robust optimization employs minmax robustness as the most commonly used concept. Light robustness is a concept in which a parameter, tolerable degradations, can be used to control the loss in the objective function values in the most typical scenario for gaining in robustness. In this paper, we develop a lightly robust interactive multiobjective optimization method, LiRoMo, to support a decision maker to find a most preferred lightly robust efficient solution with a good balance between robustness and the objective function values in the most typical scenario. In LiRoMo, we formulate a lightly robust subproblem utilizing an achievement scalarizing function which involves a reference point specified by the decision maker. With this subproblem, we compute lightly robust efficient solutions with respect to the decision maker’s preferences. With LiRoMo, we support the decision maker in understanding the lightly robust efficient solutions with an augmented value path visualization. We use two measures ‘price to be paid for robustness’ and ‘gain in robustness’ to support the decision maker in considering the trade-offs between robustness and quality. As an example to illustrate the advantages of the method, we formulate and solve a simple investment portfolio optimization problem.

Molecular distillation of olive pomace oil ─ Multiobjective optimization for tocopherol and squalene

Olive pomace oil was distilled using a laboratory scale molecular distillation unit aiming a successful separation of squalene. Pressures were 0.02, 0.1 and 0.5 mbar, and temperatures ranged from 160 to 240 °C. Changes in total tocopherol and squalene concentrations of distilled olive pomace oils were monitored. Initial squalene concentration of 10613.1 mg kg−1 was succesfully reduced to 54.58 mg kg−1 at 0.02 mbar and 240 °C which corresponds to a reduction of 99.49% of initial. However, total tocopherol concentration also reduced to 20.2 mg kg−1 from an initial of 204.93 mg kg−1 at the same conditions. Similarly, an unfortunate loss of tocopherols with 90.14% at T = 240 °C and P = 0.02 mbar was observed. As being important antioxidants, tocopherols are desired to remain in oil; therefore, a multiobjective optimization (MOO) was performed to keep tocopherols in the oil at maximum, while minimizing squalene concentration. With an interactive MOO method, namely NIMBUS, 20 different alternative conditions could be generated. 9 of 20 paths could be considered as feasible and applicable for executing both objectives. One of the optimized conditions was 160 °C and 0.072 mbar where the highest tocopherol concentration of 204.721 mg kg−1 was obtained while squalene concentration was reduced to 3741.586 mg kg−1 in oil.

Gene selection from large-scale gene expression data based on fuzzy interactive multi-objective binary optimization for medical diagnosis

An efficient fuzzy interactive multi-objective optimization method is proposed to select the sub-optimal subset of genes from large-scale gene expression data. It is based on the binary particle swarm optimization (BPSO) algorithm tuned by a chaotic method. The proposed method is able to select the sub-optimal subset of genes with the least number of features that can accurately distinguish between the two classes, e.g. the normal and cancerous samples. The proposed method is evaluated on several publicly available microarray and RNA-sequencing gene expression datasets such as leukemia, colon cancer, central nervous system, lung cancer, ovarian cancer, prostate cancer and RNA-seq lung disease. The results indicate that the proposed method can identify the minimum number of genes to achieve the most accuracy, sensitivity and specificity in the classification process. Achieving 100% accuracy in six out of the seven datasets investigated in this study, demonstrates the high capacity of the proposed algorithm to find the sub-optimal subset of genes. This approach is useful in clinical applications to extract the most influential genes on a disease and to find the treatment procedure for the disease.

Design of a Permanent Magnet Synchronous Generator Using Interactive Multiobjective Optimization

We consider an analytical model of a permanent magnet synchronous generator (PMSG) and formulate a mixed-integer constrained multiobjective optimization problem with six objective functions. We demonstrate the usefulness of solving such a problem by applying an interactive multiobjective optimization method called NIMBUS. In the NIMBUS method, a decision is iteratively involved in the optimization process and directs the solution process in order to find the most preferred Pareto optimal solution for the problem. We also employ a commonly used noninteractive evolutionary multiobjective optimization method called NSGA-II to generate a set of solutions that approximate the Pareto set and demonstrate the advantages of using an interactive method. This study is the first one to consider an interactive approach for the design of a PMSG. Thus, we promote the further usage of interactive multiobjective optimization methods in the design. Further, we see that these methods could also be very useful in the teaching of electrical machines.

Power system distribution planning considering reliability and DG owner's profit

A novel comprehensive approach to solve a distribution systems' planning problem and to determine the optimal size, location, and technology of the distributed generation (DG) units with respect to the reliability of the system is presented in this paper. The objective functions of this optimization problem are power losses, DGs installation and operation costs, the DG owner's and the Distribution Company's profits as economic objectives. In the proposed method, new indices are defined to evaluate the reliability of the system. These indices calculate energy not supplied and volt ampere reactive not supplied due to active and reactive power shortages. Also, the average interruption frequency (AIF) and average interruption duration (AID) have been considered be minimized during optimization problem. The last two (AIF and AID) are modeled by the adequacy transition rate of DGs among states and are combined as a new objective function. To handle several objective functions, an adaptive fuzzy interactive multi-objective optimization method is used. The results on the IEEE 34-bus and 69-bus power distribution system showed the efficiency of proposed indices for reliability assessment of distribution system planning.

A Tradeoff-Based Interactive Multi-Objective Optimization Method Driven by Evolutionary Algorithms

Multi-objective optimization problems involve two or more conflicting objectives, and they have a set of Pareto optimal solutions instead of a single optimal solution. In order to support the decision maker (DM) to find his/her most preferred solution, we propose an interactive multi-objective optimization method based on the DM’s preferences in the form of indifference tradeoffs. The method combines evolutionary algorithms with the gradient-based interactive step tradeoff (GRIST) method. An evolutionary algorithm is used to generate an approximate Pareto optimal solution at each iteration. The DM is asked to provide indifference tradeoffs whose projection onto the tangent hyperplane of the Pareto front provides a tradeoff direction. An approach for approximating the normal vector of the tangent hyperplane is proposed which is used to calculate the projection. A water quality management problem is used to demonstrate the interaction process of the interactive method. In addition, three benchmark problems are used to test the accuracy of the normal vector approximation approach and compare the proposed method with GRIST.

Compounding problem in an interactive multiple objective optimization method

This note finds and resolves a compounding problem in the interactive multi-objective optimization method developed by Park and Shin (2012). The compounding problem means that the algorithm generates a solution unexpected by the decision maker. A concrete example of the compounding problem is demonstrated and, to remove the problem, an improved algorithm is then developed. We also show that the improved algorithm converges to the known optimal solutions faster than the earlier algorithm.

A Productivity Outlook for a Multi-Criteria Animal Feed Formulation Problem: A Case Study of Nigerian Feed Mill Industry

Over-formulation or under-formulation of animal feed is a major challenge in a feed milling operation .While overfeeding unnecessarily increases the feed cost; underfeeding on the other hand reduces the performance of the animal and the overall productivity of the feed milling operation. This study therefore addressed how a multi-criteria feed formulation affects the productivity of feed milling business with the use of mathematical programming in bringing about an optimal solution that is both economical and brings out the best energy yield. The solution procedure employed in this study is an iterative multi-objective optimization method. Here the optimization of the metabolizable energy and ration cost is solved iteratively using a non-differentiable interactive multi-objective bundle-based optimization method which will then result into different alternative optimal formulations. These alternatives were then evaluated using the multi-factored productivity techniques to determine the interactions between each of the optimal solutions. The performance of the four alternative optimal solutions (C ingredient) generated were factored into the productivity model together with other input factors such as the cost of fuel (C fuel),cost of labour (C labour) and cost of packaging (C packaging). The productivity index estimated from the four alternative optimal formulations includes 1.13, 1.144, 1.06, and 0.96 respectively. This shows that the optimal feed formulation generated in alternative 2 produces the highest profit (14.35%) and hence highest productivity index (1.144). Hence, the multi-factored productivity index is therefore a measure of performance in a feed mill industry when considering the impact of feed formulation on the overall cost of production in a feed mill industry.

Applying the approximation method PAINT and the interactive method NIMBUS to the multiobjective optimization of operating a wastewater treatment plant

Using an interactive multiobjective optimization method called NIMBUS and an approximation method called PAINT, preferable solutions to a five-objective problem of operating a wastewater treatment plant are found. The decision maker giving preference information is an expert in wastewater treatment plant design at the engineering company Pöyry Finland Ltd. The wastewater treatment problem is computationally expensive and requires running a simulator to evaluate the values of the objective functions. This often leads to problems with interactive methods as the decision maker may get frustrated while waiting for new solutions to be computed. Thus, a newly developed PAINT method is used to speed up the iterations of the NIMBUS method. The PAINT method interpolates between a given set of Pareto optimal outcomes and constructs a computationally inexpensive mixed integer linear surrogate problem for the original wastewater treatment problem. With the mixed integer surrogate problem, the time required from the decision maker is comparatively short. In addition, a new IND-NIMBUS® PAINT module is developed to allow the smooth interoperability of the NIMBUS method and the PAINT method.

A solution process for simulation-based multiobjective design optimization with an application in the paper industry

In this paper, we address some computational challenges arising in complex simulation-based design optimization problems. High computational cost, black-box formulation and stochasticity are some of the challenges related to optimization of design problems involving the simulation of complex mathematical models. Solving becomes even more challenging in case of multiple conflicting objectives that must be optimized simultaneously. In such cases, application of multiobjective optimization methods is necessary in order to gain an understanding of which design offers the best possible trade-off. We apply a three-stage solution process to meet the challenges mentioned above. As our case study, we consider the integrated design and control problem in paper mill design where the aim is to decrease the investment cost and enhance the quality of paper on the design level and, at the same time, guarantee the smooth performance of the production system on the operational level. In the first stage of the three-stage solution process, a set of solutions involving different trade-offs is generated with a method suited for computationally expensive multiobjective optimization problems using parallel computing. Then, based on the generated solutions an approximation method is applied to create a computationally inexpensive surrogate problem for the design problem and the surrogate problem is solved in the second stage with an interactive multiobjective optimization method. This stage involves a decision maker and her/his preferences to find the most preferred solution to the surrogate problem. In the third stage, the solution best corresponding that of stage two is found for the original problem.

Beyond Markowitz with multiple criteria decision aiding

The paper is about portfolio selection in a non-Markowitz way, involving uncertainty modeling in terms of a series of meaningful quantiles of probabilistic distributions. Considering the quantiles as evaluation criteria of the portfolios leads to a multiobjective optimization problem which needs to be solved using a Multiple Criteria Decision Aiding (MCDA) method. The primary method we propose for solving this problem is an Interactive Multiobjective Optimization (IMO) method based on so-called Dominance-based Rough Set Approach (DRSA). IMO-DRSA is composed of two phases: computation phase, and dialogue phase. In the computation phase, a sample of feasible portfolio solutions is calculated and presented to the Decision Maker (DM). In the dialogue phase, the DM indicates portfolio solutions which are relatively attractive in a given sample; this binary classification of sample portfolios into ‘good’ and ‘others’ is an input preference information to be analyzed using DRSA; DRSA is producing decision rules relating conditions on particular quantiles with the qualification of supporting portfolios as ‘good’; a rule that best fits the current DM’s preferences is chosen to constrain the previous multiobjective optimization in order to compute a new sample in the next computation phase; in this way, the computation phase yields a new sample including better portfolios, and the procedure loops a necessary number of times to end with the most preferred portfolio. We compare IMO-DRSA with two representative MCDA methods based on traditional preference models: value function (UTA method) and outranking relation (ELECTRE IS method). The comparison, which is of methodological nature, is illustrated by a didactic example.

Incremental user-interface development for interactive multiobjective optimization

Interactive multiobjective optimization (IMO) is a subfield of multiple criteria decision making. In multiobjective optimization, the optimization problem is formulated with a mathematical model containing several conflicting objectives and constraints depending on decision variables. By using IMO methods, a decision maker progressively provides preference information in order to find the most satisfactory compromise between the conflicting objectives. In this paper, we consider implementation challenges of IMO methods. In particular, we consider what kind of interaction techniques can support the decision making process and information exchange between IMO methods and the decision maker. The implementation of an IMO method called Pareto Navigator is used as an example to demonstrate concrete challenges of interaction design. This paper focuses on describing the incremental development of the user interface for Pareto Navigator including empirical validation by user testing evaluation.

Bilevel heat exchanger network synthesis with an interactive multi-objective optimization method

Heat exchanger network synthesis (HENS) has been an active research area for more than 40 years because well-designed heat exchanger networks enable heat recovery in process industries in an energy- and cost-efficient manner. Due to ever increasing global competition and need to decrease the harmful effects done on the environment, there still is a continuous need to improve the heat exchanger networks and their synthesizing methods. In this work we present a HENS method that combines an interactive multi-objective optimization method with a simultaneous bilevel HENS method, where the bilevel part of the method is based on grouping of process streams and building aggregate streams from the grouped streams. This is done in order to solve medium-sized industrial HENS problems efficiently with good final solutions. The combined method provides an opportunity to solve HENS problems efficiently also regarding computing effort and at the same time optimizing all the objectives of HENS simultaneously and in a genuine multi-objective manner without using weighting factors. This enables the designer or decision maker to be in charge of the design procedure and guide the search into areas that the decision maker is most interested in. Two examples are solved with the proposed method. The purpose of the first example is to help in illustrating the steps in the overall method. The second example is obtained from the literature.

Interactive multi-objective particle swarm optimization with heatmap-visualization-based user interface

This article introduces an interactive Multi-Objective Particle Swarm Optimization (MOPSO) method that allows a human decision maker to guide the optimization process based on domain-specific knowledge and problem-specific preferences. This article also presents a novel graphical user interface based on heatmap visualization which, combined with the algorithm, greatly reduces the workload on the user, thereby decreasing unwanted side effects caused by human fatigue. The method was evaluated on a set of standard test problems and the results were compared to those of a non-interactive MOPSO method. To simulate domain-specific preferences and knowledge, the decision maker was instructed to focus the search on a specific region of the Pareto-front. The results demonstrate that the proposed method was able to obtain better solutions than the non-interactive MOPSO method in terms of convergence towards the true Pareto-front and the number and spread of focused solutions.