Högskolan i Skövde

Practical multi-criterion decision making not only involves the articulation of preferences in the objective space, but also a consideration of how the variables impact these preferences. Trend mining is a recently proposed visualization technique that offers the decision maker a quick overview of the variables' effect on the structure of the objective space and easily discover interesting variable trends. The original trend mining approach relies on a set of predefined reference directions along which an interestingness score is measured for each variable. In this paper, we relax this requirement by automating the approach to find optimal reference directions that maximize the interestingness for each variable. Additional extensions include the use of an Achievement Scalarizing Function (ASF) for ranking solutions along a given reference direction, and an updated interestingness score formulation for more appropriately handling discrete variables. We demonstrate the working of the extended approach on DTLZ2 and WFG2 benchmarks for up to five objectives and on a biobjective engineering design problem. The results show that the ability of the proposed approach to detect variable trends in high dimensional objective spaces is heavily dependent on the quality of the solutions used. 

The use of evolutionary algorithms for solving multi-objective optimization problems leaves the decision makers with a set of Pareto-optimal solutions to be considered in their decision making. Multi-objective optimization problems offer two spaces for a decision maker to analyze, the decision space and the objective space. In the literature, most of the focus has been on analyzing the objective space, however, in this paper, two procedures are presented for analyzing the decision space by identifying the variables that predominantly influence the structure of the objective space. Both procedures employ a recently proposed rule mining approach, which is used to find significant rules in terms of the variables. The rules are then combined and an influence score is calculated. The method is demonstrated on four problems, two scalable test problems (DTLZ2 and WFG2) with cases of three, five and seven objectives, one engineering design problem and one simulation-based optimization problem. The experiments show that the proposed approach is able to identify influential variables in most problem cases. 

In many practical applications, the end-goal of multi-objective optimization is to select an implementable solution that is close to the Pareto-optimal front while satisfying the decision maker’s preferences. The decision making process is challenging since it involves the manual consideration of all solutions. The field of multi-criteria decision making offers many methods that help the decision maker in this process. However, most methods only focus on analyzing the solutions’ objective values. A more informed decision generally requires the additional knowledge of how different preferences affect the variable values. One difficulty in realizing this is that while the preferences are often expressed in the objective space, the knowledge required to implement a preferred solution exists in the decision space. In this paper, we propose a decision support system that allows interactive knowledge discovery and knowledge visualization to support practitioners by simultaneously considering preferences in the objective space and their impact in the decision space. The knowledge discovery step can use either of two recently proposed data mining techniques for extracting decision rules that conform to given preferences, while the extracted knowledge is visualized via a novel graph-based approach that allows the discovery of important variables, their values and their interactions with other variables. The result is an intuitive and interactive decision support system that aids the entire decision making process — from solution visualization to knowledge visualization. We demonstrate the usefulness of this system on benchmark optimization problems up to 10 objectives and real-world problems with up to six objectives.

Practitioners of multi-objective optimization currently lack open tools that provide decision support through knowledge discovery. There exist many software platforms for multi-objective optimization, but they often fall short of implementing methods for rigorous post-optimality analysis and knowledge discovery from the generated solutions. This paper presents Mimer, a multi-criteria decision support tool for solution exploration, preference elicitation, knowledge discovery, and knowledge visualization. Mimer is openly available as a web-based tool and uses state-of-the-art web-technologies based on WebAssembly to perform heavy computations on the client-side. Its features include multiple linked visualizations and input methods that enable the decision maker to interact with the solutions, knowledge discovery through interactive data mining and graph-based knowledge visualization. It also includes a complete Python programming interface for advanced data manipulation tasks that may be too specific for the graphical interface. Mimer is evaluated through a user study in which the participants are asked to perform representative tasks simulating practical analysis and decision making. The participants also complete a questionnaire about their experience and the features available in Mimer. The survey indicates that participants find Mimer useful for decision support. The participants also offered suggestions for enhancing some features and implementing new features to extend the capabilities of the tool.

Current market requirements force manufacturing companies to face production changes more often than ever before. Reconfigurable manufacturing systems (RMS) are considered a key enabler in today's manufacturing industry to cope with such dynamic and volatile markets. The literature confirms that the use of simulation-based multi-objective optimization offers a promising approach that leads to improvements in RMS. However, due to the dynamic behavior of real-world RMS, applying conventional optimization approaches can be very time-consuming, specifically when there is no general knowledge about the quality of solutions. Meanwhile, Pareto-optimal solutions may share some common design principles that can be discovered with data mining and machine learning methods and exploited by the optimization. In this study, the authors investigate a novel knowledge-driven optimization (KDO) approach to speed up the convergence in RMS applications. This approach generates generalized knowledge from previous scenarios, which is then applied to improve the efficiency of the optimization of new scenarios. This study applied the proposed approach to a multi-part flow line RMS that considers scalable capacities while addressing the tasks assignment to workstations and the buffer allocation problems. The results demonstrate how a KDO approach leads to convergence rate improvements in a real-world RMS case.

Although an entire frontier of Pareto-optimal solutions exists for multi-objective optimization problems, in practice, decision makers are often only interested in a small subset of these solutions, called the region of interest. Specialized optimizers, such as reference-point based evolutionary algorithms, exist that can focus the search to only find solutions inside this region of interest. These algorithms typically only modify the selection mechanism of regular multi-objective optimizers to preferentially select solutions that conform to the reference point. However, a more effective search may be performed by additionally modifying the variation mechanism of the optimizers, namely the crossover and the mutation operators, to preferentially generate solutions conforming to the reference point. In this paper, we propose a modular mutation operator that uses a recent knowledge discovery technique to first find decision rules unique to the preferred solutions in each generation. These rules are then used to build an empirical distribution in the decision space that can be sampled to generate new mutated solutions which are more likely to be closer to the preferred solutions. The operator is modular in the sense that it can be used with any existing reference-point based evolutionary algorithm by simply replacing the mutation operator. We incorporate the proposed knowledge-driven mutation operator into three such algorithms, and through benchmark test problems up to 10 objectives, demonstrate that their performance improves significantly in the majority of cases according to two different performance indicators.