Preference-based Multi-objective Evolutionary Algorithm Research Articles

Preference-based multi-objective evolutionary algorithm with linear combination scalarizing function and reference point adjustment

In practice, the decision-maker (DM) may be only interested in a particular part of Pareto optimal front (PF). For this reason, many preference-based multi-objective evolutionary algorithms (MOEA) have been proposed to find a solution set that approximates the region of the interest (ROI). Most existing preference-based methods focus on selecting solutions in the ROI. Nevertheless, the enhancement of convergence in preference-based MOEAs has been neglected. Most decomposition-based approaches often employ the achievement scalarizing function (ASF) as their scalarizing function. However, it holds a weaker search ability than the weighted sum function (WSF) despite its capability to tackle problems with arbitrary PF geometries. In order to strengthen the selective pressure toward the PF, this paper proposes a new scalarizing function, LSF, which is a linear combination of the WSF and the ASF. Then, a simple adaptive penalty scheme is employed in LSF to balance the search ability and robustness. To focus the search on the ROI, we develop a reference point adjustment method that dynamically adjusts the position of the reference point according to the distance from the approximated target point. We apply the above two innovations to the MOEA/D framework and propose a new preference-based MOEA, namely RAMOEAD. Experimental results show that RAMOEAD is highly competitive when compared with five state-of-the-art preference-based MOEAs. Finally, the proposed algorithm is extended to double reference points for solving the problems in which the ROIs are defined by the reservation and aspiration points.

A novel dynamic reference point model for preference-based evolutionary multiobjective optimization

AbstractIn the field of preference-based evolutionary multiobjective optimization, optimization algorithms are required to search for the Pareto optimal solutions preferred by the decision-maker (DM). The reference point is a type of techniques that effectively describe the preferences of DM. So far, the reference point is either static or interactive with the evolutionary process. However, the existing reference point techniques do not cover all application scenarios. A novel case, i.e., the reference point changes over time due to the environment change, has not been considered. This paper focuses on the multiobjective optimization problems with dynamic preferences of the DM. First, we propose a change model of the reference point to simulate the change of the preference by the DM over time. Then, a dynamic preference-based multiobjective evolutionary algorithm framework with a clonal selection algorithm (ĝa-NSCSA) and a genetic algorithm (ĝa-NSGA-II) is designed to solve such kind of optimization problems. In addition, in terms of practical applications, the experiments on the portfolio optimization problems with the dynamic reference point model are tested. Experimental results on the benchmark problems and the practical applications show that ĝa-NSCSA exhibits better performance among the compared optimization algorithms.

A novel dynamic reference point model for preference-based evolutionary multiobjective optimization

In the field of preference-based evolutionary multiobjective optimization, optimization algorithms are required to search for the Pareto optimal solutions preferred by the decision maker (DM). The reference point is a type of techniques that effectively describe the preferences of DM. So far, the reference point is either static or interactive with the evolutionary process. However, the existing reference point techniques do not cover all application scenarios. A novel case, i.e., the reference point changes over time due to the environment change, has not been considered. This paper focuses on the multiobjective optimization problems with dynamic preferences of the DM. First, we propose a change model of the reference point to simulate the change of the preference by the DM over time. Then, a dynamic preference-based multiobjective evolutionary algorithm framework with a clonal selection algorithm (ĝa-NSCSA) and a genetic algorithm (ĝa-NSGA-II) is designed to solve such kind of optimization problems. In addition, in terms of practical applications, the experiments on the portfolio optimization problems with the dynamic reference point model are tested. Experimental results on the benchmark problems and the practical applications show that ĝa-NSCSA exhibits better performance among the compared optimization algorithms.

Novel Interactive Preference-Based Multiobjective Evolutionary Optimization for Bolt Supporting Networks

Previous methods of designing a bolt supporting network, which depend on engineering experiences, seek optimal bolt supporting schemes in terms of supporting quality. The supporting cost and time, however, have not been considered, which restricts their applications in real-world situations. We formulate the problem of designing a bolt supporting network as a three-objective optimization model by simultaneously considering such indicators as quality, economy, and efficiency. Especially, two surrogate models are constructed by support vector regression for roof-to-floor convergence and the two-sided displacement, respectively, so as to rapidly evaluate supporting quality during optimization. To solve the formulated model, a novel interactive preference-based multiobjective evolutionary algorithm is proposed. The highlight of generic methods which interactively articulate preferences is to systematically manage the regions of interest by three steps, that is, “partitioning-updating-tracking” in accordance with the cognition process of human. The preference regions of a decision-maker (DM) are first articulated and employed to narrow down the feasible objective space before the evolution in terms of nadir point, not the commonly used ideal point. Then, the DM’s preferences are tracked by dynamically updating these preference regions based on satisfactory candidates during the evolution. Finally, individuals in the population are evaluated based on the preference regions. We apply the proposed model and algorithm to design the bolt supporting network of a practical roadway. The experimental results show that the proposed method can generate an optimal bolt supporting scheme with a good balance between supporting quality and the other demands, besides speeding up its convergence.

A flexible reference point-based multi-objective evolutionary algorithm: An application to the UAV route planning problem

We study the multi-objective route planning problem of an unmanned air vehicle (UAV) moving in a continuous terrain. In this problem, the UAV starts from a base, visits all targets and returns to the base in a continuous terrain that is monitored by radars. We consider two objectives: minimizing total distance and minimizing radar detection threat. This problem has infinitely many Pareto-optimal points and generating all those points is not possible. We develop a general preference-based multi-objective evolutionary algorithm to converge to preferred solutions. Preferences of a decision maker (DM) are elicited through reference point(s) and the algorithm converges to regions of the Pareto-optimal frontier close to the reference points. The algorithm allows the DM to change his/her reference point(s) whenever he/she so wishes. We devise mechanisms to prevent the algorithm from producing dominated points at the final population. We also develop mechanisms specific to the UAV route planning problem and test the algorithm on several UAV routing problems as well as other well-known problem instances. We demonstrate that our algorithm converges to preferred regions on the Pareto-optimal frontier and adapts to changes in the reference points quickly.

An adaptive weight vector guided evolutionary algorithm for preference-based multi-objective optimization

Recently, multi-objective evolutionary algorithms (MOEAs) have been widely explored and applied to many real-world problems. Particularly, preference-based MOEAs are among the mostly studied. Several preference-based optimization algorithms have already been proposed in literature. However, most existing studies focus on how to locate the region of interest (ROI) and how to control the size of ROI, and overlook the relationship between preference information and distribution of the final solutions. Given that the distribution of the final solutions is also an important factor, in this paper, we propose a new preference-based MOEAs called MOEA/D-AWV using an adaptive weight vector generation strategy (AWV). The weight vectors are generated adaptively by the decision maker’s preference, and finally guide the solutions to converge to a preferred distribution. Solutions will converge to the reference point as close as possible with the AWV strategy, which will lead to the loss of diversity. In order to prevent the search process from being trapped at local optima, we propose an adaptive parameter tuning scheme (APT) to maintain diversity during the search process. In addition, since the distribution of weight vectors should adapt to the changes of decision makers’ preference, the APT scheme can help algorithm find desired results in different scenarios. Compared with five state-of-the-art preference-based MOEAs on 23 test instances, MOEA/D-AWV achieves the best performance. Especially, in many-objective optimization problems with high-dimensional objective space, our proposed MOEA/D-AWV still shows a competitive performance.

Multi-objective evolutionary algorithm for optimizing the partial area under the ROC curve

The measure called partial area under the curve (pAUC) has attracted increasing interest in recent years due to the wide range of real-world applications it can be used for, such as biomarker selection and pedestrian detection. Compared with AUC, pAUC only acts upon a partial (instead of a full) area under the ROC curve. In this paper, a multi-objective evolutionary algorithm termed MOPA is proposed to optimize the pAUC in an arbitrary false positive range. Within this range, two important components are proposed to focus on a particular region within the AUC. First, a new metric (K-FPR), is proposed that is created by considering the partial range of the false positive rate (FPR). This is combined with the true positive rate (TPR) to provide the two optimized objectives of MOPA. Second, a preference-based multi-objective evolutionary algorithm is developed within the framework of a recently proposed algorithm (AR-MOEA), by which the search is concentrated on a partial area under the ROC curve. Numerical experiments on different data sets demonstrate the competitiveness of the proposed method in comparison with state-of-the-art algorithms.

A Preference-Based Multi-Objective Evolutionary Algorithm for Semiautomatic Sensor Ontology Matching

This article describes how with the advent of sensors for collecting environmental data, many sensor ontologies have been developed. However, the heterogeneity of sensor ontologies blocks semantic interoperability between them and limits their applications. Ontology matching is an effective technique to solve the problem of sensor ontology heterogeneity. To improve the quality of sensor ontology alignment, the authors propose a semiautomatic ontology matching technique based on a preference-based multi-objective evolutionary algorithm (PMOEA), which can utilize the user's knowledge of the solution's quality to direct MOEA to effectively match the heterogeneous sensor ontologies. The authors specifically construct a new multi-objective optimal model for the sensor ontology matching problem, propose a user preference-based t-dominance rule, and design a PMOEA to solve the sensor ontology matching problem. The experimental results show that their approach can significantly improve the sensor ontology alignment's quality under different heterogeneous situations.

Preference-Based Evolutionary Many-Objective Optimization for Agile Satellite Mission Planning

With the development of aerospace technologies, the mission planning of agile earth observation satellites has to consider several objectives simultaneously, such as profit, observation task number, image quality, resource balance, and observation timeliness. In this paper, a five-objective mixed-integer optimization problem is formulated for agile satellite mission planning. Preference-based multi-objective evolutionary algorithms, i.e., T-MOEA/D-TCH, T-MOEA/D-PBI, and T-NSGA-III are applied to solve the problem. Problem-specific coding and decoding approaches are proposed based on heuristic rules. Experiments have shown the advantage of integrating preferences in many-objective satellite mission planning. A comparative study is conducted with other state-of-the-art preference-based methods (T-NSGA-II, T-RVEA, and MOEA/D-c). Results have demonstrated that the proposed T-MOEA/D-TCH has the best performance with regard to IGD and elapsed runtime. An interactive framework is also proposed for the decision maker to adjust preferences during the search. We have exemplified that a more satisfactory solution could be gained through the interactive approach.

A preference-based multi-objective evolutionary algorithm using preference selection radius

In traditional preference-based multi-objective optimization, the reference points in different regions often impact the performance of the algorithms so that the region of interest (ROI) cannot easily be obtained by the decision maker (DM). In dealing with many-objective optimization problems, the objective space is filled with non-dominated solutions in terms of the Pareto dominance relationship, since the dominance relationship cannot differentiate the mutual relationship between the solutions. To solve the above problems, this paper proposes a new selection mechanism with two main steps. First, we construct a preference radius to divide the whole population into two distinct parts: a dispreferred solution set and a preferred solution set. Second, the algorithm selects the optimal solutions in the preferred solution set by means of the Pareto dominance relationship. If the number of the obtained solutions does not satisfy the quantity’s upper limit, it selects those dispreferred solutions which have smaller distances to the reference direction until the number matches the size of the population. Experimental results show that the algorithm applying the mechanism is able to adapt to different reference points in varying regions in objective space. Moreover, it assists the DM in obtaining different sizes of ROI by adjusting the length of the radius of ROI. In dealing with many-objective problems, the mechanism can dramatically contribute to the convergence of an algorithm proposed in this paper, in comparison with other two state-of-the-art algorithms: g-dominance and r-dominance. Thus, this paper provides a new way to deal with user preference-based multi-objective optimization problems.

The iPICEA-g: a new hybrid evolutionary multi-criteria decision making approach using the brushing technique

Various preference-based multi-objective evolutionary algorithms have been developed to help a decision-maker search for his/her preferred solutions to multi-objective problems. In most of the existing approaches the decision-maker preferences are formulated either by mathematical expressions such as the utility function or simply by numerical values such as aspiration levels and weights. However, in some sense a decision-maker may find it easier to specify preferences visually by drawing rather than using numbers. This paper introduces such a method, namely, the brushing technique. Using this technique the decision-maker can specify his/her preferences easily by drawing in the objective space. Combining the brushing technique with one existing algorithm PICEA-g, we present a novel approach named iPICEA-g for an interactive decision-making. The performance of iPICEA-g is tested on a set of benchmark problems and is shown to be good.

A two-stage preference-based evolutionary multi-objective approach for capability planning problems

As a type of long-term planning problems, capability planning problems (CPPs) have received considerable attention in the defense and military area. In this paper, we model CPPs as a type of project scheduling problems, referred to as multi-mode resource investment project scheduling problems (MRIPSPs). The makespan and the cost are simultaneously considered. To deliver decision support, a two-stage approach is developed considering both operational and strategic perspectives. At both levels, knowledge of experts or preference of decision makers is utilized. By integrating domain knowledge at the operational level and preference information at the strategic level into the optimization algorithm, a two-stage preference-based multi-objective evolutionary algorithm is proposed. A hypothetical case with 16 tasks is studied. The experimental results show that by focusing computational efforts on the sub-regions where experts or decision makers are interested, we can obtain the solutions which are not only closer to the true Pareto front in objective space, but also hold good characteristics in decision space.

Preference-based multi-objective evolutionary algorithms for power-aware application mapping on NoC platforms

Network-on-chip (NoC) are considered the next generation of communication infrastructure in embedded systems. In the platform-based design methodology, an application is implemented by a set of collaborative intellectual property (IP) blocks. The selection of the most suited set of IPs as well as their physical mapping onto the NoC infrastructure to implement efficiently the application at hand are two hard combinatorial problems that occur during the synthesis process of Noc-based embedded system implementation. In this paper, we propose an innovative preference-based multi-objective evolutionary methodology to perform the assignment and mapping stages. We use one of the well-known and efficient multi-objective evolutionary algorithms NSGA-II and microGA as a kernel. The optimization processes of assignment and mapping are both driven by the minimization of the required silicon area and imposed execution time of the application, considering that the decision maker’s preference is a pre-specified value of the overall power consumption of the implementation.

Guest Editorial Special Issue on Preference-Based Multiobjective Evolutionary Algorithms

The four papers in this special issue focus on preference-based multiobjective evolutionary algorithms.

An Interactive Territory Defining Evolutionary Algorithm: iTDEA

We develop a preference-based multiobjective evolutionary algorithm that interacts with the decision maker (DM) during the course of optimization. We create a territory around each solution where no other solutions are allowed. We define smaller territories around the preferred solutions in order to obtain denser coverage of these regions. At each interaction, the algorithm asks the DM to choose his/her best solution among a set of representative solutions to guide the search toward the neighborhood of the selected solution. The algorithm aims to converge to a final preferred region of the DM. We test the algorithm on three problems using three different utility function types to simulate the DM's responses. The results show that the algorithm converges the DM's simulated preferred regions well.

Special issue on preference-based multiobjective evolutionary algorithms

Special issue on preference-based multiobjective evolutionary algorithms