Preference-based Multi-objective Optimization Research Articles

Cubic Chaos Preference Multi-Objective Optimization Algorithm with Adaptive Dual-Mode Mutation

<p>In the study of preference-based multi-objective optimization algorithms, the performance significantly depends on the preference information provided by the decision-maker. Over-reliance on this preference information can lead the algorithms to become trapped in locally optimal solutions, potentially overlooking high-quality solutions in other regions. Therefore, this paper proposes a Cubic Chaos Preference Multi-Objective Optimization Algorithm with Adaptive Dual-mode Mutation (CPMOP-DM). Firstly, this algorithm utilizes the cubic chaos strategy to initialize population. This strategy possesses better chaos traversal and optimization speed and then, helps enhance the search breadth and global convergence of the optimization algorithm. Secondly, a dynamic focused preference exploration strategy is proposed to enhance the quality and satisfaction of the selected solutions. This strategy can gradually refine the search scope via, constructing dynamically shrinking exploration circles. Compared to traditional preference-based algorithms, experimental results demonstrate the competitiveness of the proposed algorithm. It effectively balances exploration and exploitation searching of the algorithm, thereby enhancing the algorithm’s diversity and distribution. It also avoids the local optimum problem caused by over-reliance on preference information.</p> <p> </p>

Preference-Based Multiobjective Optimization of Nonresonant Wireless Charging System

Preference-Based Multiobjective Optimization of Nonresonant Wireless Charging System

Multi-objective design method for high-power microwave source devices based on preferred PIC/gNSGA-II

To solve the challenging problem of multi-objective optimization for high-power microwave sources, a specialized preference-based multi-objective optimization method, namely PIC/gNSGA-II, is proposed. Additionally, to achieve the quantitative optimization of the frequency spectrum and power of high-power microwave source devices, objective functions for both the spectrum and power are designed. PIC/gNSGA-II is employed to carry out structural optimization tests on relativistic backward wave oscillators (RBWO). The optimized results produced novel device structures that meet the specified frequency bands: in the X-band, the average output power is 845.85 MW, and the operating frequency is 9.53 GHz; in the Ku-band, the average output power is 167.25 MW, and the operating frequency is 14.73 GHz. This demonstrates that by controlling the parameters of such objective functions, the code can simultaneously optimize the spectrum and power of RBWOs. Comparing the optimization results of PIC/gNSGA-II with those of NSGA-II, PIC/gNSGA-II demonstrates better optimization efficiency and the ability to design device structures that meet various performance criteria.

A weight vector generation method based on normal distribution for preference-based multi-objective optimization

A weight vector generation method based on normal distribution for preference-based multi-objective optimization

An improved preference-based variable neighborhood search algorithm with ar-dominance for assembly line balancing considering preventive maintenance scenarios

For assembly line balancing problem considering preventive maintenance scenarios (ALBP-PM), the production managers’ preferences should be concerned and hence the derived Pareto-optimal solution set (POS) should be advanced towards the corresponding region-of-interest. Otherwise, production managers might select a final solution far from their interests, and then obviously reducing the quality and efficiency of decision-making. Thus, a preference-based multi-objective optimization problem is formulated to simultaneously minimize the cycle times under different scenarios and total task adjustments among scenarios. An improved variable neighborhood search algorithm (IVNS) with novel ar-dominance and three modifications is proposed to obtain a preferred POS. Specifically, ar-dominance is integrated into it to guide the advancement direction of the preferred POS. Enhanced neighborhood structures based on critical stations are proposed to generate better-quality neighbor solutions whose cycle times are mathematically proven smaller. On this basis, a local search strategy is designed to randomly select a neighbor solution to guarantee quality and decrease the computational cost. A problem-specific adaptive restart mechanism is developed to escape from the local optimum. Computational results suggest that the IVNS obtains a better preferred POS than other eight state-of-the-art algorithms in terms of convergence, distribution and closeness to the preferences, and furthermore, incorporating preferences into the ALBP-PM helps production managers make final decisions in a more precise and faster way.

Preference-Based Multi-Objective Optimization for Synchromodal Transport Using Adaptive Large Neighborhood Search

Decision-makers in synchromodal transport (ST) have different preferences toward different objectives, such as cost, time, and emissions. To solve the conflicts among objectives and obtain preferred solutions, a preference-based multi-objective optimization model is developed. In ST, containers need to be transferred across modes, therefore the optimization problem is formulated as a pickup and delivery problem with transshipment. The preferences of decision-makers are usually expressed in linguistic terms, so weight intervals, that is, minimum and maximum weights, are assigned to objectives to represent such vague preferences. An adaptive large neighborhood search is developed and used to obtain non-dominated solutions to construct the Pareto frontier. Moreover, synchronization is an important feature of ST and it makes available resources fully utilized. Therefore, four synchronization cases are identified and studied to make outgoing vehicles cooperate with changes of incoming vehicles’ schedules at transshipment terminals. Case studies in the Rhine-Alpine corridor are designed and the results show that the proposed approach provides non-dominated solutions which are in line with preferences. Moreover, the mode share under different preferences is analyzed, which signals that different sustainability policies in transportation will influence the mode share.

Preference-Based Multi-Objective Optimization for Synchromodal Transport Using Adaptive Large Neighborhood Search

Preference-Based Multi-Objective Optimization for Synchromodal Transport Using Adaptive Large Neighborhood Search

Reference point based evolutionary multi-objective optimization algorithms with convergence properties using KKTPM and ASF metrics

In a preference-based multi-objective optimization task, the goal is to find a subset of the Pareto-optimal set close to a supplied set of aspiration points. The reference point based non-dominated sorting genetic algorithm (R-NSGA-II) was proposed for such problem-solving tasks. R-NSGA-II aims to finding Pareto-optimal points close, in the sense of Euclidean distance in the objective space, to the supplied aspiration points, instead of finding the entire Pareto-optimal set. In this paper, R-NSGA-II method is modified using recently proposed Karush–Kuhn–Tucker proximity measure (KKTPM) and achievement scalarization function (ASF) metrics, instead of Euclidean distance metric. While a distance measure may not produce desired solutions, KKTPM-based distance measure allows a theoretically-convergent local or global Pareto solutions satisfying KKT optimality conditions and the ASF measure allows Pareto-compliant solutions to be found. A new technique for calculating KKTPM measure of a solution in the presence of an aspiration point is developed in this paper. The proposed modified R-NSGA-II methods are able to solve as many as 10-objective problems as effectively or better than the existing R-NSGA-II algorithm.

A preference-based multi-objective building performance optimization method for early design stage

A large number of cases show that the multi-objective optimization method can significantly improve building performance. The method for multi-objective building performance optimization (BPO) design has achieved rapid development in recent years. However, the BPO method still needs to be improved. Specifically, weak interaction between the optimization process and the decision-making process results in low optimization efficiency, which limits the widespread application of the optimization method in early design stage. In this paper, a new interactive BPO mode is explored to strengthen the interaction between the optimization process and decision-making process, and a preference-based multi-objective BPO method is proposed to account for designers’ decision preferences during the optimization process, making the objective more controllable, improving the optimization efficiency and ensuring the diversity of solutions. Firstly, this paper illustrates the proposed method in detail, defines the concept of performance preference, expounds the flow of the preference-based multi-objective optimization algorithm, and proposes three indicators to evaluate the algorithm, which includes convergence speed, preference satisfaction rate, and diversity measurement. Secondly, through testing and comparison, it is found that the proposed preference-based algorithm has advantages over the non-preference optimization algorithm (represented by the NSGA-II algorithm). The proposed method leads to faster convergence and higher preference satisfaction, so it is more suitable for the BPO process in the early design stage. Specially, the proposed method can achieve 100% preference satisfaction rate with only 2400 simulations, while the non-preference method can only achieve 20% preference satisfaction rate after 5800 simulations. In this paper, a preference-based multi-objective BPO method is proposed to make the optimization process closely interact with the decision-making process and make the design preferences be accounted during the BPO process, thereby improving the optimization efficiency. In addition, this study first proposes two indicators to measure the quality of optimization results: preference satisfaction rate and diversity measurement. This study aims to guide the development of BPO methods towards providing high satisfaction rate and high quality optimization results.

Experimental investigation and optimization of sustainable performance measures during wire-cut EDM of Ti-6Al-4V alloy employing preference-based TLBO algorithm

ABSTRACT This article evaluates performance of wire-cut electrical discharge machining technique on Ti6Al4V alloy. Taguchi L16 experimental design is employed considering four cutting variables each at four different levels. Two sustainable performance measures viz., material removal rate (MRR) and surface roughness (SR) were investigated. Multiple response optimization (MRR and SR) was performed employing teaching-learning-based optimization (TLBO) using various weight combinations. A set of optimal solutions close to Pareto optimal fronts were obtained for each pair of weights, which helps decision maker to select appropriate cutting conditions obtain desired MRR and SR. The proposed preference-based multi objective optimization using TLBO (PBMOO-TLBO) methodology exhibited faster convergence and obtained optimal solutions in less than 20 iterations. Optimization result showed 40.51% improvement in MRR and SR recorded to decrease by 15.66% with highest preference as compared to equal weightage assigned. Result of optimization obtained in the present study can be used to produce Ti/6Al/4 V alloy components having desired SR with higher MRR. Experimental study of responses and surface morphology study are also presented.

Collective intelligence approaches in interactive evolutionary multi-objective optimization

AbstractEvolutionary multi-objective optimization algorithms (EMOAs) have been successfully applied in many real-life problems. EMOAs approximate the set of trade-offs between multiple conflicting objectives, known as the Pareto optimal set. Reference point approaches can alleviate the optimization process by highlighting relevant areas of the Pareto set and support the decision makers to take the more confident evaluation. One important drawback of this approaches is that they require an in-depth knowledge of the problem being solved in order to function correctly. Collective intelligence has been put forward as an alternative to deal with situations like these. This paper extends some well-known EMOAs to incorporate collective preferences and interactive techniques. Similarly, two new preference-based multi-objective optimization performance indicators are introduced in order to analyze the results produced by the proposed algorithms in the comparative experiments carried out.

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 network reconfiguration approach for power system restoration based on preference-based multiobjective optimization

Rapid load restoration after large-scale power system blackouts is of virtual importance to reduce economic losses. Network reconfiguration is an essential foundation of load restoration. Incorporating the preference for different objectives, a network reconfiguration approach based on preference-based multiobjective optimization is proposed for network reconfiguration schemes. On the one hand, considering the influences of generators, lines and loads, three evaluation indicators are proposed as objectives to establish a preference multiobjective optimization model. On the other hand, a preference-based discrete nondominated sorting genetic algorithm II (PD-NSGA-II) is designed considering the preference and high discreteness of the suggested model. For efficient decision making, the algorithm is equipped with two sorts of population and two dominance relations to obtain solutions with required quantity and high quality. The simulation results demonstrate that the preference-based multiobjective optimization can reasonably leverage the tradeoff among different factors about network reconfiguration. Furthermore, comparison with other algorithms indicates the efficiency of PD-NSGA-II in solving network reconfiguration optimization problems.

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.

Improving the performance of a preference-based multi-objective algorithm to optimize food treatment processes

ABSTRACTThis work focuses on the optimization of some high-pressure and temperature food treatments. In some cases, when dealing with real-life multi-objective optimization problems, such as the one considered here, the computational cost of evaluating the considered objective functions is usually quite high. Therefore, only a reduced number of iterations is affordable for the optimization algorithm. However, using fewer iterations can lead to inaccurate solutions far from the real Pareto optimal front. In this article, different mechanisms are analysed and compared to improve the convergence of a preference-based multi-objective optimization algorithm called the Weighting Achievement Scalarizing Function Genetic Algorithm (WASF-GA). The combination of these techniques has been applied to optimize a particular food treatment process. In particular, one of the proposed methods, based on the introduction of an advanced population, achieves important improvements in the quality indicator measures considered.

Interactive evolutionary multi-objective optimization and decision-making on life-cycle seismic design of bridge

Considering future seismic risk and life-cycle cost, the life-cycle seismic design of bridge is formulated as a preference-based multi-objective optimization and decision-making problem, in which the conflicting design criteria that minimize life-cycle cost and maximize seismic capacity are treated simultaneously. Specifically, the preference information based on theoretical analysis and engineering judgment is embedded in the optimization procedure. Based on reasonable displacement ductility, the cost preference and safety preference information are used to progressively construct value function, directing the evolutionary multi-objective optimization algorithm’s search to more preferred solutions. The seismic design of a reinforced concrete pier is presented as an application example using the proposed procedure for the global Pareto front corresponding with engineering designers’ preference. The results indicate that the proposed model is available to find the global Pareto front satisfying the corresponding preference and overcoming the difficulties of the traditional multi-objective optimization algorithm in obtaining a full approximation of the entire Pareto optimal front for large-dimensional problems as well as cognitive difficulty in selecting one preferred solution from all these solutions.

A mini-review on preference modeling and articulation in multi-objective optimization: current status and challenges

Evolutionary multi-objective optimization aims to provide a representative subset of the Pareto front to decision makers. In practice, however, decision makers are usually interested in only a particular part of the Pareto front of the multi-objective optimization problem. This is particularly true when the number of objectives becomes large. Over the past decade, preference-based multi-objective optimization has attracted increasing attention from both academia and industry due to its significance in both theory and practice. Significant progress has been made in evolutionary multi-objective optimization and multi-criteria decision communities, although many open issues still remain to be addressed. This paper provides a concise review on preference-based multi-objective optimization, including various preference modeling methods and existing preference-based optimization methods, as well as a brief discussion of the main future challenges.

Reservoir flood control operation using multi-objective evolutionary algorithm with decomposition and preferences

In this paper we propose a preference-based multi-objective optimization model for reservoir flood control operation (RFCO). This model takes the water preserving demand into consideration while optimizing two conflicting flood control objectives. A preference based multi-objective evolutionary algorithm with decomposition, named MOEA/D-PWA, is developed for solving the proposed RFCO model. For RFCO, it is challenging to define the preferred region formally, as the preference information is implicit and difficult to formulate. MOEA/D-PWA estimates the preferred region dynamically according to the final water level of solutions in the population, and then guides the search by propelling solutions towards the preferred region. Experimental results on four types of floods at the Ankang reservoir have illustrated that the suggested MOEA/D-PWA can successfully produce solutions in the preferred region of the Pareto front. The schedules obtained by MOEA/D-PWA can significantly reduce the flood peak and guarantee the dam safety as well. The proposed MOEA/D-PWA is also efficient in term of computational cost.

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.

Decomposing the user-preference in multiobjective optimization

Preference information (such as the reference point) of the decision maker (DM) is often used in multiobjective optimization; however, the location of the specified reference point has a detrimental effect on the performance of multiobjective evolutionary algorithms (MOEAs). Inspired by multiobjective evolutionary algorithm-based decomposition (MOEA/D), this paper proposes an MOEA to decompose the preference information of the reference point specified by the DM into a number of scalar optimization subproblems and deals with them simultaneously (called MOEA/D-PRE). This paper presents an approach of iterative weight to map the desired region of the DM, which makes the algorithm easily obtain the desired region. Experimental results have demonstrated that the proposed algorithm outperforms two popular preference-based approaches, g-dominance and r-dominance, on continuous multiobjective optimization problems (MOPs), especially on many-objective optimization problems. Moreover, this study develops distinct models to satisfy different needs of the DM, thus providing a new way to deal with preference-based multiobjective optimization. Additionally, in terms of the shortcoming of MOEA/D-PRE, an improved MOEA/D-PRE that dynamically adjusts the size of the preferred region is proposed and has better performance on some problems.