Reference Point Adaptation Research Articles

A constrained many-objective evolutionary algorithm with learning vector quantization-based reference point adaptation

A constrained many-objective evolutionary algorithm with learning vector quantization-based reference point adaptation

Multi-strategy multi-objective differential evolutionary algorithm with reinforcement learning

Multiobjective evolutionary algorithms (MOEAs) have gained much attention due to their high effectiveness and efficiency in solving multiobjective optimization problems (MOPs). However, when solving MOPs, it is important but difficult to maintain a good balance of exploration and exploitation. In addition, some reference point based MOEAs with fixed reference points perform poorly on MOPs with irregular frontiers. Therefore, this paper proposes a new multistrategy multiobjective differential evolutionary (DE) algorithm, named RLMMDE. In RLMMDE, a multistrategy and multicrossover DE optimizer is utilized to alleviate the exploration and exploitation dilemma. An adaptive reference point activation mechanism based on RL is proposed to activate the adaptive adjustment of reference points. Moreover, a reference point adaptation method is proposed to improve the performance of RLMMDE on irregular frontier problems. Experimental results of RLMMDE tested on some benchmark test suites (i.e., ZDT, DTLZ, UF, WFG, and LSMOP) and two practical mixed-variable optimization problems show that the algorithm outperforms some advanced MOEAs.

Preference incorporation into many-objective optimization: An Ant colony algorithm based on interval outranking

In this paper, we enriched Ant Colony Optimization (ACO) with interval outranking to develop a novel multi-objective ACO optimizer to approach problems with many objective functions. This proposal is suitable if the preferences of the Decision Maker (DM) can be modeled through outranking relations. The introduced algorithm (Interval Outranking-based ACO, IO-ACO) is the first ant-colony optimizer that embeds an outranking model to bear vagueness and ill-definition of the DM's preferences. This capacity is the most differentiating feature of IO-ACO because this issue is highly relevant in practice. IO-ACO biases the search towards the Region of Interest (RoI), the privileged zone of the Pareto frontier containing the solutions that better match the DM's preferences. Two widely studied benchmarks were utilized to measure the efficiency of IO-ACO, i.e., the DTLZ and WFG test suites. Accordingly, IO-ACO was compared with four competitive multi-objective optimizers: The Indicator-based Many-Objective ACO, the Multi-objective Evolutionary Algorithm Based on Decomposition, the Reference Vector-Guided Evolutionary Algorithm using Improved Growing Neural Gas, and the Indicator-based Multi-objective Evolutionary Algorithm with Reference Point Adaptation. The numerical results show that IO-ACO approximates the RoI better than leading metaheuristics based on approximating the Pareto frontier alone.

A many-objective evolutionary algorithm based on dominance and decomposition with reference point adaptation

Achieving balance between convergence and diversity is a challenge in many-objective optimization problems (MaOPs). Many-objective evolutionary algorithms (MaOEAs) based on dominance and decomposition have been developed successfully for solving partial MaOPs. However, when the optimization problem has a complicated Pareto front (PF), these algorithms show poor versatility in MaOPs. To address this challenge, this paper proposes a co-guided evolutionary algorithm by combining the merits of dominance and decomposition. An elitism mechanism based on cascading sort is exploited to balance the convergence and diversity of the evolutionary process. At the same time, a reference point adaptation method is designed to adapt to different PFs. The performance of our proposed method is validated and compared with seven state-of-the-art algorithms on 200 instances of 27 widely employed benchmark problems. Experimental results fully demonstrate the superiority and versatility of our proposed method on MaOPs with regular and irregular PFs.

An enhanced-indicator based many-objective evolutionary algorithm with adaptive reference point

Abstract Indicator based many-objective evolutionary algorithms generally introduce the performance indicator as the selection criterion in environmental selection. In the calculation of some indicators, the reference points as sampled points on Pareto fronts are very important for their calculation. However, it is difficult to obtain good reference points on various types of Pareto fronts. To address this issue, this paper proposes an enhanced-indicator based many-objective evolutionary algorithm with adaptive reference point, termed EIEA. The algorithm proposes a reference point adaptation method to dynamically adapt the reference points for the calculation of indicators. Moreover, the calculation of IGD-NS is enhanced by employing the modified distance calculation to introduce the Pareto compliant which can further comprehensively measure the convergence and diversity. The proposed EIEA adopts Pareto dominance and the enhanced IGD-NS as the first selection criterion and the secondary selection criterion in environmental selection, respectively. The intensive experiments demonstrate that the proposed algorithm has good performance in solving problems with various types of Pareto fronts, surpassing several representative many-objective evolutionary algorithms for many-objective optimization.

Multi-Objective Optimal Operation of the Inter-Basin Water Transfer Project Considering the Unknown Shapes of Pareto Fronts

Studies have shown that the performance of multi-objective evolutionary algorithms depends to a large extent on the shape of the Pareto fronts of the problem. Although, most existing algorithms have poor applicability in dealing with this problem, especially in the multi-objective optimization operation of reservoirs with unknown Pareto fronts. Therefore, this paper introduces an evolutionary algorithm with strong versatility and robustness named the Multi-Objective Evolutionary Algorithm with Reference Point Adaptation (AR-MOEA). In this paper, we take two water conservancy hubs (Huangjinxia and Sanhekou) of the Hanjiang to Wei River Water Diversion Project as example, and build a multi-objective operation model including water supply, ecology, and power generation. We use the AR-MOEA, the Non-dominated Sorting Genetic Algorithm II (NSGA-II), the Multi-Objective Evolutionary Algorithm based on Decomposition (MOEA/D) and the Indicator-Based Evolutionary Algorithm (IBEA) to search the optimal solutions, respectively. We analyze the performance of four algorithms and the operation rules in continuous dry years. The results indicate that (1) the AR-MOEA can overcome the difficulty of the shape and distribution of the unknown Pareto fronts in the multi-objective model. (2) AR-MOEA can improve the convergence and uniformity of the Pareto solution. (3) If we make full use of the regulation ability of the Sanhekou reservoir in the dry season, the water supply for coping with possible continuous dry years can be guaranteed. The study results contribute to the identification of the relationship among objectives, and is valued for water resources management of the Hanjiang to Wei River Water Diversion Project.

Dynamic Hybrid Multiple Attribute Decision-Making Problem Based on Reference Point Adaptation

Individuals’ decision-making depends on reference points in prospect theory. This research considers the bounded rationality of decision makers and constructs a dynamic hybrid multiple attribute decision-making (DHMADM) model. Unlike existing models, the DHMADM model focuses on dynamic reference point, which has been proven in prospect theory. This research presents the effects of reference point adaptation on decision-making through model calculation. The optimal choice of decision makers changed with the change of the reference point in the DHMADM model. By experiment, we found that the DHMADM model considering reference point adaptation can more accurately express the final choice of decision makers than models only considering the static reference point.

Maximizing receiver operating characteristics convex hull via dynamic reference point-based multi-objective evolutionary algorithm

The receiver operating characteristic convex hull (ROCCH) is a popular technique for analyzing the performance of classifiers, which is particularly effective for the tasks with unbalanced data distribution. Although maximization of ROCCH can be tackled as a bi-objective optimization problem, existing multi-objective evolutionary algorithms (MOEAs) encounter difficulties in obtaining an ROCCH, since ROCCH is always convex but the Pareto front obtained by MOEAs may be concave. To address the issue, in this paper, a dynamic reference point-based MOEA, namely DR-MOEA is proposed for maximizing ROCCH performance. Specifically, in DR-MOEA, a reference point-based sorting is suggested, where the solutions are sorted by their distances to the reference points instead of Pareto dominance. Hence an ROCCH rather than a Pareto front is expected to be obtained. In addition, a reference point adaptation strategy is also designed, with which the reference points are dynamically adjusted during the evolutionary process, and the performance of DR-MOEA is further enhanced. Empirical studies are conducted by comparing the proposed algorithm with several state-of-the-arts on different data sets. Experimental results demonstrate the superiority of DR-MOEA over the comparison methods in solving the ROCCH maximization problem.

An Indicator-Based Multiobjective Evolutionary Algorithm With Reference Point Adaptation for Better Versatility

During the past two decades, a variety of multiobjective evolutionary algorithms (MOEAs) have been proposed in the literature. As pointed out in some recent studies, however, the performance of an MOEA can strongly depend on the Pareto front shape of the problem to be solved, whereas most existing MOEAs show poor versatility on problems with different shapes of Pareto fronts. To address this issue, we propose an MOEA based on an enhanced inverted generational distance indicator, in which an adaptation method is suggested to adjust a set of reference points based on the indicator contributions of candidate solutions in an external archive. Our experimental results demonstrate that the proposed algorithm is versatile for solving problems with various types of Pareto fronts, outperforming several state-of-the-art evolutionary algorithms for multiobjective and many-objective optimization.

Entropy based evolutionary algorithm with adaptive reference points for many-objective optimization problems

Many-objective optimization problems (MaOPs) have attracted more and more attention due to its challenges for multi-objective evolutionary algorithms. Reference points or weight vectors based evolutionary algorithms have been developed successfully for solving MaOPs. However, these algorithms do not solve efficiently the MaOPs with irregular Pareto fronts, such as disconnected, degenerate, and inverted. Although some algorithms with adaptive weight vectors or reference points are designed to handle the problems with irregular shapes of Pareto fronts, they still exist some drawbacks. These adaptive algorithms do not obtain good performance in solving regular problem. For solving regular and irregular Pareto fronts of the problems, a novel entropy based evolutionary algorithm with adaptive reference points, named EARPEA, is proposed to solve regular and irregular many-objective optimization problems. Entropy computed based on reference points and a learning period are employed to control adaptation of the reference points. In addition, in order to maintain diversity of the reference points, a reference point adaptation method based on cosine similarity is designed in the adjusting reference point phase. The proposed algorithm is empirically compared with eight state-of-the-art many-objective evolutionary algorithms on 72 instances of 18 benchmark problems. The comparative results demonstrate that the overall performance of the proposed algorithm is superior to the counterparts on MaOPs with regular and irregular Pareto fronts.

Risk taking after absolute and relative wealth changes: The role of reference point adaptation

We conducted an experiment to compare subjects’ attitudes toward risk before and after they experienced wealth changes induced by a real-effort task. We identified and estimated the subjects’ levels of reference point adaptation to absolute and relative wealth changes. We found that after experiencing a larger loss than others, the subjects did not completely adapt their reference points to the absolute wealth loss and the relative negative wealth gap, and thus significantly increased their risk-taking behavior. However, the subjects also did not adjust their attitudes toward risk after experiencing a smaller loss than others, a smaller gain than others, or a larger gain than others. This may be because they promptly adapted to wealth changes or because they did not adapt to wealth changes but the effects of absolute and relative wealth changes mostly offset each other.

Realization Utility with Adaptive Reference Points

We consider a dynamic trading problem in which an agent decides when to sell a stock to maximize her wealth utility and realization utility with her reference point adapting to the stock's gain and loss asymmetrically. We study, both theoretically and numerically, the optimal trading strategies and asset pricing implications of two types of agents: adaptive agents who realize prospectively the reference point adaptation in the future and naive agents who fail to do so. We find that an adaptive agent sells the stock more (less) frequently when the stock is at a gain (at a loss) than a naive agent does, and that the adaptive agent asks for a higher risk premium for the stock than the naive agent does in equilibrium. Moreover, compared to a nonadaptive agent whose reference point does not adapt to the stock's gain and loss, both the adaptive and naive agents sell the stock less frequently, and the naive agent requires the same risk premium as the nonadaptive agent does.

Dynamic Trading with Reference Point Adaptation and Loss Aversion

We formalize the reference point adaptation process by relating it to a way people perceive prior gains and losses. We then develop a dynamic trading model with reference point adaptation and loss aversion, and derive its semi-analytical solution. The derived optimal stock holding has an asymmetric V-shaped form with respect to prior outcomes, and the related sensitivities are directly determined by the sensitivities of reference point shifts with respect to the outcomes. We also find that the effects of reference point adaptation can be used to shed light on some well documented trading patterns, e.g., house money, break even, and disposition effects.

Is disposition related to momentum in Chinese market?

Purpose – The purpose of this paper is to examine whether the framework of Prospect Theory and Mental Accounting proposed by Grinblatt and Han (2005) can be applied to analyzing the relationship between the disposition effect and momentum in the Chinese stock market. Design/methodology/approach – The paper applies the methodology proposed by Grinblatt and Han (2005). Findings – Using firm-level data, with a sample period from January 1998 to June 2013, the authors find evidence that the momentum effect in the Chinese stock market is not driven by the disposition effect, contradicting the findings of Grinblatt and Han (2005) concerning the US stock market. The discrepancies in the findings between the Chinese and US stock markets are robust and independent of sample periods. Research limitations/implications – The findings suggest that Grinblatt and Han’s model may not be applicable to the Chinese stock market. This is possibly because of the regulatory differences between the two stock markets and cross-national variation in investor behavior; in particular, the short-selling prohibition in the Chinese stock market and greater reference point adaptation to unrealized gains/losses among Chinese compared to Americans. Originality/value – This study provides evidence of the inapplicability of Grinblatt and Han’s model for the Chinese stock market, and shows the differences in the relationship between disposition effect and momentum between the Chinese and US stock markets.

Non‐monotonicity of Observed Hypervolume in 1‐Greedy S‐Metric Selection

ABSTRACTThe progression of the dominated hypervolume in the course of the optimization process, with respect to a global reference point, is thought to be monotonically increasing. This intuition is based on the observation that in each iteration, the solution that contributes the least to the dominated hypervolume is eliminated. Derived from results of multiple optimization runs with incorporated reference point adaptation, we show that this does not always hold for two‐dimensional and three‐dimensional objective spaces. For the two‐dimensional case, this is because the two boundary solutions are always retained in the population regardless of their hypervolume contribution. For the three‐dimensional case, we are able to show that the cause of the drop in dominated hypervolume is the continuous adaption of the reference point during selection. Copyright © 2012 John Wiley & Sons, Ltd.

Constant Proportion Portfolio Insurance Strategies under Cumulative Prospect Theory with Reference Point Adaptation

Constant Proportion Portfolio Insurance (CPPI) is a significant and highly popular investment strategy within the structured product market. This has led to recent work which attempts to explain the popularity of CPPI by showing that it is compatible with Cumulative Prospect Theory (CPT). We demonstrate that this cannot explain the popularity of ratcheted CPPI products which lock-in gains during strong growth in the portfolio. In this paper we conjecture that CPPI investors not only follow CPT, but crucially that they also adapt their reference point over time. This important distinction explains investors preference for ratcheted products

Persistent Profit and Portfolio Adjustment

This study investigates investors’ behaviors on the ir portfolio adjustment after gain and loss. Using a unique data set of transaction data, the study supports the prospect theory that the investors will be more cautious after two consecuti ve gains. They reduce their portfolio’s systematic risk by giving less weight on large capi talization stocks. Investors fix their gain or loss relative to the purchasing price of the stocks . A number of literature show that investors’ risk pr eferences towards risk are not symmetric as being assumed in a traditional framework. Kaheneman and Tversky (1979) first proposed the prospect theory. The theory replaces utility function with value function that is concave on gain and convex on loss relative to the initial wealth to explain investors’ preference. The new function can explain both risk-taking and r isk-averse behaviors normally found in the market. Recent empirical studies that use experime ntal data and market data support the idea. Using a unique data set of Thai investors’ portfoli o, this study contributes in two areas. It is the first study that investigates gain or loss from two -consecutive trading. Secondly, it investigates the portfolio adjustment of investors after gain or loss. The study measures the adjustment in terms of systematic risk, diversification, and sent iment. The results confirm asymmetric impact on trading st rategy made by investors after gain or loss. The two-consecutive trading day framework allows us to confirm that the investors lower their portfolio’s risk after two consecutive profitable trading days. They seem to fix their reference points in judging gain or loss with the p urchasing price. Since one third of the portfolio is invested in large capitalization stock s, the result is in line with Kliger and Kudryavtsev (2008) who suggested that the reference point adaptation is mostly found in low capitalization stock with limited information. If the investors realize their gain in the first perio d and still have profitable trade in the second perio d, they will readjust weights of existing stocks in their portfolio to be more diversified rather th an buying a new stock. The impact is profound when their portfolio consists mainly of the large c apitalization stocks. The investors become

A cross-cultural study of reference point adaptation: Evidence from China, Korea, and the US

We examined reference point adaptation following gains or losses in security trading using participants from China, Korea, and the US. In both questionnaire studies and trading experiments with real money incentives, reference point adaptation was larger for Asians than for Americans. Subjects in all countries adapted their reference points more after a gain than after an equal-sized loss. When we introduced a forced sale intervention that is designed to close the mental account for a prior outcome, Americans showed greater adaptation toward the new price than their Asian counterparts. We offer possible explanations both for the cross-cultural similarities and the cross-cultural differences.

Aging, Probability Weighting, and Reference Point Adaptation: Experimental Evidence

Aging, Probability Weighting, and Reference Point Adaptation: Experimental Evidence

Reference Point Adaptation and Disposition Effect: Evidence from Institutional Trading

Using a large proprietary database of institutional trades, we investigate whether, and to what extent, the dynamic adaptation of reference point translates into variations in the disposition effect, and establish three key results. First, the propensity to realize losses declines sharply with the magnitude of prior losses due to insufficient adaptation of reference point. Second, recent adverse information accelerates investors’ adaptation to price depreciation and increases investors’ willingness to realize losses. Finally, a priori of losing money in highly speculative investments decreases investors’ aversion to realize losses. Collectively, the findings suggest that both prior outcomes and recent expectations contribute to the reference point adaptation and the variations in disposition effect.