A technique based on trade‐off maps to visualise and analyse relationships between objectives in optimisation problems

Understanding the relationships between objectives in a multiobjective optimisation problem is important for developing tailored and efficient solving techniques. In particular, when tackling combinatorial optimisation problems with many objectives, that arise in real‐world logistic scenarios, better support for the decision maker can be achieved through better understanding of the often complex fitness landscape. This paper makes a contribution in this direction by presenting a technique that allows a visualisation and analysis of the local and global relationships between objectives in optimisation problems with many objectives. The proposed technique uses four steps: First, the global pairwise relationships are analysed using the Kendall correlation method; then, the ranges of the values found on the given Pareto front are estimated and assessed; next, these ranges are used to plot a map using Gray code, similar to Karnaugh maps, that has the ability to highlight the trade‐offs between multiple objectives; and finally, local relationships are identified using scatter plots. Experiments are presented for three combinatorial optimisation problems: multiobjective multidimensional knapsack problem, multiobjective nurse scheduling problem, and multiobjective vehicle routing problem with time windows . Results show that the proposed technique helps in the gaining of insights into the problem difficulty arising from the relationships between objectives.     

Output‐sensitive complexity of multiobjective combinatorial optimization

We study output‐sensitive algorithms and complexity for multiobjective combinatorial optimization problems. In this computational complexity framework, an algorithm for a general enumeration problem is regarded efficient if it is output‐sensitive, that is, its running time is bounded by a polynomial in the input and the output size. We provide both practical examples of multiobjective combinatorial optimization problems for which such an efficient algorithm exists as well as problems for which no efficient algorithm exists under mild complexity theoretic assumptions.     

An interactive multiobjective programming approach to combinatorial data analysis

Combinatorial optimization problems in the social and behavioral sciences are frequently associated with a variety of alternative objective criteria. Multiobjective programming is an operations research methodology that enables the quantitative analyst to investigate tradeoffs among relevant objective criteria. In this paper, we describe an interactive procedure for multiobjective asymmetric unidimensional seriation problems. This procedure uses a dynamic-programming algorithm to partially generate the efficient set of sequences for small to medium-sized problems, and a multioperation heuristic to estimate the efficient set for larger problems. The interactive multiobjective procedure is applied to an empirical data set from the psychometric literature. We conclude with a discussion of other potential areas of application in combinatorial data analysis.Stephanie Stahl is a freelance writer and editor. She can be reached via e-mail at s-stahl@worldnet.att.net.     

MOSA method: a tool for solving multiobjective combinatorial optimization problems

The success of modern heuristics (Simulated Annealing (S.A.), Tabu Search, Genetic Algorithms, …) in solving classical combinatorial optimization problems has drawn the attention of the research community in multicriteria methods. In fact, for large‐scale problems, the simultaneous difficulties of 𝒩𝒫‐hard complexity and of multiobjective framework make most Multiobjective Combinatorial Optimization (MOCO) problems intractable for exact methods. This paper develops the so‐called MOSA (Multiobjective Simulated Annealing) method to approximate the set of efficient solutions of a MOCO problem. Different options for the implementation are illustrated and extensive experiments prove the efficiency of the approach. Its results are compared to exact methods on bi‐objective knapsack problems. Copyright © 1999 John Wiley & Sons, Ltd.     

Against Two Modest Conceptions of Hard Paternalism

People in our liberal pluralistic society have conflicting intuitions about the legitimacy of coercive hard paternalism, though respect for agency provides a common source of objection to it. The hard paternalist must give adequate reasons for her coercion which are acceptable to a free and equal agent. Coercion that fails to meet with an agent’s reasonable evaluative commitments is at least problematic and risks being authoritarian. Even if the coercer claims no normative authority over the coercee, the former still uses coercion to replace the latter’s reasons or will with his own reasons or will. But does every hard paternalistic view have to invite such objection? Throughout I will assume that defenders of what I will call “Neutral Paternalism” (NP) and “Commonsense Paternalism” (CP) aim to offer reasons for coercion all can reasonably endorse despite evaluative diversity, in opposition to more objectionable forms of coercive paternalism, such as those which defend it on religious or perfectionist grounds. I will argue, nonetheless, that Gerald Dworkin’s defense of NP and Danny Scoccia’s defense of CP succumb to the same problems of objectionable imposition that saddle other forms of coercive paternalism. The shortcomings in their views suggest that even modest hard paternalism is nonetheless problematic for liberals.     

People are more likely to be insincere when they are more likely to accidentally tell the truth

Although people lie often, and mostly for self-serving reasons, they do not lie as much as they could. The “fudge factor” hypothesis suggests that one reason for people not to lie is that they do not wish to self-identify as liars. Accordingly, self-serving lies should be more likely when they are less obvious to the liars themselves. Here we show that the likelihood of self-serving lies increases with the probability of accidentally telling the truth. Players in our game could transmit sincere or insincere recommendations to their competitors. In line with the fudge factor hypothesis, players lied when their beliefs were based on flimsy evidence and did not lie when their beliefs were based on solid evidence. This is the first demonstration of a new moral hypocrisy paradox: People are more likely to be insincere when they are more likely to accidentally tell the truth.     

Comparing graphic and symbolic classification in interactive multiobjective optimization

In interactive multiobjective optimization systems, the classification of objective functions is a convenient way to direct the solution process in order to search for new, more satisfactory, solutions in the set of Pareto optimal solutions. Classification means that the decision maker assigns the objective functions into classes depending on what kind of changes in their values (in relation to the current values) are desirable. Here we study the role of user interfaces in implementing classification in multiobjective optimization software and how classification should be realized. In this way, we want to pay attention to the usability of multiobjective optimization software. Typically, this topic has not been of interest in the multiobjective optimization literature. However, usability aspect is important because in interactive classification‐based multiobjective optimization methods, the classification is the core of the solution process. We can say that the more convenient the classification is, the more efficient the system or the method is and the better it supports the work of the decision maker. We report experiments with two classification options, graphic and symbolic ones, which are used in connection with an interactive multiobjective optimization system WWW‐NIMBUS. The ideas and conclusions given are applicable for other interactive classification‐based method, as well. Copyright © 2005 John Wiley & Sons, Ltd.     

A global optimization approach for generating efficient points for multiobjective concave fractional programs

In this article, we present a global optimization approach for generating efficient points for multiobjective concave fractional programming problems. The main work of the approach involves solving an instance of a concave multiplicative fractional program (W̄). Problem (W̄) is a global optimization problem for which no known algorithms are available. Therefore, to render the approach practical, we develop and validate a branch and bound algorithm for globally solving problem (W̄). To illustrate the performance of the global optimization approach, we use it to generate efficient points for a sample multiobjective concave fractional program. Copyright © 2006 John Wiley & Sons, Ltd.     

Answer Sets and Qualitative Optimization

One of the major reasons for the success of answer set programmingin recent years was the shift from a theorem proving to a constraintprogramming view: problems are represented such that stablemodels, respectively answer sets, rather than theorems correspondto solutions. This shift in perspective proved extremely fruitfulin many areas. We believe that going one step further from a"hard" to a "soft" constraint programming paradigm, or, in otherwords, to a paradigm of qualitative optimization, will proveequally fruitful. In this paper we try to support this claimby showing that several generic problems in logic based problemsolving can be understood as qualitative optimization problems,and that these problems have simple and elegant formulationsgiven adequate optimization constructs in the knowledge representationlanguage.     

Hard Determinism,Humeanism, and Virtue Ethics

Hard determinists hold that we never have alternative possibilities of action—that we only can do what we actually do. This means that if hard determinists accept the “ought implies can” principle, they must accept that it is never the case that we ought to do anything we do not do. In other words, they must reject the view that there can be “ought”‐based moral reasons to do things we do not do. Hard determinists who wish to accommodate moral reasons to do things we do not do can instead appeal to Humean moral reasons that are based on desires to be virtuous. Moral reasons grounded on desires to be virtuous do not depend on our being able to act on those reasons in the way that “ought”‐based moral reasons do.     

Multiobjective Blockmodeling for Social Network Analysis

To date, most methods for direct blockmodeling of social network data have focused on the optimization of a single objective function. However, there are a variety of social network applications where it is advantageous to consider two or more objectives simultaneously. These applications can broadly be placed into two categories: (1) simultaneous optimization of multiple criteria for fitting a blockmodel based on a single network matrix and (2) simultaneous optimization of multiple criteria for fitting a blockmodel based on two or more network matrices, where the matrices being fit can take the form of multiple indicators for an underlying relationship, or multiple matrices for a set of objects measured at two or more different points in time. A multiobjective tabu search procedure is proposed for estimating the set of Pareto efficient blockmodels. This procedure is used in three examples that demonstrate possible applications of the multiobjective blockmodeling paradigm.     

A note on the estimation of the Pareto efficient set for multiobjective matrix permutation problems

There are a number of important problems in quantitative psychology that require the identification of a permutation of the n rows and columns of an n × n proximity matrix. These problems encompass applications such as unidimensional scaling, paired‐comparison ranking, and anti‐Robinson forms. The importance of simultaneously incorporating multiple objective criteria in matrix permutation applications is well recognized in the literature; however, to date, there has been a reliance on weighted‐sum approaches that transform the multiobjective problem into a single‐objective optimization problem. Although exact solutions to these single‐objective problems produce supported Pareto efficient solutions to the multiobjective problem, many interesting unsupported Pareto efficient solutions may be missed. We illustrate the limitation of the weighted‐sum approach with an example from the psychological literature and devise an effective heuristic algorithm for estimating both the supported and unsupported solutions of the Pareto efficient set.     

Betting Against Hard Determinism

The perennial fear associated with the free will problem is the prospect of hard determinism being true. Unlike prevalent attempts to reject hard determinism by defending compatibilist analyses of freedom and responsibility, this article outlines a pragmatic argument to the effect that we are justified in betting that determinism is false even though we may retain the idea that free will and determinism are incompatible. The basic argument is that as long as we accept that libertarian free will is worth wanting, there is a defensible rationale, given the uncertainty which remains as to whether determinism is true or false, to refrain from acting on hard determinism, and thus to bet that libertarian free will exists. The article closes by discussing two potentially decisive objections to this pragmatic argument.     

Cross validation issues in multiobjective clustering

The implementation of multiobjective programming methods in combinatorial data analysis is an emergent area of study with a variety of pragmatic applications in the behavioural sciences. Most notably, multiobjective programming provides a tool for analysts to model trade offs among competing criteria in clustering, seriation, and unidimensional scaling tasks. Although multiobjective programming has considerable promise, the technique can produce numerically appealing results that lack empirical validity. With this issue in mind, the purpose of this paper is to briefly review viable areas of application for multiobjective programming and, more importantly, to outline the importance of cross‐validation when using this method in cluster analysis.     

A review of multiobjective programming and its application in quantitative psychology

Multiobjective programming, a technique for solving mathematical optimization problems with multiple conflicting objectives, has received increasing attention among researchers in various academic disciplines. A summary of multiobjective programming techniques and a review of their applications in quantitative psychology are provided.     

Methodology to select solutions for multiobjective optimization problems: Weighted stress function method

The weighted stress function method is proposed here as a new way of identifying the best solution from a set of nondominated solutions according to the decision maker's preferences, expressed in terms of weights. The method was tested using several benchmark problems from the literature, and the results obtained were compared with those of other methods, namely, the reference point evolutionary multiobjective optimization (EMO), the weighted Tchebycheff metric, and a goal programming method. The weighted stress function method can be seen to exhibit a more direct correspondence between the weights set by the decision maker and the final solutions obtained than the other methods tested.     

Effects of Item Difficulty on the Retrieval of Solutions during Cognitive Skill Acquisition: Age Differences

ABSTRACT

In cognitive skill learning, shifts to better strategies for obtaining solutions often occur while associations between problems and solutions are being strengthened. In two skill learning experiments, we examined the effects of item difficulty on the retrieval of solutions and the learning of problem–solution associations in younger and older adults. The results of both experiments demonstrated an ‘easy effect’ in both younger and older adults, such that the retrieval of solutions as well recognition memory for problems was best for the easier items. In addition, a ‘hard effect’ was found in younger adults, but not in older adults, whereby the retrieval of solutions as well as recognition memory for problems was better for harder items than for medium-difficulty items. The finding that increased computational demands at the item level delayed item memorization and the retrieval of solutions in older adults but not younger adults is consistent with a general-resources account of age-related differences in skill learning.     

Multiobjective Optimization for the Asset Allocation of European Nonlife Insurance Companies

An optimal asset allocation is crucial for nonlife insurance companies. The most previous studies focused on this topic use a mono‐objective technique optimization. This technique usually allows the maximization of shareholders' expected utility. As nonlife insurance company is a complex system, it has many stakeholders other than shareholders. So, the satisfaction of the shareholders' expected utility cannot lead usually to the satisfaction of other stakeholders' objectives. Therefore, the focus on utility maximization can be a destruction source of other objectives such as productivity, competitiveness and solvency. Our developed model integrates simulation approach with a multiobjective particle swarm optimization algorithm. This model insures an optimal asset allocation that maximizes, simultaneously, shareholders expected utility and technical efficiency of European nonlife insurance companies. The empirical application conducts a comparison between the attained results with multiobjective optimization technique and mono‐objective technique to search the optimal asset allocation for nonlife insurance companies. Our results show that the investment portfolio will be more diversified between most available investment assets. In addition, any decision maker should take account of different stakeholders' objectives. Accordingly, multiobjective optimization allows us to find the best asset allocation that maximizes simultaneously expected utility and technical efficiency of nonlife insurance companies. Copyright © 2013 John Wiley & Sons, Ltd.     

Consciousness: a preliminary multidisciplinary mapping of concepts

A preliminary mapping of conceptions associated with consciousness studies is proposed. The mapping illustrates how the “easy” problems and “hard” problems of consciousness can be placed on a range of operational specificity. Additional conceptions of consciousness are shown within this overall mapping idea. It is concluded that while the “hard problems” of consciousness carry “surplus meaning”, they are amenable to higher degrees of operational specification.     

Relating reference points and weights in MOLP

A frequent problem for decision makers (DMs) analysing decisions involving multiple objectives is the identification and selection of the most preferred option from the set of non‐dominated solutions. Two techniques, weighted sum optimization and reference point optimization, have been developed to address this problem for multiobjective linear programming problems (MOLP). In this paper, we examine the relationship between these two techniques. We demonstrate that the values of the dual variables associate with auxiliary constraints of the reference point technique are equal to the weight values used to compute the same non‐dominated solution via the weighted sum technique. This insight will enable the development of new interactive solution procedures for MOLPs which allow the DM to readily switch from one method to the other during the search for the most preferred non‐dominated solution. The advantages of the approach are discussed in the paper. Copyright © 1999 John Wiley & Sons, Ltd.