Approximately Efficient Solutions in Vector Optimization

An approach to approximating solutions in vector optimization is developed for vector optimization problems with arbitrary ordering cones. This paper presents a study of approximately efficient points of a given set with respect to a convex cone in an ordered Banach space. Existence results for such approximately efficient points are obtained. A domination property related to these existence results is observed and then it is proved that each element of a given set is approximated by the sum of a point in a convex cone inducing the ordering and a point in a finite set consisting of such approximately efficient points of the set.     

Divergence Behaviour of the Successive Geometric Mean Method of Pairwise Comparison Matrix Generation for a Multiple Stage,Multiple Objective Optimization Problem

This paper focuses on the divergence behaviour of the successive geometric mean (SGM) method used to generate pairwise comparison matrices while solving a multiple stage, multiple objective (MSMO) optimization problem. The SGM method can be used in the matrix generation phase of our three‐phase methodology to obtain pairwise comparison matrix at each stage of an MSMO optimization problem, which can be subsequently used to obtain the weight vector at the corresponding stage. The weight vectors across the stages can be used to convert an MSMO problem into a multiple stage, single objective (MSSO) problem, which can be solved using dynamic programming‐based approaches. To obtain a practical set of non‐dominated solutions (also referred to as Pareto optimal solutions) to the MSMO optimization problem, it is important to use a solution approach that has the potential to allow for a better exploration of the Pareto optimal solution space. To accomplish a more exhaustive exploration of the Pareto optimal solution space, the weight vectors that are used to scalarize the MSMO optimization problem into its corresponding MSSO optimization problem should vary across the stages. Distinct weight vectors across the stages are tied directly with distinct pairwise comparison matrices across the stages. A pairwise comparison matrix generation method is said to diverge if it can generate distinct pairwise comparison matrices across the stages of an MSMO optimization problem. In this paper, we demonstrate the SGM method's divergence behaviour when the three‐phase methodology is used in conjunction with an augmented high‐dimensional, continuous‐state stochastic dynamic programming method to solve a large‐scale MSMO optimization problem. Copyright © 2013 John Wiley & Sons, Ltd.     

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.     

口腔专业适宜技术与诊疗最优化

推行适宜技术和诊疗最优化的原则是避免过度医疗的有效途径。而在口腔专业中必须要体现其特殊性。口腔治疗的总体目标是健康、美观,这一目标有赖于患者的主观评价;患者在治疗中具有自主选择的权利,而医生提供专业上的支持和具体的执行。因此口腔科适宜技术的基本要求是:适合患者的自身条件和需求、符合医学专业诊疗原则的要求以及适合医生的个人技术水平。然而对于我国现阶段而言,适宜技术是一个宽泛且较低的标准,而口腔临床工作中应该以最优化的治疗作为实际追求的目标。     

Categorical Abstract Algebraic Logic: Referential Algebraic Semantics

Wójcicki has provided a characterization of selfextensional logics as those that can be endowed with a complete local referential semantics. His result was extended by Jansana and Palmigiano, who developed a duality between the category of reduced congruential atlases and that of reduced referential algebras over a fixed similarity type. This duality restricts to one between reduced atlas models and reduced referential algebra models of selfextensional logics. In this paper referential algebraic systems and congruential atlas systems are introduced, which abstract referential algebras and congruential atlases, respectively. This enables the formulation of an analog of Wójcicki’s Theorem for logics formalized as π-institutions. Moreover, the results of Jansana and Palmigiano are generalized to obtain a duality between congruential atlas systems and referential algebraic systems over a fixed categorical algebraic signature. In future work, the duality obtained in this paper will be used to obtain one between atlas system models and referential algebraic system models of an arbitrary selfextensional π-institution. Using this latter duality, the characterization of fully selfextensional deductive systems among the selfextensional ones, that was obtained by Jansana and Palmigiano, can be extended to a similar characterization of fully selfextensional π-institutions among appropriately chosen classes of selfextensional ones.     

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.     

A convex approach for multicriteria decision making in hierarchical systems

In this paper hierarchical multicriteria optimization problems are addressed in a convex programming framework. It is assumed that the criteria are aggregated into a nonlinear function, which renders the problem nonseparable, in general. The projection of the problem onto the criteria space is used to obtain an equivalent separable problem, solved through a relaxation procedure implemented on basis of a multilevel structure. At the upper level of the structure, the decision making process involves the solution of a multicriteria problem formulated in the criteria space. The solution encountered at the upper level originates a lower level parametric optimization problem with separable structure that can be treated by standard coordination-decomposition techniques. The convergence of the overall procedure is ensured. The paper includes an application of the approach proposed for the control of dynamic systems with linear quadratic structure. © 1998 John Wiley & Sons, Ltd.     

A Multicriteria Decision‐Making Application to the Conceptual Design of Mechanical Components

Early design is crucial for the success of the final product. In the conceptual design phase, several constraints, criteria, objectives and disciplines have to be considered. To this aim, multidisciplinary optimization has proven effective for the solution of engineering design problems, even in the industrial every‐day practice, to improve and simplify the work of designers in a successful quest of the best compromise solution. In this paper, a multicriteria decision‐making (MCDM)‐based design platform for early optimal design of industrial components is proposed. In a group decision‐making context, the selection of the most suitable component among several possible layouts is performed by means of a group Fuzzy Technique for Order of Preference by Similarity to Ideal Solution approach. Hence, a multi‐objective optimization is performed on the selected component by applying a multi‐objective particle swarm optimization for finding optimal component dimensions. An industrial case study is presented for showing the efficiency of the multicriteria decision‐making‐based design platform, regarding an innovative and low‐cost solution to increase the duration of heel tips in women's shoes. Copyright © 2016 John Wiley & Sons, Ltd.     

A bare bones bacterial foraging optimization algorithm

Bacterial foraging optimization (BFO), based on the social foraging behaviors of bacteria, is a new intelligent optimizer. It has been widely accepted as an optimization algorithm of current interest for a variety of fields. However, compared with other optimizers, the BFO possesses a poor convergence performance over complex optimization problems. To improve the optimization capability of the BFO, in this paper a bare bones bacterial foraging optimization (BBBFO) algorithm is developed. First, a chemotactic strategy based on Gaussian distribution is incorporated into this method through making use of both the historical information of individual and the share information of group. Then the swarm diversity is introduced in the reproduction strategy to promote the exploration ability of the algorithm. The performance of BBBFO is verified on various benchmark functions, the comparative results reveal that the proposed approach is more superior to its counterparts.     

Is consent for research genuinely informed? Using decision aid tools to obtain informed consent in the global south

Gaining informed consent among marginalized groups that include decisionally incapacitated individuals and those outside of the researcher's own geo-social and ethnic background still challenges many researchers. We suggest that there is a need for consideration of a different approach to research ethics in international settings. Based on extensive field work in West Africa on medical knowledge transfers and patient–healer relationships, this paper will discuss the challenges posed in obtaining informed individual consent in international settings. It is argued that while being on the whole convincing, the top-down approach of the proposed solutions, which clearly dominates the participative approach, fails in building sustainable capacity, decision-making competency, and empowerment in the communities in which the research is conducted. Using appropriate decision aids can help resolve these issues.     

Distributive lattices with an operator

It was shown in [3] (see also [5]) that there is a duality between the category of bounded distributive lattices endowed with a join-homomorphism and the category of Priestley spaces endowed with a Priestley relation. In this paper, bounded distributive lattices endowed with a join-homomorphism, are considered as algebras and we characterize the congruences of these algebras in terms of the mentioned duality and certain closed subsets of Priestley spaces. This enable us to characterize the simple and subdirectly irreducible algebras. In particular, Priestley relations enable us to characterize the congruence lattice of the Q-distributive lattices considered in [4]. Moreover, these results give us an effective method to characterize the simple and subdirectly irreducible monadic De Morgan algebras [7].The duality considered in [4], was obtained in terms of the range of the quantifiers, and such a duality was enough to obtain the simple and subdirectly irreducible algebras, but not to characterize the congruences.I would like to thank my research supervisor Dr. Roberto Cignoli for his helpful suggestions during the preparation of this paper and the referee for calling my attention to Goldblatt's paper [5].     

The impact of corrections for faking on the validity of noncognitive measures in selection settings

In selection research and practice, there have been many attempts to correct scores on noncognitive measures for applicants who may have faked their responses somehow. A related approach with more impact would be identifying and removing faking applicants from consideration for employment entirely, replacing them with high-scoring alternatives. The current study demonstrates that under typical conditions found in selection, even this latter approach has minimal impact on mean performance levels. Results indicate about .1 SD change in mean performance across a range of typical correlations between a faking measure and the criterion. Where trait scores were corrected only for suspected faking, and applicants not removed or replaced, the minimal impact the authors found on mean performance was reduced even further. By comparison, the impact of selection ratio and test validity is much larger across a range of realistic levels of selection ratios and validities. If selection researchers are interested only in maximizing predicted performance or validity, the use of faking measures to correct scores or remove applicants from further employment consideration will produce minimal effects.     

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.     

Finding The Positives in Psychology: What Are We Doing?

The purpose of this article is to delineate some of the consequential aspects of the intrinsic duality that is created in the pursuit of knowledge around positive psychological and asset-based constructs. I will reflect on what we have learned during studies in educational psychology that focused on assets and strengths, by drawing on highlights from particularized studies. I will then specifically problematize the use of the asset-based approach in educational psychology, by pointing out key challenges encountered at the coalface of knowledge creation in the asset-based approach and Positive Psychology. The article concludes with suggestions for pathways of inquiry, with specific reference to the questions we might be asking. Sensitivity to the discourses we construct in our psychological endeavours, and multi-layered, complex understandings is preferenced.     

Free Variation and the Intuition of Geometric Essences: Some Reflections on Phenomenology and Modern Geometry

Edmund Husserl has argued that we can intuit essences and, moreover, that it is possible to formulate a method for intuiting essences. Husserl calls this method ‘ideation’. In this paper I bring a fresh perspective to bear on these claims by illustrating them in connection with some examples from modern pure geometry. I follow Husserl in describing geometric essences as invariants through different types of free variations and I then link this to the mapping out of geometric invariants in modern mathematics. This view leads naturally to different types of spatial ontologies and it can be used to shed light on Husserl's general claim that there are different ontologies in the eidetic sciences that can be systematically related to one another. The paper is rounded out with a consideration of the role of ideation in the origins of modern geometry, and with a brief discussion of the use of ideation outside of pure geometry. What would be the study that would draw the soul away from the world of becoming to the world of being?… Geometry and arithmetic would be among the studies we are seeking … a philosopher must learn them because he must arise out of the region of generation and lay hold on essence or he can never become a true reckoner … they facilitate the conversion of the soul itself from the world of generation to essence and truth… they are knowledge of that which always is and not of something which at some time comes into being and passes away.     

Trade‐off ranking method for multi‐criteria decision analysis

Multi‐criteria decision analysis presumes trade‐off between different criteria. As a result, the optimal solution is not unique and can be represented by the Pareto frontier in the objective space. Each Pareto solution is a compromise between different objectives. Despite a limited number of Pareto optimal solutions, the decision‐maker eventually has to choose only one option. Such a choice has to be made with the use of additional preferences not included in the original formulation of the optimization problem. The paper represents a new approach to an automatic ranking that can help the decision‐maker. In contrast to the other methodologies, the proposed method is based on the minimization of trade‐off between different Pareto solutions. To be realized, the approach presumes the existence of a well‐distributed Pareto set representing the entire Pareto frontier. In the paper, such a set is generated with the use of the directed search domain algorithm. The method is applied to a number of test cases and compared against two existing alternative approaches.     

On Reasons,Evidence of Oughts,and Morally Fitting Motives

In a series of papers, Stephen Kearns and Daniel Star defend the following general account of reasons: R: Necessarily, a fact F is a reason for an agent A to Φ iff F is evidence that an agent ought to Φ. In this paper, I argue that the reasons as evidence view will run afoul of a motivational constraint on moral reasons, and that this is a powerful reason to reject the reasons as evidence view. The motivational constraint is as follows: M: For some consideration C to be a moral reason for an agent to Φ it must be possible for C to figure as part of the agent’s motivation for Φing without thereby undercutting (either partially or wholly) the positive moral evaluation of the agent in acting as she does. M presents a problem for Kearns and Star’s view because there will be cases where some consideration is evidence that an agent ought to Φ, but where if an agent was motivated by that consideration the agent’s action would thereby be worse from a moral perspective for that very reason. Further, I argue that this problem will likely arise on any moral theory that evaluates the motivation of an agent as a component of assessing the moral status of acts.     

Selecting Predictor Subsets: Considering validity and adverse impact

The paper proposes a procedure for designing Pareto‐optimal selection systems considering validity, adverse impact and constraints on the number of predictors from a larger subset that can be included in an operational selection system. The procedure determines Pareto‐optimal composites of a given maximum size thereby solving the dual task of identifying the predictors that will be included in the reduced set and determining the weights with which the retained predictors will be combined to the composite predictor. Compared with earlier proposals, the simultaneous consideration of both tasks makes it possible to combine several strategies for reducing adverse impact in a single procedure. In particular, the present approach allows integrating (a) investigating a large number of possible predictors (such as multitest battery of ability tests, or a collection of ability and nonability measures); (b) explicit predictor weighting within feasible test procedures of a given limited size.     

Uniform Test Assembly

In educational practice, a test assembly problem is formulated as a system of inequalities induced by test specifications. Each solution to the system is a test, represented by a 0–1 vector, where each element corresponds to an item included (1) or not included (0) into the test. Therefore, the size of a 0–1 vector equals the number of items n in a given item pool. All solutions form a feasible set—a subset of 2 ⁿ vertices of the unit cube in an n-dimensional vector space. Test assembly is uniform if each test from the feasible set has an equal probability of being assembled. This paper demonstrates several important applications of uniform test assembly for educational practice. Based on Slepian’s inequality, a binary program was analytically studied as a candidate for uniform test assembly. The results of this study establish a connection between combinatorial optimization and probability inequalities. They identify combinatorial properties of the feasible set that control the uniformity of the binary programming test assembly. Computer experiments illustrating the concepts of this paper are presented.     

The topological approach to perceptual organization

To address the fundamental question of “what are the primitives of visual perception”, a theory of topological structure and functional hierarchy in visual perception has been proposed. This holds that the global nature of perceptual organization can be described in terms of topological invariants, global topological perception is prior to the perception of other featural properties, and the primitives of visual form perception are geometric invariants at different levels of structural stability. In Part I of this paper, I will illustrate why and how the topological approach to perceptual organization has been advanced. In Part II, I will provide empirical evidence supporting the early topological perception, while answering some commonly considered counteraccounts. In Part III, to complete the theory, I will apply the mathematics of tolerance spaces to describe global properties in discrete sets. In Part IV, I will further present experimental data to demonstrate the global-to-local functional hierarchy in form perception, which is stratified with respect to structural stability defined by Klein's Erlangen Program. Finally, in Part V, I will discuss relations of the global-to-local topological model to other theories: The topological approach reformulates both classical Gestalt holism and Gibson's direct perception of invariance, while providing a challenge to computational approaches to vision based on the local-to-global assumption.