Large Set Of Alternatives Research Articles

Optimization of Multi-Criterial Selection Algorithm with a Dynamically Filled Large Set of Alternatives

We consider the problem of the correct ranking of a dynamically replenished large set of alternatives in multicriteria choice problems that use in the solution the previously obtained modified method for analyzing hierarchies, based on the operation of additive convolution of local priorities not on the obtained set of characteristics of paired comparison matrices (as in the classical method), but on a set of pairs the relative weights of the coordinates of the eigenvectors being compared with each other for each criterion and the subsequent operation of additive convolution according to the criteria and alternatives in each pair. In this version, the algorithm ensures that previously achieved preferences are preserved when adding new alternatives and, thereby, makes it possible to optimize when processing large volumes of dynamically changing data, which significantly expands the applicability of the popular algorithm.

Thompson Sampling for Combinatorial Network Optimization in Unknown Environments

Influence maximization, adaptive routing, and dynamic spectrum allocation all require choosing the right action from a large set of alternatives. Thanks to the advances in combinatorial optimization, these and many similar problems can be efficiently solved given an environment with known stochasticity. In this paper, we take this one step further and focus on combinatorial optimization in unknown environments. We consider a very general learning framework called combinatorial multi-armed bandit with probabilistically triggered arms and a very powerful Bayesian algorithm called Combinatorial Thompson Sampling (CTS). Under the semi-bandit feedback model and assuming access to an oracle without knowing the expected base arm outcomes beforehand, we show that when the expected reward is Lipschitz continuous in the expected base arm outcomes CTS achieves O(Σ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i=1</sub> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m</sup> logT /(p <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i</sub> Δ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i</sub> )) regret and a O(max{E[m√TlogT/p*], E[m <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> /p*]}) Bayesian regret, where m denotes the number of base arms, pi and Δi denote the minimum non-zero triggering probability and the minimum suboptimality gap of base arm i respectively, T denotes the time horizon, and p* denotes the overall minimum non-zero triggering probability. We also show that when the expected continuity, CTS achieves O(max{m√TlogT , m <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> }) Bayesian reward satisfies the triggering probability modulated Lipschitz regret, and when triggering probabilities are non-zero for all base arms, CTS achieves O(1/p* log(1/p*)) regret independent of the time horizon. Finally, we numerically compare CTS with algorithms based on upper confidence bounds in several networking problems and show that CTS outperforms these algorithms by at least an order of magnitude in majority of the cases.

A Novel Recommendation Model for Online-to-Offline Service Based on the Customer Network and Service Location

ABSTRACT We propose a new online-to-offline (O2O) service recommendation method based on a novel customer network and service location (CNLRec) in order to help customer to choose the “ideal” O2O services from a large set of alternatives. Our customer network, based on the “co-used” behaviors obtained from the online rating matrix, captures customers’ online behaviors while service location reflects offline behavior characteristic of the customer. For a target customer, a ranking of candidate services based on their locations and this network is generated, in which customer scale usage bias is eliminated. Our experimental results show that: First, even though the rating matrix is sparse, most customers are connected to our proposed customer network, which largely addresses the problem of sparse data. Second, CNLRec outperforms widely-used and state-of-the-art recommendation methods. In addition, e-commerce recommendations that use CNLRec without including item location information (CNRec) has better performance than existing methods. Third, all attributes in CNLRec, including network attributes (relationship degree and customer attribute) and location attributes, play a significant role in recommendations. Specially, O2O service location plays an important role in O2O service selection. In our research, we find the optimal combinations of these attributes.

The Structure of Two-Valued Strategy-Proof Social Choice Functions With Indifference

We give a structure theorem for all coalitionally strategy-proof social choice functions whose range is a subset of cardinality two of a given larger set of alternatives. We provide this in the case where the voters/agents are allowed to express indifference and the domain consists of profiles of preferences over a society of arbitrary cardinality. The theorem, that takes the form of a representation formula, can be used to construct all functions under consideration.

An MINLP formulation for the optimization of multicomponent distillation configurations

Designing configurations for multicomponent distillation, a ubiquitous process in chemical and petrochemical industries, is often challenging. This is because, as the number of components increases, the number of admissible distillation configurations grows rapidly and these configurations vary substantially in their energy needs. Consequently, if a method could identify a few energy-efficient choices from this large set of alternatives, it would be extremely attractive to process designers. This paper develops such a method by solving a Mixed Integer Nonlinear Program (MINLP) that is formulated to pick, among the regular-column configurations of Shah and Agrawal (2010b), those configurations that have a low vapor-duty requirement. To compute the minimum vapor-duty requirement for each column within the configuration, we use techniques that rely on the Underwood’s method. The combined difficulty arising from the nonlinearity of Underwood equations and the combinatorial explosion of the choice-set of alternatives poses unmistakable challenges for the branch-and-bound algorithm, the current method of choice to globally solve MINLPs. To address this difficulty, we exploit the structure of Underwood equations and derive valid cuts that expedite the convergence of branch-and-bound by enabling global solvers, such as BARON, infer tighter bounds on Underwood roots. This provides a quick way to identify a few lucrative alternative configurations for separation of a given non-azeotropic mixture. We illustrate the practicality of our approach on a case-study concerning heavy-crude distillation and on various other examples from the literature.

A Graphical Screening Approach for Group Decisions Based on the Extended Case-Based Distance Method

For multiple criteria decision problems, screening is a helpful process for reducing a larger set of alternatives to a smaller one containing the best alternatives so that decision makers (DMs) can concentrate on evaluating alternatives within a smaller set. This study proposes a graphical approach based on the extended case-based distance method to assist individual as well as group DMs in screening and observing the case distances between alternatives and selected cases. Benchmark cases can thus be examined. The screening results of all DMs and the collective group decisions can be simultaneously observed on the same plane. An individual DM can also examine his/her own screening results and those of the group to identify the differences between individual judgments and the group's collective opinions. An interactive screening procedure for group decisions is represented to provide flexibility so that DMs can check and adjust their preferences iteratively.

Optimization-Based Approaches for Maximizing Aggregate Recommendation Diversity

Recommender systems are being used to help users find relevant items from a large set of alternatives in many online applications. Most existing recommendation techniques have focused on improving recommendation accuracy; however, diversity of recommendations has also been increasingly recognized in research literature as an important aspect of recommendation quality. This paper proposes several optimization-based approaches for improving aggregate diversity of top-N recommendations, including a greedy maximization heuristic, a graph-theoretic approach based on maximum flow or maximum bipartite matching computations, and an integer programming approach. The proposed approaches are evaluated using real-world movie rating data sets and demonstrate substantial improvements in both diversity and accuracy as compared to the recommendation reranking approaches, which have been introduced in prior literature for the purposes of diversity improvement and were used for baseline comparisons in our study. The paper also discusses the computational complexity and the scalability of the proposed approaches, as well as the potential directions for future work.

Numerical analysis of a time allocation model accounting for choice overload

The cost of time has been suggested as a factor associated with the choice overload problem. This term refers to the discomfort or paralysis experienced by individuals when facing a choice within a large set of alternatives, as it has been evidenced in experiments by behavioural and social psychologists. We introduce a rational model of time allocation to analyse how increasing the number of options of a given product may change consumer's allocation of time and in turn affect her welfare. Under some standard assumptions, the numerical analysis of the model reproduces two key experimental findings, namely choice paralysis – i.e. the choice problem is abandoned if the number of options is too large – and choice dissatisfaction – that is, the apparent paradox that increasing the number of considered options beyond certain limit, in turn choosing better, eventually diminishes welfare. The model analysis provides specific threshold values for the occurrence of both phenomena.

Stock screening with use of factor analysis and fuzzy multiple criteria decision making

Screening is a process in which a large set of alternatives is reduced to a smaller set that most likely contains the best choice. In this paper, a new method for stock screening is proposed. Two general criteria are used. The first of them is based on the financial indices and may be treated as the criterion of firm’s ‘health’. The second one is the firm’s market success criterion that is based on the stock prices. Previous research has shown that there are many factors that are important for financial analysis. Factor analysis is a data reduction technique, which can be applied in financial analysis. This technique thus applied to determine the factors that are important for stock screening. The method rests on the selection of the stocks with a great correlation of the firm’s financial performance and its market success. As an example, the values of financial ratios and prices of 24 firms from the pharmaceutical industry of Tehran stock exchange were used. It is shown that the proposed method makes it ...

A case-based distance method for screening in multiple-criteria decision aid

Screening is a process of multiple-criteria decision aid (MCDA) in which a large set of alternatives is reduced to a smaller set that most likely contains the best choice. We propose screening using a distance model calibrated on the basis of the decision-maker's own judgement. Viewing MCDA as preference aggregation based on consequence data, we define consequence and preference expressions (values and weights) and describe how they are aggregated. Then we define screening and explain some of its properties. Using an appropriate definition of distance, our case-based distance method screens a set of alternatives using criterion weights and a distance threshold obtained by quadratic optimization using the decision-maker's selection of alternatives from a test set. This case-based method can elicit the decision maker's preferences more expeditiously and accurately than direct inquiry. An application in water supply planning is used to demonstrate the procedure.

Solving multiple criteria choice problems by interactive trichotomy segmentation

The paper describes a method for multiple criteria choice problems with an explicitly given but relatively large set of alternatives. The approach can be placed between methods with a priori specification of the decision maker's (DM's preferences and interactive procedures. The method presented includes some interaction with the DM, but is based on an assumption that, at the beginning of the solution process, he/she has already relatively well-defined preferences. The DM's preferences are modeled with an outranking relation in the neighborhood of a reference profile in the non-dominated set. This preference model is used in order to define a trichotomy of the non-dominated set in terms of accepting good alternatives, rejecting non-interesting ones and defining alternatives that can neither be accepted, nor rejected based on the available preference information. The method stops if the class of good alternatives is sufficiently; small and if the DM is able to select one of them as the best compromise. Otherwise, the DM can modify the preferential information by changing either the reference profile, or the thresholds used to build the outranking relation. In other words, the DM defines dynamically the three categories. The description of the procedure is followed by presentation of an application.

Testing a Parametric Model Against a Semiparametric Alternative

This paper describes a method for testing a parametric model of the mean of a random variable Y conditional on a vector of explanatory variables X against a semiparametric alternative. The test is motivated by a conditional moment test against a parametric alternative and amounts to replacing the parametric alternative model with a semiparametric model. The resulting semiparametric test is consistent against a larger set of alternatives than are parametric conditional moments tests based on finitely many moment conditions. The results of Monte Carlo experiments and an application illustrate the usefulness of the new test.

An application of the AHP to bank strategic planning: The mergers and acquisitions process

Strategic planning is one of the most complex and ill-structured tasks faced by banks. It usually requires adopting a course of action from a large set of alternatives with uncertain long-term outcomes which depend, to a large extent, on unknown and turbulent environments. In deriving these strategies bankers usually try to achieve multiple, and sometimes conflicting objectives such as profitability, growth, liquidity, and market share subject to constraints on credit and exchange risks and regulatory requirements. Moreover, specific strategies are normally determined by a board of directors whose members have different backgrounds, judgments and personal goals. This paper describes the application of the AHP methodology to the evaluation of bank Mergers and Acquisitions (M&A) strategy. The model developed for this important problem was tested with the assistance of the board of directors of a billion dollar bank holding company. Although it is difficult to generalize from one experiment dealing with a single issue, there was nothing unique in the situation where the test was performed. Hence it is safe to assume that the AHP methodology can be applied to other complex and ill-defined strategic issues faced by other banking institutions. Compared with existing techniques on the one hand, and with qualitative managerial judgement on the other hand, the AHP provides a useful, simple and powerful tool for dealing with strategic planning in banking.

On asymptotically optimal tests

We first consider a general statistical model and give asymptotic lower bounds for the type II errors in the case where the type I error tends to 0 exponentially fast. As a particular case we study the problem of testing hypotheses on the infinitesimal generator of a finite state space continous-time Markov process. If the exponential rate of convergence serves as measure of the asymptotic performance, appropriate sequences of discretized likelihood-ratio statistics are shown to be uniformly asymptotically optimal on a very large set of alternatives. Finally the Bahadur slope of the proposed test statistic is investigated.