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Convex Analysisの二,三の進展について

The Theory of Incentives I: The Principal-Agent Model

Evolutionary algorithms (EAs) have shown to be promising in solving many-objective optimization problems (MaOPs), where the performance of these algorithms heavily depends on whether solutions that can accelerate convergence toward the Pareto front and maintaining a high degree of diversity will be selected from a set of nondominated solutions. In this paper, we propose a knee point-driven EA to solve MaOPs. Our basic idea is that knee points are naturally most preferred among nondominated solutions if no explicit user preferences are given. A bias toward the knee points in the nondominated solutions in the current population is shown to be an approximation of a bias toward a large hypervolume, thereby enhancing the convergence performance in many-objective optimization. In addition, as at most one solution will be identified as a knee point inside the neighborhood of each solution in the nondominated front, no additional diversity maintenance mechanisms need to be introduced in the proposed algorithm, considerably reducing the computational complexity compared to many existing multiobjective EAs for many-objective optimization. Experimental results on 16 test problems demonstrate the competitiveness of the proposed algorithm in terms of both solution quality and computational efficiency.

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A Knee Point-Driven Evolutionary Algorithm for Many-Objective Optimization

Software systems nowadays are complex and difficult to maintain due to continuous changes and bad design choices. To handle the complexity of systems, software products are, in general, decomposed in terms of packages/modules containing classes that are dependent. However, it is challenging to automatically remodularize systems to improve their maintainability. The majority of existing remodularization work mainly satisfy one objective which is improving the structure of packages by optimizing coupling and cohesion. In addition, most of existing studies are limited to only few operation types such as move class and split packages. Many other objectives, such as the design semantics, reducing the number of changes and maximizing the consistency with development change history, are important to improve the quality of the software by remodularizing it. In this article, we propose a novel many-objective search-based approach using NSGA-III. The process aims at finding the optimal remodularization solutions that improve the structure of packages, minimize the number of changes, preserve semantics coherence, and reuse the history of changes. We evaluate the efficiency of our approach using four different open-source systems and one automotive industry project, provided by our industrial partner, through a quantitative and qualitative study conducted with software engineers.

Many-Objective Software Remodularization Using NSGA-III

In this work we consider the following hazmat transportation network design problem. A given set of hazmat shipments has to be shipped over a road transportation network in order to transport a given amount of hazardous materials from specific origin points to specific destination points, and we assume there are regional and local government authorities that want to regulate the hazmat transportations by imposing restrictions on the amount of hazmat traffic over the network links. In particular, the regional authority aims to minimize the total
transport risk induced over the entire region in which the transportation network is
embedded, while local authorities want the risk over their local jurisdictions to be the lowest possible, forcing the regional authority to assure also risk equity. We provide a linear bilevel programming formulation for this hazmat transportation network design problem that takes into account both total risk minimization and risk equity. We transform the bilevel model into a single-level mixed integer linear program by replacing the second level (follower) problem by its KKT conditions and by linearizing the complementary constraints, and then we solve the MIP problem with a commercial optimization solver. The optimal solution may not be
stable, and we provide an approach for testing its stability and for evaluating the range of the its solution values when it is not stable. Moreover, since the bilevel model is difficult to be solved optimally and its optimal solution may not be stable, we provide a heuristic algorithm for the bilevel model able to always find a stable solution. The proposed bilevel model and
heuristic algorithm are experimented on real scenarios of an Italian regional network.

A Bilevel flow model for HazMat transportation network design

A knee point is almost always a preferred trade-off solution, if it exists in a bicriteria optimization problem. In this article, an attempt is made to improve understanding of a knee point and investigate the properties of a bicriteria problem that may exhibit a knee on its Pareto-optimal front. Past studies are reviewed and a couple of new definitions are suggested. Additionally, a knee region is defined for problems in which, instead of one, a set of knee-like solutions exists. Edge-knee solutions, which behave like knee solutions but lie near one of the extremes on the Pareto-optimal front, are also introduced. It is interesting that in many problem-solving tasks, despite the existence of a number of solution methodologies, only one or a few of them are commonly used. Here, it is argued that often such common solution principles are knee solutions to a bicriteria problem formed with two conflicting goals of the underlying problem-solving task. The argument is illustrated on a number of tasks, such as ...

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Understanding knee points in bicriteria problems and their implications as preferred solution principles

Among the various governmental schemes that support agriculture, support prices have been adopted by many developing countries. A support price for an agricultural crop is a guaranteed price at which a governmental entity agrees to purchase that crop from farmers. Despite this surety, a surprising practice of “distressed” selling† has been widely observed in practice: Farmers sell a significant portion of their crops to outside agents at prices much lower than the support price. We build a tractable stochastic dynamic programming model that captures the salient features of the ground realities - limited as well as uncertain procurement capacity, high holding costs for the farmers, and lack of affordable credit - that conspire to induce distressed selling and, consequently, a significant loss of welfare of the farmers. Using real data on procurement under a support-price program, we establish the accuracy of our model's prediction on the volume of distressed sales. Finally, we show how our model and its solution can serve as a simple and useful tool for policy-makers to assess the relative impact of the improvements in the main determinants of distressed sales.

This article is protected by copyright. All rights reserved.

Distressed Selling by Farmers: Model, Analysis, and Use in Policy-Making

In a bi-criteria optimization problem, often the user is interested in a subset of solutions lying in the knee region. On the other hand in many problem-solving tasks, often one or a few methodologies are commonly used. In this paper, we argue that there is a link between the knee solutions in bi-criteria problems and the preferred methodologies when viewed from a conflicting bi-criterion standpoint. We illustrate our argument with the help of a number of popularly used problem-solving tasks. Each task, when perceived as a bicriteria problem, seems to exhibit a knee or a knee-region and the commonly-used methodology seems to lie within the knee-region. This linking is certainly an interesting finding and may have a long-term implication in the development of efficient solution methodologies for different scientific and other problem-solving tasks.

Towards a Link between Knee Solutions and Preferred Solution Methodologies

Descending mechanisms for procurement (or, ascending mechanisms for selling) have been well-recognized for their simplicity from the viewpoint of bidders—they require less bidder sophistication as compared to sealed-bid mechanisms. In this study, we consider procurement under each of two types of constraints: (1) Individual/Group Capacities: limitations on the amounts that can be sourced from individual and/or subsets of suppliers, and (2) Business Rules: lower and upper bounds on the number of suppliers to source from, and on the amount that can be sourced from any single supplier. We analyze two procurement problems, one that incorporates individual/group capacities and another that incorporates business rules. In each problem, we consider a buyer who wants to procure a fixed quantity of a product from a set of suppliers, where each supplier is endowed with a privately known constant marginal cost. The buyer's objective is to minimize her total expected procurement cost. For both problems, we present descending auction mechanisms that are optimal mechanisms. We then show that these two problems belong to a larger class of mechanism design problems with constraints specified by polymatroids, for which we prove that optimal mechanisms can be implemented as descending mechanisms

Optimal Descending Mechanisms for Constrained Procurement

The present paper deals with the steady-state solution of the queuing system in which i units arrive according to a Poisson distribution; ii the queue discipline is first-come, first-served; and iii the service time distribution is hyper-exponential with n branches. Assuming a finite waiting space, we derive the system-size distribution and the mean number of units in the system therefrom. Results are also deduced when an infinite waiting space is allowed. Another interesting case is discussed when only the mean service rate over all the n branches is assigned. In the end we study the case when no queue is allowed.

Shivam Gupta

Papers

Understanding knee points in bicriteria problems and their implications as preferred solution principles

Distressed Selling by Farmers: Model, Analysis, and Use in Policy-Making

Towards a Link between Knee Solutions and Preferred Solution Methodologies

Optimal Descending Mechanisms for Constrained Procurement

Queues with Poisson Input and Hyper-Exponential Output with Finite Waiting Space