Fast approximation schemes for multi-criteria flow, knapsack, and scheduling problems

Includes bibliographical references (p. 40-42).Supported by an NSF Presidential Young Investigator grant. Supported by the Air Force Office of Scientific Research. AFOSR-88-0088 Supported by the NSF. DDM-8921835by Hershel M. Safer, James B. Orlin

On a Simple Hedonic Game with Graph-Restricted Communication

International audienceWe study a hedonic game for which the feasible coalitions are prescribed by a graph representing the agents' social relations. A group of agents can form a feasible coalition if and only if their corresponding vertices can be spanned with a star. This requirement guarantees that agents are connected, close to each other, and one central agent can coordinate the actions of the group. In our game everyone strives to join the largest feasible coalition. We study the existence and computational complexity of both Nash stable and core stable partitions. Then, we provide tight or asymptotically tight bounds on their quality, with respect to both the price of anarchy and stability, under two natural social functions, namely, the number of agents who are not in a singleton coalition, and the number of coalitions. We also derive refined bounds for games in which the social graph is restricted to be claw-free. Finally, we investigate the complexity of computing socially optimal partitions as well as extreme Nash stable ones

Generalized Decision Rule Approximations for Stochastic Programming via Liftings

Stochastic programming provides a versatile framework for decision-making under uncertainty, but the resulting optimization problems can be computationally demanding. It has recently been shown that, primal and dual linear decision rule approximations can yield tractable upper and lower bounds on the optimal value of a stochastic program. Unfortunately, linear decision rules often provide crude approximations that result in loose bounds. To address this problem, we propose a lifting technique that maps a given stochastic program to an equivalent problem on a higherdimensional probability space. We prove that solving the lifted problem in primal and dual linear decision rules provides tighter bounds than those obtained from applying linear decision rules to the original problem. We also show that there is a one-to-one correspondence between linear decision rules in the lifted problem and families of non-linear decision rules in the original problem. Finally, we identify structured liftings that give rise to highly flexible piecewise linear decision rules and assess their performance in the context of a stylized investment planning problem.

A General Equilibrium Financial Asset Economy with Transaction Costs and Trading Constraints

This paper presents a unified framework for examining the general equilibrium effects of transactions costs and trading constraints on security market trades and prices. The model uses a discrete time/state framework and Kuhn-Tucker theory to characterize the optimal decisions of consumers and financial intermediaries. Transaction costs and constraints give rise to regions of no trade and to bid-ask spreads: their existence frustrate the derivation of standard results in arbitrage-based pricing. Nevertheless, we are able to obtain as dual characterizations of our primal problems, one-sided arbitrage pricing results and a personalized martingale representation of asset pricing. These pricing results are identical to those derived by Jouini and Kallal (1995) using arbitrage arguments. The paper's framework incorporates a number of specialized existing models and results, proves new results and discusses new directions for research. In particular, we include characterizations of intermediaries who hold optimal portfolios; brokers who do not hold portfolios, and consumer-specific transactions costs and trading constraints. Furthermore we show that in the special case of equiproportional transaction costs and a sufficient number of assets, there is an analogue of the arbitrage pricing result for European derivatives where prices are interpreted as mid-prices between the bid-ask spread. We discuss the effects of non-convex transaction technologies on prices and trades.Financial Markets, Transaction Costs, Trading Constraints, Asset Pricing, General Equilibrium, Incomplete Markets

Data-driven Distributionally Robust Optimization Using the Wasserstein Metric: Performance Guarantees and Tractable Reformulations

We consider stochastic programs where the distribution of the uncertain parameters is only observable through a finite training dataset. Using the Wasserstein metric, we construct a ball in the space of (multivariate and non-discrete) probability distributions centered at the uniform distribution on the training samples, and we seek decisions that perform best in view of the worst-case distribution within this Wasserstein ball. The state-of-the-art methods for solving the resulting distributionally robust optimization problems rely on global optimization techniques, which quickly become computationally excruciating. In this paper we demonstrate that, under mild assumptions, the distributionally robust optimization problems over Wasserstein balls can in fact be reformulated as finite convex programs---in many interesting cases even as tractable linear programs. Leveraging recent measure concentration results, we also show that their solutions enjoy powerful finite-sample performance guarantees. Our theoretical results are exemplified in mean-risk portfolio optimization as well as uncertainty quantification.Comment: 42 pages, 10 figure

A similarity-based cooperative co-evolutionary algorithm for dynamic interval multi-objective optimization problems

The file attached to this record is the author's final peer reviewed version. The Publisher's final version can be found by following the DOI link.Dynamic interval multi-objective optimization problems (DI-MOPs) are very common in real-world applications. However, there are few evolutionary algorithms that are suitable for tackling DI-MOPs up to date. A framework of dynamic interval multi-objective cooperative co-evolutionary optimization based on the interval similarity is presented in this paper to handle DI-MOPs. In the framework, a strategy for decomposing decision variables is first proposed, through which all the decision variables are divided into two groups according to the interval similarity between each decision variable and interval parameters. Following that, two sub-populations are utilized to cooperatively optimize decision variables in the two groups. Furthermore, two response strategies, rgb0.00,0.00,0.00i.e., a strategy based on the change intensity and a random mutation strategy, are employed to rapidly track the changing Pareto front of the optimization problem. The proposed algorithm is applied to eight benchmark optimization instances rgb0.00,0.00,0.00as well as a multi-period portfolio selection problem and compared with five state-of-the-art evolutionary algorithms. The experimental results reveal that the proposed algorithm is very competitive on most optimization instances

Novel Hedonic Games and Stability Notions

We present here work on matching problems, namely hedonic games, also known as coalition formation games. We introduce two classes of hedonic games, Super Altruistic Hedonic Games (SAHGs) and Anchored Team Formation Games (ATFGs), and investigate the computational complexity of finding optimal partitions of agents into coalitions, or finding - or determining the existence of - stable coalition structures. We introduce a new stability notion for hedonic games and examine its relation to core and Nash stability for several classes of hedonic games