In this paper, we approximately solve the multiple-choice multi-dimensional knapsack problem. We propose a hybrid algorithm based on branch and bound method and Pareto-algebraic operations. The algorithm starts by an initial solution and then combines one-by-one groups of the problem instance to generate partial solutions in each iteration. Most of these partial solutions are discarded by Paret...

This paper addresses the optimal design of residential ventilation systems in an apartment floor plan in Korea. The term “optimal design” refers to the selection of a ventilation method (mechanical, hybrid), type of heat recovery (total, sensible only), outdoor airflow rate, and the optimal sizing and location of supply diffusers/exhaust registers. Decision-making criteria include initial and o...

We consider the problem of allocating an infinitely divisible commodity among a group of agents with single-peaked preferences. A rule that has played a central role in the analysis of the problem is the so-called uniform rule. Chun (2001) proves that the uniform rule is the only rule satisfying Pareto optimality, no-envy, separability, and -continuity. We obtain an alternative characterization...

The notion of optimality naturally arises in many areas of applied mathematics and computer science concerned with decision making. Here we consider this notion in the context of two formalisms used for different purposes and in different research areas: graphical games and soft constraints. We relate the notion of optimality used in the area of soft constraint satisfaction problems (SCSPs) to ...

Matching problems involve a set of participants, where each participant has a capacity and a subset of the participants rank a subset of the others in order of preference (strictly or with ties). Matching problems are motivated in practice by large-scale applications, such as automated matching schemes, which assign participants together based on their preferences over one another. This thesis ...

This paper presents a natural extension of Bayesian decision theory from the domain of individual decisions to the domain of group decisions. We assume that each group member accepts the assumptions of subjective expected utility theory with respect to the alternatives from which they must choose, but we do not assume, a priori, that the group as a whole accepts those assumptions. Instead, we i...

When dealing with multi-criteria decision making problems, the concept of Pareto-optimality and Pareto-dominance may be inefficient (e.g. generally multiple solutions exist), especially when there is a large number of criteria. Our paper considers the fuzzy multi-criteria decision making problem based on Zadeh’s linguistic approach to P-optimality and P-dominance. The construction, analysis and...

In this paper, a cooperative Continuous static game (F-CCSG) with fuzzy parameters in the cost function of the player is presented. Through the use of the ?-level sets of fuzzy numbers, the F-CCSG is converted to the corresponding ?-CCSG and an extended Pareto optimality concept called the ?-Pareto optimality is introduced. An algorithm for solving the ?-CCSG is suggested. The algorithm is base...

Design is a multi-objective decision-making process considering manufacturing, cost, aesthetics, usability among many other product attributes. The set of optimal solutions, the Pareto set, indicates the tradeoffs between objectives. Decision-makers generally select their own optima from the Pareto set based on personal preferences or other judgements. However, uncertainties from manufacturing ...