Given a multi-armed bandit problem it may be desirable to achieve a smallerthan-usual worst-case regret for some special actions. I show that the price for such unbalanced worst-case regret guarantees is rather high. Specifically, if an algorithm enjoys a worst-case regret of B with respect to some action, then there must exist another action for which the worst-case regret is at least Ω(nK/B),...

There has been a surge of research interest in developing tools and analysis for Bayesian optimization, the task of finding the global maximizer of an unknown, expensive function through sequential evaluation using Bayesian decision theory. However, many interesting problems involve optimizing multiple, expensive to evaluate objectives simultaneously, and relatively little research has addresse...

1. Abstract Multiobjective genetic algorithms (MOGAs) have successfully been used on a wide range of real world problems. However, it is generally accepted that the performance of most state-of-the-art multiobjective genetic algorithms tend to perform poorly for problems with more than four objectives, termed many-objective problems. The contribution of this paper is a new approach for identify...

Evolutionary algorithms have been recognized to be suitable for extracting approximate solutions of multi-objective problems because of their capability to evolve a set of non-dominated solutions distributed along the Pareto frontier‎. ‎This paper applies an evolutionary optimization scheme‎, ‎inspired by Multi-objective Invasive Weed Optimization (MOIWO) and Non-dominated Sorting (NS) strategi...

During the last decade, the stringent pressures from environmental and social requirements have spurred an interest in designing a reverse logistics (RL) network. The success of a logistics system may depend on the decisions of the facilities locations and vehicle routings. The location-routing problem (LRP) simultaneously locates the facilities and designs the travel routes for vehicles among ...

Welfare economics provides the basis for judging the achievements of markets and policy makers in allocating resources. Its most powerful conceptual tool is the utility possibility frontier. This defines the set of utility allocations that can be achieved in a society subject to the constraints of tastes and technologies. Any allocation on the frontier cannot be Pareto dominated and hence would...

This paper characterizes the utility possibility frontier resulting in a model of private voluntary provision of a public good. It is shown that ex-ante lotteries over resource distributions among the agents can be Pareto improving. A corollary is that an equal distribution of resources among the agents, or any distribution where all agents contribute in equilibrium, is always Pareto dominated ...

In this paper, we propose to integrate particle swarm optimization algorithm into cultural algorithms frame to develop a more efficient cultural particle swarm algorithms (CPSA) for constrained multi-objective optimization problem. In our CPSA, the population space of cultural algorithms consists of n+1 subswarms which are used to search for the n single-objective optimums and an additional mul...

In this paper, several new set quality metrics are introduced that can be used to evaluate the ‘‘goodness’’ of an observed Pareto solution set. These metrics, which are formulated in closed-form and geometrically illustrated, include hyperarea difference, Pareto spread, accuracy of an observed Pareto frontier, number of distinct choices and cluster. The metrics should enable a designer to eithe...

We consider a general framework where each agent has an outside option of privately known value. First, we show that if the designer seeks to (weakly) Pareto-improve an individually rational and participation-maximal benchmark mechanism, there is at most one strategy-proof candidate. Consequently, many known mechanisms are on the Pareto frontier of strategy-proof mechanisms. Second, we characte...