Utilitarian Mechanism Design for Multiobjective Optimization

In a classic optimization problem, the complete input data is assumed to be known to the algorithm. This assumption may not be true anymore in optimization problems motivated by the Internet where part of the input data is private knowledge of independent selfish agents. The goal of algorithmic mechanism design is to provide (in polynomial time) a solution to the optimization problem and a set of incentives for the agents such that disclosing the input data is a dominant strategy for the agents. In the case of NP-hard problems, the solution computed should also be a good approximation of the optimum. In this paper we focus on mechanism design for multiobjective optimization problems. In this setting we are given a main objective function and a set of secondary objectives which are modeled via budget constraints. Multiobjective optimization is a natural setting for mechanism design as many economical choices ask for a compromise between different, partially conflicting goals. The main contribution of this paper is showing that two of the main tools for the design of approximation algorithms for multiobjective optimization problems, namely, approximate Pareto sets and Lagrangian relaxation, can lead to truthful approximation schemes. By exploiting the method of approximate Pareto sets, we devise truthful deterministic and randomized multicriteria fully polynomial-time approximation schemes (FPTASs) for multiobjective optimization problems whose exact version admits a pseudopolynomial-time algorithm, as, for instance, the multibudgeted versions of minimum spanning tree, shortest path, maximum (perfect) matching, and matroid intersection. Our construction also applies to multidimensional knapsack and multiunit combinatorial auctions. Our FPTASs compute a $(1+\varepsilon)$-approximate solution violating each budget constraint by a factor $(1+\varepsilon)$. When feasible solutions induce an independence system, i.e., when subsets of feasible solutions are feasible as well, we present a PTAS (not violating any constraint), which combines the approach above with a novel monotone way to guess the heaviest elements in the optimum solution. Finally, we present a universally truthful Las Vegas PTAS for minimum spanning tree with a single budget constraint, where one wants to compute a minimum cost spanning tree whose length is at most a given value $L$. This result is based on the Lagrangian relaxation method, in combination with our monotone guessing step and with a random perturbation step (ensuring low expected running time). This result can be derandomized in the case of integral lengths. All the mentioned results match the best known approximation ratios, which are, however, obtained by nontruthful algorithms

A survey of diversity-oriented optimization

The concept of diversity plays a crucial role in many optimization approaches: On the one hand, diversity can be formulated as an essential goal, such as in level set approximation or multiobjective optimization where the aim is to find a diverse set of alternative feasible or, respectively, Pareto optimal solutions. On the other hand, diversity maintenance can play an important role in algorithms that ultimately searc

Human-aligned artificial intelligence is a multiobjective problem

As the capabilities of artificial intelligence (AI) systems improve, it becomes important to constrain their actions to ensure their behaviour remains beneficial to humanity. A variety of ethical, legal and safety-based frameworks have been proposed as a basis for designing these constraints. Despite their variations, these frameworks share the common characteristic that decision-making must consider multiple potentially conflicting factors. We demonstrate that these alignment frameworks can be represented as utility functions, but that the widely used Maximum Expected Utility (MEU) paradigm provides insufficient support for such multiobjective decision-making. We show that a Multiobjective Maximum Expected Utility paradigm based on the combination of vector utilities and non-linear action–selection can overcome many of the issues which limit MEU’s effectiveness in implementing aligned AI. We examine existing approaches to multiobjective AI, and identify how these can contribute to the development of human-aligned intelligent agents. © 2017, Springer Science+Business Media B.V

Advances and applications in high-dimensional heuristic optimization

“Applicable to most real-world decision scenarios, multiobjective optimization is an area of multicriteria decision-making that seeks to simultaneously optimize two or more conflicting objectives. In contrast to single-objective scenarios, nontrivial multiobjective optimization problems are characterized by a set of Pareto optimal solutions wherein no solution unanimously optimizes all objectives. Evolutionary algorithms have emerged as a standard approach to determine a set of these Pareto optimal solutions, from which a decision-maker can select a vetted alternative. While easy to implement and having demonstrated great efficacy, these evolutionary approaches have been criticized for their runtime complexity when dealing with many alternatives or a high number of objectives, effectively limiting the range of scenarios to which they may be applied. This research introduces mechanisms to improve the runtime complexity of many multiobjective evolutionary algorithms, achieving state-of-the-art performance, as compared to many prominent methods from the literature. Further, the investigations here presented demonstrate the capability of multiobjective evolutionary algorithms in a complex, large-scale optimization scenario. Showcasing the approach’s ability to intelligently generate well-performing solutions to a meaningful optimization problem. These investigations advance the concept of multiobjective evolutionary algorithms by addressing a key limitation and demonstrating their efficacy in a challenging real-world scenario. Through enhanced computational efficiency and exhibited specialized application, the utility of this powerful heuristic strategy is made more robust and evident”--Abstract, page iv

Computing leximin-optimal solutions in constraint networks

AbstractIn many real-world multiobjective optimization problems one needs to find solutions or alternatives that provide a fair compromise between different conflicting objective functions—which could be criteria in a multicriteria context, or agent utilities in a multiagent context—while being efficient (i.e. informally, ensuring the greatest possible overall agents' satisfaction). This is typically the case in problems implying human agents, where fairness and efficiency requirements must be met. Preference handling, resource allocation problems are another examples of the need for balanced compromises between several conflicting objectives. A way to characterize good solutions in such problems is to use the leximin preorder to compare the vectors of objective values, and to select the solutions which maximize this preorder. In this article, we describe five algorithms for finding leximin-optimal solutions using constraint programming. Three of these algorithms are original. Other ones are adapted, in constraint programming settings, from existing works. The algorithms are compared experimentally on three benchmark problems

Optimization Models for Sustainable Design and Management of Biopower Supply Chains

This dissertation presents optimization models to aid with the sustainable design and management of biopower (biomass cofiring) supply chains. We address three main challenges associated with today’s biopower projects: i) high cost of biomass collection, storage and delivery, ii) inefficiency of the mechanisms used to incentivize biomass usage for generating electricity, and iii) lack of clear understanding about the trade-offs between economic and environmental impacts of biopower supply chains. In order to address the high cost of delivering biomass, we present a novel mixed integer nonlinear program that integrates production and transportation decisions at power plants. Proposed model captures the loss in process efficiencies from using biomass, in-vestment and operational costs associated with cofiring, and savings due to production tax credit (PTC), a major governmental incentive to support biopower. We develop a La-grangian relaxation approach to provide upper bounds, and two linear approximations to provide lower bounds for the problem. An important finding is that the one-size-fits-all approach of PTC is not effective in motivating plants to utilize biomass and there is a need for sophisticated incentive schemes. In order to address the second issue, we propose alter-natives for the existing PTC incentive. The proposed flexible alternatives are functions of plant capacity and biomass cofiring ratio. We use a resource allocation framework to model and analyze the profit-earning potentials and fairness of the proposed incentive schemes. Finally, in order to address the last challenge, we propose a stochastic biobjective optimiza-tion model to analyze the economic and environmental impacts of biopower supply chains. The economic objective function maximizes the potential profits in the supply chain and the environmental objective function minimizes the life cycle greenhouse gasses (GHG). We use a life cycle assessment (LCA) approach to derive the emission factors for this objective function. We capture uncertainties of biomass quality and supply via the use of chance constraints. The results of this dissertation work are useful for electric utility companies and policy makers. Utility companies can use the proposed models to identify ways to improve biopower production, have better environmental performance, and make use of the existing incentives. Policy makers would gain insights on designing incentive schemes for a more efficient utilization of biomass and a fairer distribution of tax-payers money