Analysis of an Algorithm for Identifying Pareto Points in Multi-Dimensional Data Sets

Yukish, Michael A.; Simpson, Timothy W.

doi:10.2514/6.2004-4324

Cited by 28 publications

(23 citation statements)

References 14 publications

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“…The Pareto front size for a random set X of size N is expected as H(N), where H is the harmonic number and closely related to log(N) [22,23]. This interacts in a fortunate way with dynamic programming, where for input size n, the search space X grows with O(2 n ), and we can expect Pareto fronts of size O(n).…”

Section: Key Operations In Pareto Optimization and Dynamic Programmingmentioning

confidence: 99%

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Integrating Pareto Optimization into Dynamic Programming

2016

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Pareto optimization combines independent objectives by computing the Pareto front of the search space, yielding a set of optima where none scores better on all objectives than any other. Recently, it was shown that Pareto optimization seamlessly integrates with algebraic dynamic programming: when scoring schemes A and B can correctly evaluate the search space via dynamic programming, then so can Pareto optimization with respect to A and B. However, the integration of Pareto optimization into dynamic programming opens a wide range of algorithmic alternatives, which we study in substantial detail in this article, using real-world applications in biosequence analysis, a field where dynamic programming is ubiquitous. Our results are two-fold: (1) We introduce the operation of a "Pareto algebra product" in the dynamic programming framework of Bellman's GAP. Users of this framework can now ask for Pareto optimization with a single keystroke. Careful evaluation of the implementation alternatives by means of an extended Bellman's GAP compiler demonstrates the dependence of the best implementation choice on the application at hand. (2) We extract from our experiments several pieces of advice to programmers who do not use a system such as Bellman's GAP, but who choose to hand-craft their dynamic programming recurrences, incorporating Pareto optimization from scratch.

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Section: Key Operations In Pareto Optimization and Dynamic Programmingmentioning

confidence: 99%

“…For d > 2 dimensions, the Pareto front size for a random set X of size N is expected as H (d) (N), where H (d) is the generalized harmonic number and closely related to log d−1 (N) [23]. Hence, increasing the dimension increases the expected front size exponentially.…”

Section: Key Operations In Pareto Optimization and Dynamic Programmingmentioning

confidence: 99%

Integrating Pareto Optimization into Dynamic Programming

2016

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“…Kung and Bentley [Kung et al 1975;Bentley 1980] developed a divide-and-conquer approach, that is still the algorithm with the best worst-case computational complexity, et al 1975;Yukish 2004], where N is the number of points in the set being minimized and d is the dimensionality of these points. A very simple algorithm for Pareto minimization is the Simple Cull algorithm [Preparata and Shamos 1985;Yukish 2004], also known as a block-nested loop algorithm [Borzsonyi et al 2001]. Simple Cull is a nested loop that essentially compares configurations in the set of points to be minimized in a pairwise fashion, leading to an O(N 2 ) worst-case complexity.…”

Section: Methodsmentioning

confidence: 99%

A fast and scalable multidimensional multiple-choice knapsack heuristic

Shojaei

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et al. 2013

ACM Trans. Des. Autom. Electron. Syst.

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Many combinatorial optimization problems in the embedded systems and design automation domains involve decision making in multi-dimensional spaces. The multi-dimensional multiple-choice knapsack problem (MMKP) is among the most challenging of the encountered optimization problems. MMKP problem instances appear for example in chip multiprocessor run-time resource management and in global routing of wiring in circuits. Chip multiprocessor resource management requires solving MMKP under real-time constraints, whereas global routing requires scalability of the solution approach to extremely large MMKP instances. This paper presents a novel MMKP heuristic, CPH (for Compositional Pareto-algebraic Heuristic), which is a parameterized compositional heuristic based on the principles of Pareto algebra. Compositionality allows incremental computation of solutions. The parameterization allows tuning of the heuristic to the problem at hand. These aspects make CPH a very versatile heuristic. When tuning CPH for computation time, MMKP instances can be solved in real time with better results than the fastest MMKP heuristic so far. When tuning CPH for solution quality, it finds several new solutions for standard benchmarks that are not found by any existing heuristic. CPH furthermore scales to extremely large problem instances. We illustrate and evaluate the use of CPH in both chip multiprocessor resource management and in global routing.

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“…As the number of portfolios is small, we first calculate the expected cost for each of the 243 portfolios, using equation (14), then identify non-dominated sets using the simple cull algorithm introduced by (Yukish 2004). …”

Section: Iii1 Energy Technology Portfolio Modelmentioning

confidence: 99%

Finding Common Ground When Experts Disagree: Robust Portfolio Decision Analysis

2017

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Within the IEB framework, the Chair of Energy Sustainability promotes research into the production, supply and use of the energy needed to maintain social welfare and development, placing special emphasis on economic, environmental and social aspects. There are three main research areas of interest within the program: energy sustainability, competition and consumers, and energy firms. The energy sustainability research area covers topics as energy efficiency, CO2 capture and storage, R+D in energy, green certificate markets, smart grids and meters, green energy and biofuels. The competition and consumers area is oriented to research on wholesale markets, retail markets, regulation, competition and consumers. The research area on energy firms is devoted to the analysis of business strategies, social and corporative responsibility, and industrial organization. Disseminating research outputs to a broad audience is an important objective of the program, whose results must be relevant both at national and international level.The Chair of Energy Sustainability of the University of Barcelona-IEB is funded by the following enterprises ACS, CEPSA, CLH, Enagas, Endesa, FCC Energia, HC Energia, Gas Natural Fenosa, and Repsol) through FUNSEAM (Foundation for Energy and Environmental Sustainability). introducing an approach we call Robust Portfolio Decision Analysis. We introduce the idea of Belief Dominance as a prescriptive operationalization of a concept that has appeared in the literature under a number of names. We use this concept to derive a set of non-dominated portfolios; and then identify robust individual alternatives from the non-dominated portfolios. The Belief Dominance concept allows us to synthesize multiple conflicting sources of information by uncovering the range of alternatives that are intelligent responses to the range of beliefs. This goes beyond solutions that are optimal for any specific set of beliefs to uncover defensible solutions that may not otherwise be revealed. We illustrate our approach using a problem in the climate change and energy policy context: choosing among clean energy technology R&D portfolios. We demonstrate how the Belief Dominance concept can uncover portfolios that would otherwise remain hidden and identify robust individual investments.

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Analysis of an Algorithm for Identifying Pareto Points in Multi-Dimensional Data Sets

Cited by 28 publications

References 14 publications

Integrating Pareto Optimization into Dynamic Programming

Integrating Pareto Optimization into Dynamic Programming

A fast and scalable multidimensional multiple-choice knapsack heuristic

Finding Common Ground When Experts Disagree: Robust Portfolio Decision Analysis

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