Sorted Pareto Dominance: An Extension to Pareto Dominance and Its Application in Soft Constraints

O'Mahony, Conor; Wilson, Nic

doi:10.1109/ictai.2012.113

Cited by 3 publications

(10 citation statements)

References 22 publications

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“…T . From Theorem 1 in [13], we have that ≤ F = sp . Now, let F be the set of all possible weight functions such that f ∈ F if and only if f is strictly monotonic w.r.t.…”

Section: Sorted-pareto and Min-sum Of Weightsmentioning

confidence: 98%

“…In this section, we recall definitions for Sorted-Pareto dominance from [13], and show how this ordering relates to min-sum of weights. Min-Sum of Weights.…”

Section: Sorted-pareto and Min-sum Of Weightsmentioning

confidence: 99%

“…Let [α] F denote the F -equivalence class of α ∈ A, where [α] F = {β ∈ A : α ≡ F β}. Since we have from Theorem 1 in [13] that ≤ F is equal to sp , i.e., sp = f ∈F ≤ f , then we have that ≡ F is equal to ≡ sp , i.e., ≡ sp is the intersection of ≡ f over all f ∈ F , which gives us the result in Proposition 3. …”

Section: Sorted-pareto Modsmentioning

confidence: 99%

“…In this section, we look at methods for generating the different optimality classes for Sorted-Pareto MODS S. Here we assume that there is some procedure to generate CSD(S), i.e., that calculates the preference vectors for each decision and compares them using Sorted-Pareto dominance to generate the set of decisions that are non-dominated. For example, the branch and bound search algorithms detailed in [13] do exactly this; however other search procedures can be used. From CSD(S), NO(S) can be calculated by comparing all the solutions in CSD(S) with one another to see if any Sorted-Pareto dominate all others.…”

Section: Proposition 6 For Mods S Po(s) ⊆ Csd(s)mentioning

confidence: 99%

“…this new relation, which we call the Sorted-Pareto relation. This leads to a smaller, more manageable set of Sorted-Pareto optimal solutions, that are still Pareto optimal, as shown in [13].…”

Section: Introductionmentioning

confidence: 99%

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Sorted-Pareto Dominance and Qualitative Notions of Optimality

O'Mahony

Wilson

2013

Lecture Notes in Computer Science

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Access to the full text of the published version may require a subscription. Abstract. Pareto dominance is often used in decision making to compare decisions that have multiple preference values -however it can produce an unmanageably large number of Pareto optimal decisions. When preference value scales can be made commensurate, then the SortedPareto relation produces a smaller, more manageable set of decisions that are still Pareto optimal. Sorted-Pareto relies only on qualitative or ordinal preference information, which can be easier to obtain than quantitative information. This leads to a partial order on the decisions, and in such partially-ordered settings, there can be many different natural notions of optimality. In this paper, we look at these natural notions of optimality, applied to the Sorted-Pareto and min-sum of weights case; the Sorted-Pareto ordering has a semantics in decision making under uncertainty, being consistent with any possible order-preserving function that maps an ordinal scale to a numerical one. We show that these optimality classes and the relationships between them provide a meaningful way to categorise optimal decisions for presenting to a decision maker. Rights

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“…T . From Theorem 1 in [13], we have that ≤ F = sp . Now, let F be the set of all possible weight functions such that f ∈ F if and only if f is strictly monotonic w.r.t.…”

Section: Sorted-pareto and Min-sum Of Weightsmentioning

confidence: 98%

“…In this section, we recall definitions for Sorted-Pareto dominance from [13], and show how this ordering relates to min-sum of weights. Min-Sum of Weights.…”

Section: Sorted-pareto and Min-sum Of Weightsmentioning

confidence: 99%

Section: Sorted-pareto Modsmentioning

confidence: 99%

Section: Proposition 6 For Mods S Po(s) ⊆ Csd(s)mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Sorted-Pareto Dominance and Qualitative Notions of Optimality

O'Mahony

Wilson

2013

Lecture Notes in Computer Science

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Kursawe and ZDT functions optimization using hybrid micro genetic algorithm (HMGA)

2015

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Accuracy degradation aware bit rate allocation for layer-wise uniform quantization of weights in neural network

Nikolić,

Tomić,

Perić

et al. 2024

Journal of Electrical Engineering

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Motivated by the fact that optimizing quantization error fails to minimize the accuracy degradation caused by the quantization of Neural Network (NN) weights, in this paper, we highlight the need for a comprehensive analysis of post-training quantization, covering average bit rate, accuracy degradation and SQNR. One such analysis, for the layer-wise uniform quantization and its application is NN weight compression is presented in this paper. We introduce an additional aspect of Uniform Quantizer (UQ) choice, and we allow the selection of one of two UQs (2-bit or 3-bit UQs) for each layer of NN. However, choosing a particular bit rate allocation to minimize average bit rate and accuracy degradation requires finding a trade-off solution. To solve the issue underpinning our motivation, for a post-training layer-wise uniform quantization framework with two UQs, we propose an algorithm for generating bit rate allocation patterns and corresponding pairs of average bit rate and accuracy degradation. We analyze the output of this algorithm and determine a solution of the elaborated two-objective optimization problem. To confirm the validity of the results we also apply the Pareto dominance method. This work can be considered a solid foundation for further analyses of more complex and deeper NNs.

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Sorted Pareto Dominance: An Extension to Pareto Dominance and Its Application in Soft Constraints

Cited by 3 publications

References 22 publications

Sorted-Pareto Dominance and Qualitative Notions of Optimality

Sorted-Pareto Dominance and Qualitative Notions of Optimality

Kursawe and ZDT functions optimization using hybrid micro genetic algorithm (HMGA)

Accuracy degradation aware bit rate allocation for layer-wise uniform quantization of weights in neural network

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