scholarly journals Difficulty Scaling in Proof of Work for Decentralized Problem Solving

Ledger ◽  
2020 ◽  
Vol 5 ◽  
Author(s):  
Pericles Philippopoulos ◽  
Alessandro Ricottone ◽  
Carlos G. Oliver
Keyword(s):  
Problem Solving ◽  
Optimization Problems ◽  
Scientific Interest ◽  
Simple Modification ◽  
Scientific Computation ◽  
Simulation Results ◽  
Computational Resources

We propose DIPS (Difficulty-based Incentives for Problem Solving), a simple modification of the Bitcoin proof-of-work algorithm that rewards blockchain miners for solving optimization problems of scientific interest. The result is a blockchain which redirects some of the computational resources invested in hash-based mining towards scientific computation, effectively reducing the amount of energy ‘wasted’ on mining. DIPS builds the solving incentive directly in the proof-of-work by providing a reduction in block hashing difficulty when optimization improvements are found. A key advantage of this scheme is that decentralization is not greatly compromised while maintaining a simple blockchain design. We study two incentivization schemes and provide simulation results showing that DIPS is able to reduce the amount of hash-power used in the network while generating solutions to optimization problems.

scholarly journals GBUO: “The Good, the Bad, and the Ugly” Optimizer

2021 ◽  
Vol 11 (5) ◽  
pp. 2042
Author(s):  
Hadi Givi ◽  
Mohammad Dehghani ◽  
Zeinab Montazeri ◽  
Ruben Morales-Menendez ◽  
Ricardo A. Ramirez-Mendoza ◽  
...  
Keyword(s):  
High Dimension ◽  
Essential Role ◽  
Optimization Problems ◽  
Optimization Algorithms ◽  
Stochastic Search ◽  
Objective Functions ◽  
Science And Engineering ◽  
Fixed Dimension ◽  
Dimension Functions ◽  
Simulation Results

Optimization problems in various fields of science and engineering should be solved using appropriate methods. Stochastic search-based optimization algorithms are a widely used approach for solving optimization problems. In this paper, a new optimization algorithm called “the good, the bad, and the ugly” optimizer (GBUO) is introduced, based on the effect of three members of the population on the population updates. In the proposed GBUO, the algorithm population moves towards the good member and avoids the bad member. In the proposed algorithm, a new member called ugly member is also introduced, which plays an essential role in updating the population. In a challenging move, the ugly member leads the population to situations contrary to society’s movement. GBUO is mathematically modeled, and its equations are presented. GBUO is implemented on a set of twenty-three standard objective functions to evaluate the proposed optimizer’s performance for solving optimization problems. The mentioned standard objective functions can be classified into three groups: unimodal, multimodal with high-dimension, and multimodal with fixed dimension functions. There was a further analysis carried-out for eight well-known optimization algorithms. The simulation results show that the proposed algorithm has a good performance in solving different optimization problems models and is superior to the mentioned optimization algorithms.

Boosting branch-and-bound MaxSAT solvers with clause learning

2021 ◽  
pp. 1-21
Author(s):  
Chu-Min Li ◽  
Zhenxing Xu ◽  
Jordi Coll ◽  
Felip Manyà ◽  
Djamal Habet ◽  
...  
Keyword(s):  
Experimental Investigation ◽  
Combinatorial Optimization ◽  
Problem Solving ◽  
Branch And Bound ◽  
Real World ◽  
Optimization Problems ◽  
Satisfiability Problem ◽  
Maximum Satisfiability ◽  
Combinatorial Optimization Problems ◽  
Clause Learning

The Maximum Satisfiability Problem, or MaxSAT, offers a suitable problem solving formalism for combinatorial optimization problems. Nevertheless, MaxSAT solvers implementing the Branch-and-Bound (BnB) scheme have not succeeded in solving challenging real-world optimization problems. It is widely believed that BnB MaxSAT solvers are only superior on random and some specific crafted instances. At the same time, SAT-based MaxSAT solvers perform particularly well on real-world instances. To overcome this shortcoming of BnB MaxSAT solvers, this paper proposes a new BnB MaxSAT solver called MaxCDCL. The main feature of MaxCDCL is the combination of clause learning of soft conflicts and an efficient bounding procedure. Moreover, the paper reports on an experimental investigation showing that MaxCDCL is competitive when compared with the best performing solvers of the 2020 MaxSAT Evaluation. MaxCDCL performs very well on real-world instances, and solves a number of instances that other solvers cannot solve. Furthermore, MaxCDCL, when combined with the best performing MaxSAT solvers, solves the highest number of instances of a collection from all the MaxSAT evaluations held so far.

scholarly journals The Strength of Nesterov's Extrapolation2019

2020 ◽  
Author(s):  
Qing Tao
Keyword(s):  
Machine Learning ◽  
Large Scale ◽  
Convergence Rates ◽  
Optimization Problems ◽  
Gradient Methods ◽  
Learning Problems ◽  
Smooth Convex ◽  
Simple Modification ◽  
Convex Problems ◽  
Hinge Loss

The extrapolation strategy raised by Nesterov, which can accelerate the convergence rate of gradient descent methods by orders of magnitude when dealing with smooth convex objective, has led to tremendous success in training machine learning tasks. In this paper, we theoretically study its strength in the convergence of individual iterates of general non-smooth convex optimization problems, which we name \textit{individual convergence}. We prove that Nesterov's extrapolation is capable of making the individual convergence of projected gradient methods optimal for general convex problems, which is now a challenging problem in the machine learning community. In light of this consideration, a simple modification of the gradient operation suffices to achieve optimal individual convergence for strongly convex problems, which can be regarded as making an interesting step towards the open question about SGD posed by Shamir \cite{shamir2012open}. Furthermore, the derived algorithms are extended to solve regularized non-smooth learning problems in stochastic settings. {\color{blue}They can serve as an alternative to the most basic SGD especially in coping with machine learning problems, where an individual output is needed to guarantee the regularization structure while keeping an optimal rate of convergence.} Typically, our method is applicable as an efficient tool for solving large-scale $l_1$-regularized hinge-loss learning problems. Several real experiments demonstrate that the derived algorithms not only achieve optimal individual convergence rates but also guarantee better sparsity than the averaged solution.

scholarly journals Algoritma Elephant Herding Optimization: Permasalahan Multiple Constraints Knapsack 0-1

2018 ◽  
Vol 18 (1) ◽  
pp. 13
Author(s):  
Yulia Dewi Regita ◽  
Kiswara Agung Santoso ◽  
Ahmad Kamsyakawuni
Keyword(s):  
Knapsack Problem ◽  
Simplex Method ◽  
Optimization Problems ◽  
Optimal Solution ◽  
Secondary Data ◽  
Multiple Constraints ◽  
Microsoft Excel ◽  
Storage Media ◽  
Simulation Results ◽  
Selection Of

Optimization problems are often found in everyday life, such as when determining goods to be a limited storage media. This causes the need for the selection of goods in order to obtain profits with the requirements met. This problem in mathematics is usually called a knapsack. Knapsack problem itself has several variations, in this study knapsack type used is multiple constraints knapsack 0-1 which is solved using the Elephant Herding Optimization (EHO) algorithm. The aim of this study is to obtain an optimal solution and study the effectiveness of the algorithm comparing it to the Simplex method in Microsoft Excel. This study uses two data, consisting of primary and secondary data. Based on the results of parameter testing, the proven parameters are nClan, nCi,α,β and MaxGen have a significant effect. The final simulation results have also shown a comparison of the EHO algorithm with the Simplex method having a very small percentage deviation. This shows that the EHO algorithm is effective for completing optimization multiple constraints knapsack 0-1. Keywords: EHO Algorithm, Multiple Constraints Knapsack 0-1 Problem.

scholarly journals AN OVERVIEW OF SWARM INTELLIGENCE IN ARTIFICIAL INTELLIGENT SYSTEMS

2021 ◽  
Vol 9 (08) ◽  
pp. 673-675
Author(s):  
Kalpana C. Dalwai ◽  
Keyword(s):  
Information Processing ◽  
Problem Solving ◽  
Swarm Intelligence ◽  
Intelligent Systems ◽  
Optimization Problems ◽  
Artificial Intelligent

Swarm intelligence refers to a kind of problem-solving ability that emerges in the interactions of simple information-processing units. The concept of a swarm suggests multiplicity, stochasticity, randomness, and messiness. Advancement of technology has led to problems that are complex and more challenging.Swarm intelligence techniques were mostly developed for solving optimization problems.

scholarly journals Damage progression from impact in layered glass modeled with peridynamics

2012 ◽  
Vol 2 (4) ◽  
Author(s):  
Florin Bobaru ◽  
Youn Ha ◽  
Wenke Hu
Keyword(s):  
Spatial Resolution ◽  
Damage Evolution ◽  
Dynamic Interaction ◽  
Stress Waves ◽  
Three Dimensions ◽  
Contact Conditions ◽  
Peridynamic Model ◽  
Simulation Results ◽  
Simple Contact ◽  
Computational Resources

AbstractDynamic fracture in brittle materials has been difficult to model and predict. Interfaces, such as those present in multi-layered glass systems, further complicate this problem. In this paper we use a simplified peridynamic model of a multi-layer glass system to simulate damage evolution under impact with a high-velocity projectile. The simulation results are compared with results from recently published experiments. Many of the damage morphologies reported in the experiments are captured by the peridynamic results. Some finer details seen in experiments and not replicated by the computational model due to limitations in available computational resources that limited the spatial resolution of the model, and to the simple contact conditions between the layers instead of the polyurethane bonding used in the experiments. The peridynamic model uncovers a fascinating time-evolution of damage and the dynamic interaction between the stress waves, propagating cracks, interfaces, and bending deformations, in three-dimensions.

Comparisons of DES and LES Turbulent Model for Simulation of Surface Ship Airwake

2016 ◽  
Author(s):  
Congmin Li ◽  
Weijian Jiang ◽  
Jie Cheng ◽  
Zongxin Yu ◽  
Zhiguo Zhang
Keyword(s):  
Experimental Measurement ◽  
Measurement Data ◽  
Separated Flow ◽  
Flow Region ◽  
Turbulent Model ◽  
Ship Model ◽  
Surface Ship ◽  
Simulation Results ◽  
Turbulent Models ◽  
Computational Resources

Due to the combination of the forward speed and the prevailing wind for surface ship traveling in the ocean, the airflow passing over the ship’s superstructure causes the formation of a disturbed flow region and the large speed gradients of the mean wind over the flight deck, known as the ship airwake. This airwake would cause significant influence on the performance of the helicopter rotor during its taking off or landing, increase the operation workload of the pilot and even cause safe-landing issues, especially when the wind sweeps over the deck. This paper presents a numerical simulation of flow across the ship superstructure using DES and LES turbulent model. The ship model used for simulation is the standard SF2 surface ship model with experimental measurement data which could be used for the CFD code validation. The simulation results are compared with the experimental measurement data, and the comparison with experimental results shows good match for both DES and LES turbulent models. Simulation results show that a series of vortex had been generated after the flow separation with asymmetric characteristics. From upstream to downstream, the vortex intensity decreases, but suddenly increases after encountering the chimney. The comparison between DES and LES turbulent models shows the similar flow field and vortex structure around the ship superstructure with same grid sets. Both DES and LES are superior to RANS in solving ship airwake. The comparisons of DES and LES turbulent models show that DES can reflect the separated flow with limited computational resource and LES simulation could get higher resolution of the fluid flow structure with enough computational resources.

scholarly journals A PARALLEL SOLVER FOR THE DESIGN OF OIL FILTERS

2011 ◽  
Vol 16 (1) ◽  
pp. 326-341 ◽  
Author(s):  
Vadimas Starikovičius ◽  
Raimondas Čiegis ◽  
Oleg Iliev
Keyword(s):  
Automotive Industry ◽  
Optimization Problem ◽  
Optimization Problems ◽  
Geometry Optimization ◽  
Parallel Optimization ◽  
Parallel Solvers ◽  
Flow Through ◽  
And Performance ◽  
Easy Integration ◽  
Computational Resources

Nowadays, it is widely recognized that computer simulation plays a crucial role in designing oil filters used in the automotive industry. However, even a single direct simulation of the flow usually requires significant computational resources. Thus, it is obvious that solution of optimization problems is only feasible using parallel computers and algorithms.In this paper, we present a general master-slave parallel template, which was specially designed for the easy integration of direct parallel solvers into a parallel optimization tool. We show how an already existing direct solver for the 3D simulation of flow through the oil filter is integrated into our template to obtain a parallel optimization solver. Some capabilities and performance of this solver are demonstrated by solving geometry optimization problem of a filter element.

scholarly journals Projection Path Explorer: Exploring Visual Patterns in Projected Decision-making Paths

2021 ◽  
Vol 11 (3-4) ◽  
pp. 1-29
Author(s):  
Andreas Hinterreiter ◽  
Christian Steinparz ◽  
Moritz SchÖfl ◽  
Holger Stitz ◽  
Marc Streit
Keyword(s):  
Problem Solving ◽  
Optimization Problems ◽  
Initial Conditions ◽  
Dimensional Space ◽  
Dimensional Representation ◽  
Self Similarity ◽  
Solution Strategies ◽  
Network Training ◽  
Strategy Games ◽  
Lower Dimensional Space

In problem-solving, a path towards a solutions can be viewed as a sequence of decisions. The decisions, made by humans or computers, describe a trajectory through a high-dimensional representation space of the problem. By means of dimensionality reduction, these trajectories can be visualized in lower-dimensional space. Such embedded trajectories have previously been applied to a wide variety of data, but analysis has focused almost exclusively on the self-similarity of single trajectories. In contrast, we describe patterns emerging from drawing many trajectories—for different initial conditions, end states, and solution strategies—in the same embedding space. We argue that general statements about the problem-solving tasks and solving strategies can be made by interpreting these patterns. We explore and characterize such patterns in trajectories resulting from human and machine-made decisions in a variety of application domains: logic puzzles (Rubik’s cube), strategy games (chess), and optimization problems (neural network training). We also discuss the importance of suitably chosen representation spaces and similarity metrics for the embedding.

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