scholarly journals A MILP Model for a Byzantine Fault Tolerant Blockchain Consensus

2020 ◽  
Vol 12 (11) ◽  
pp. 185
Author(s):  
Vitor Nazário Coelho ◽  
Rodolfo Pereira Araújo ◽  
Haroldo Gambini Santos ◽  
Wang Yong Qiang ◽  
Igor Machado Coelho
Keyword(s):  
Optimization Problems ◽  
Programming Model ◽  
Fault Tolerant ◽  
State Of The Art ◽  
Mixed Integer ◽  
Maximization Problem ◽  
Objective Functions ◽  
Objective Model ◽  
Adversarial Model ◽  
Algebraic Proofs

Mixed-integer mathematical programming has been widely used to model and solve challenging optimization problems. One interesting feature of this technique is the ability to prove the optimality of the achieved solution, for many practical scenarios where a linear programming model can be devised. This paper explores its use to model very strong Byzantine adversaries, in the context of distributed consensus systems. In particular, we apply the proposed technique to find challenging adversarial conditions on a state-of-the-art blockchain consensus: the Neo dBFT. Neo Blockchain has been using the dBFT algorithm since its foundation, but, due to the complexity of the algorithm, it is challenging to devise definitive algebraic proofs that guarantee safety/liveness of the system (and adjust for every change proposed by the community). Core developers have to manually devise and explore possible adversarial attacks scenarios as an exhaustive task. The proposed multi-objective model is intended to assist the search of possible faulty scenario, which includes three objective functions that can be combined as a maximization problem for testing one-block finality or a minimization problem for ensuring liveness. Automated graphics help developers to visually observe attack conditions and to quickly find a solution. This paper proposes an exact adversarial model that explores current limits for practical blockchain consensus applications such as dBFT, with ideas that can also be extended to other decentralized ledger technologies.

Data-Driven Optimization of Reward-Risk Ratio Measures

2020 ◽  
Author(s):  
Ran Ji ◽  
Miguel A. Lejeune
Keyword(s):  
Optimization Problems ◽  
State Of The Art ◽  
Convergence Property ◽  
Computational Study ◽  
Data Driven ◽  
Mixed Integer ◽  
Finite Convergence ◽  
Integer Nonlinear Programming ◽  
Distributionally Robust ◽  
Risk Ratios

We investigate a class of fractional distributionally robust optimization problems with uncertain probabilities. They consist in the maximization of ambiguous fractional functions representing reward-risk ratios and have a semi-infinite programming epigraphic formulation. We derive a new fully parameterized closed-form to compute a new bound on the size of the Wasserstein ambiguity ball. We design a data-driven reformulation and solution framework. The reformulation phase involves the derivation of the support function of the ambiguity set and the concave conjugate of the ratio function. We design modular bisection algorithms which enjoy the finite convergence property. This class of problems has wide applicability in finance, and we specify new ambiguous portfolio optimization models for the Sharpe and Omega ratios. The computational study shows the applicability and scalability of the framework to solve quickly large, industry-relevant-size problems, which cannot be solved in one day with state-of-the-art mixed-integer nonlinear programming (MINLP) solvers.

A Memetic Optimization Strategy Based on Dimension Reduction in Decision Space

2015 ◽  
Vol 23 (1) ◽  
pp. 69-100 ◽  
Author(s):  
Handing Wang ◽  
Licheng Jiao ◽  
Ronghua Shang ◽  
Shan He ◽  
Fang Liu
Keyword(s):  
Dimension Reduction ◽  
Optimization Problems ◽  
State Of The Art ◽  
Search Space ◽  
Optimization Strategy ◽  
Objective Functions ◽  
Multi Objective Optimization ◽  
Decision Space ◽  
Multi Objective ◽  
Decision Variables

There can be a complicated mapping relation between decision variables and objective functions in multi-objective optimization problems (MOPs). It is uncommon that decision variables influence objective functions equally. Decision variables act differently in different objective functions. Hence, often, the mapping relation is unbalanced, which causes some redundancy during the search in a decision space. In response to this scenario, we propose a novel memetic (multi-objective) optimization strategy based on dimension reduction in decision space (DRMOS). DRMOS firstly analyzes the mapping relation between decision variables and objective functions. Then, it reduces the dimension of the search space by dividing the decision space into several subspaces according to the obtained relation. Finally, it improves the population by the memetic local search strategies in these decision subspaces separately. Further, DRMOS has good portability to other multi-objective evolutionary algorithms (MOEAs); that is, it is easily compatible with existing MOEAs. In order to evaluate its performance, we embed DRMOS in several state of the art MOEAs to facilitate our experiments. The results show that DRMOS has the advantage in terms of convergence speed, diversity maintenance, and portability when solving MOPs with an unbalanced mapping relation between decision variables and objective functions.

A Multi-Objective Model for Taiwan Notebook Computer Distribution Problem

2006 ◽  
pp. 171-182
Author(s):  
Ling-Lang Tang ◽  
Yei-Chun Kuo ◽  
E. Stanley Lee
Keyword(s):  
Customer Service ◽  
Mixed Integer Linear Programming ◽  
Programming Model ◽  
Performance Criteria ◽  
Mixed Integer ◽  
Analytic Hierarchy ◽  
Multi Objective ◽  
Notebook Computer ◽  
Objective Model ◽  
Hierarchy Process

A multi-objective model of global distribution for the Taiwan notebook computer industry is proposed. The proposed two-stage approach involves a mixed integer linear programming model and the fuzzy analytic hierarchy process (AHP) approach. The analytic method provides quantitative assessment of the relationships between manufacturers and customer service. To show the effectiveness of the proposed approach, a Taiwan notebook computer model is solved. The results of this multi-objective model show some dynamic characteristics among various performance criteria of the outbound logistics.

A Smart Structural Algorithm (SSA) Based on Infeasible Region to Solve Mixed Integer Problems

2017 ◽  
Vol 8 (1) ◽  
pp. 24-44 ◽  
Author(s):  
Mohammad Hassan Salmani ◽  
Kourosh Eshghi
Keyword(s):  
Heuristic Algorithm ◽  
Feasible Solution ◽  
Heuristic Algorithms ◽  
Optimization Problems ◽  
Mixed Integer ◽  
Feasible Region ◽  
Limited Area ◽  
Objective Functions ◽  
Fields Of Study ◽  
Best Value

Optimization is an important fields of study in science where researchers seek to make the best and most practical decisions. Solving real optimization problems is an intractable issue which calls for generating an approximate using meta-heuristic algorithms. This study proposes a meta-heuristic algorithm which mainly searches the infeasible region. In this approach, the authors start from an infeasible solution, and while they try to get near to the feasible region, they ensure that the best value is kept for the objective function. The algorithm examines the space in such terms as Infeasibility and Objective Functions, Neighborhood Limited Area, Random Smart Points, and the calculation of new solutions. The algorithm can convert an infeasible solution to an appropriate corresponding feasible solution by applying a simple mathematical methodology. Finally, to test the efficiency of our algorithm, a sample random MIP problem and a hard benchmark TSP instance are solved and discussed in detail.

scholarly journals A State-of-the-Art Review of the Sensor Location, Flow Observability, Estimation, and Prediction Problems in Traffic Networks

2015 ◽  
Vol 2015 ◽  
pp. 1-26 ◽  
Author(s):  
Enrique Castillo ◽  
Zacarías Grande ◽  
Aida Calviño ◽  
W. Y. Szeto ◽  
Hong K. Lo
Keyword(s):  
Relative Error ◽  
Optimization Problems ◽  
State Of The Art ◽  
Mathematical Optimization ◽  
Integrated Approach ◽  
Specific Model ◽  
Traffic Networks ◽  
Objective Functions ◽  
Estimation And Prediction ◽  
Prediction Problems

A state-of-the-art review of flow observability, estimation, and prediction problems in traffic networks is performed. Since mathematical optimization provides a general framework for all of them, an integrated approach is used to perform the analysis of these problems and consider them as different optimization problems whose data, variables, constraints, and objective functions are the main elements that characterize the problems proposed by different authors. For example, counted, scanned or “a priori” data are the most common data sources; conservation laws, flow nonnegativity, link capacity, flow definition, observation, flow propagation, and specific model requirements form the most common constraints; and least squares, likelihood, possible relative error, mean absolute relative error, and so forth constitute the bases for the objective functions or metrics. The high number of possible combinations of these elements justifies the existence of a wide collection of methods for analyzing static and dynamic situations.

scholarly journals A Hybrid Method for Modeling and Solving Supply Chain Optimization Problems with Soft and Logical Constraints

2016 ◽  
Vol 2016 ◽  
pp. 1-16 ◽  
Author(s):  
Paweł Sitek ◽  
Krzysztof Bzdyra ◽  
Jarosław Wikarek
Keyword(s):  
Supply Chain ◽  
Hybrid Method ◽  
Optimization Problems ◽  
Programming Model ◽  
Combinatorial Problem ◽  
Search Space ◽  
Mixed Integer ◽  
Optimization Models ◽  
Supply Chain Optimization ◽  
Logical Constraints

This paper presents a hybrid method for modeling and solving supply chain optimization problems with soft, hard, and logical constraints. Ability to implement soft and logical constraints is a very important functionality for supply chain optimization models. Such constraints are particularly useful for modeling problems resulting from commercial agreements, contracts, competition, technology, safety, and environmental conditions. Two programming and solving environments, mathematical programming (MP) and constraint logic programming (CLP), were combined in the hybrid method. This integration, hybridization, and the adequate multidimensional transformation of the problem (as a presolving method) helped to substantially reduce the search space of combinatorial models for supply chain optimization problems. The operation research MP and declarative CLP, where constraints are modeled in different ways and different solving procedures are implemented, were linked together to use the strengths of both. This approach is particularly important for the decision and combinatorial optimization models with the objective function and constraints, there are many decision variables, and these are summed (common in manufacturing, supply chain management, project management, and logistic problems). TheECLiPSesystem with Eplex library was proposed to implement a hybrid method. Additionally, the proposed hybrid transformed model is compared with the MILP-Mixed Integer Linear Programming model on the same data instances. For illustrative models, its use allowed finding optimal solutions eight to one hundred times faster and reducing the size of the combinatorial problem to a significant extent.

scholarly journals Modeling and Formulation of Optimization Problems for Optimal Scheduling of Multi-Generation and Hybrid Energy Systems: Review and Recommendations

Electronics ◽  
2021 ◽  
Vol 10 (14) ◽  
pp. 1688
Author(s):  
Sheroze Liaquat ◽  
Muhammad Fahad Zia ◽  
Mohamed Benbouzid
Keyword(s):  
Energy Source ◽  
Optimization Problems ◽  
State Of The Art ◽  
Photovoltaic System ◽  
Energy Sources ◽  
Thermal Source ◽  
Objective Functions ◽  
Hybrid Energy ◽  
Different Types ◽  
Optimization Function

Increasing power demands require multiple generating units interconnected with each other to maintain the power balance of the system. This results in a highly dense power system consisting of multiple generating units which coordinate with each other to maintain the balanced performance of the system. Among different energy sources, the thermal source, the hydro energy source, the photovoltaic system, and the wind energy source are the most popular ones. Researchers have developed several optimization problems in the literature known as dispatch problems to model the system consisting of these different types of energy sources. The constraints for each system depend upon the generation type and the nature of the objective functions involved. This paper provides a state-of-the-art review of different dispatch problems and the nature of the objective functions involved in them and highlights the major constraints associated with each optimization function.

scholarly journals Adaptive Plant Propagation Algorithm for Solving Economic Load Dispatch Problem

2017 ◽  
Author(s):  
Sayan Nag
Keyword(s):  
Optimization Problems ◽  
State Of The Art ◽  
Economic Load Dispatch ◽  
Objective Functions ◽  
Plant Propagation ◽  
Propagation Algorithm ◽  
Highly Nonlinear ◽  
Plant Intelligence ◽  
Classical Optimization

Optimization problems in design engineering are complex by nature, often because of the involvement of critical objective functions accompanied by a number of rigid constraints associated with the products involved. One such problem is Economic Load Dispatch (ED) problem which focuses on the optimization of the fuel cost while satisfying some system constraints. Classical optimization algorithms are not sufficient and also inefficient for the ED problem involving highly nonlinear, and non-convex functions both in the objective and in the constraints. This led to the development of metaheuristic optimization approaches which can solve the ED problem almost efficiently. This paper presents a novel robust plant intelligence based Adaptive Plant Propagation Algorithm (APPA) which is used to solve the classical ED problem. The application of the proposed method to the 3-generator and 6-generator systems shows the efficiency and robustness of the proposed algorithm. A comparative study with another state-of-the-art algorithm (APSO) demonstrates the quality of the solution achieved by the proposed method along with the convergence characteristics of the proposed approach.

scholarly journals Network Models for Multiobjective Discrete Optimization

2021 ◽  
Author(s):  
David Bergman ◽  
Merve Bodur ◽  
Carlos Cardonha ◽  
Andre A. Cire
Keyword(s):  
Shortest Path ◽  
Discrete Optimization ◽  
Optimization Problems ◽  
State Of The Art ◽  
Pareto Frontier ◽  
Network Models ◽  
Set Covering ◽  
Objective Functions ◽  
Nondominated Solutions ◽  
Discrete Optimization Problems

This paper provides a novel framework for solving multiobjective discrete optimization problems with an arbitrary number of objectives. Our framework represents these problems as network models, in that enumerating the Pareto frontier amounts to solving a multicriteria shortest-path problem in an auxiliary network. We design techniques for exploiting network models in order to accelerate the identification of the Pareto frontier, most notably a number of operations to simplify the network by removing nodes and arcs while preserving the set of nondominated solutions. We show that the proposed framework yields orders-of-magnitude performance improvements over existing state-of-the-art algorithms on five problem classes containing both linear and nonlinear objective functions. Summary of Contribution: Multiobjective optimization has a long history of research with applications in several domains. Our paper provides an alternative modeling and solution approach for multiobjective discrete optimization problems by leveraging graphical structures. Specifically, we encode the decision space of a problem as a layered network and propose graph reduction operators to preserve only solutions whose image are part of the Pareto frontier. The nondominated solutions can then be extracted through shortest-path algorithms on such a network. Numerical results comparing our method with state-of-the-art approaches on several problem classes, including the knapsack, set covering, and the traveling salesperson problem (TSP), suggest orders-of-magnitude runtime speed-ups for exactly enumerating the Pareto frontier, especially when the number of objective functions grows.

scholarly journals An Efficient Framework for Multi-Objective Risk-Informed Decision Support Systems for Drainage Rehabilitation

2020 ◽  
Vol 25 (4) ◽  
pp. 73
Author(s):  
Xiatong Cai ◽  
Abdolmajid Mohammadian ◽  
Hamidreza Shirkhani
Keyword(s):  
Optimization Problems ◽  
Drainage System ◽  
Mixed Integer ◽  
Engineering Optimization ◽  
Continuous Variables ◽  
Objective Functions ◽  
Multi Objective Optimization ◽  
Integer Optimization ◽  
Framework Structure ◽  
Multi Objective

Combining multiple modules into one framework is a key step in modelling a complex system. In this study, rather than focusing on modifying a specific model, we studied the performance of different calculation structures in a multi-objective optimization framework. The Hydraulic and Risk Combined Model (HRCM) combines hydraulic performance and pipe breaking risk in a drainage system to provide optimal rehabilitation strategies. We evaluated different framework structures for the HRCM model. The results showed that the conventional framework structure used in engineering optimization research, which includes (1) constraint functions; (2) objective functions; and (3) multi-objective optimization, is inefficient for drainage rehabilitation problem. It was shown that the conventional framework can be significantly improved in terms of calculation speed and cost-effectiveness by removing the constraint function and adding more objective functions. The results indicated that the model performance improved remarkably, while the calculation speed was not changed substantially. In addition, we found that the mixed-integer optimization can decrease the optimization performance compared to using continuous variables and adding a post-processing module at the last stage to remove the unsatisfying results. This study (i) highlights the importance of the framework structure inefficiently solving engineering problems, and (ii) provides a simplified efficient framework for engineering optimization problems.

Sign in / Sign up

Export Citation Format

Share Document