scholarly journals COMPLETENESS IN DIFFERENTIAL APPROXIMATION CLASSES

2005 ◽  
Vol 16 (06) ◽  
pp. 1267-1295 ◽  
Author(s):  
GIORGIO AUSIELLO ◽  
CRISTINA BAZGAN ◽  
MARC DEMANGE ◽  
VANGELIS TH. PASCHOS
Keyword(s):  
Approximation Algorithm ◽  
Optimization Problems ◽  
Differential Approximation ◽  
Np Optimization ◽  
Hard Problems ◽  
Approximation Classes

We study completeness in differential approximability classes. In differential approximation, the quality of an approximation algorithm is the measure of both how far is the solution computed from a worst one and how close is it to an optimal one. We define natural reductions preserving approximation and prove completeness results for the class of the NP optimization problems (class NPO), as well as for DAPX, the differential counterpart of APX, and for a natural subclass of DGLO, the differential counterpart of GLO. We also define class 0-APX of the NPO problems that are not differentially approximable within any ratio strictly greater than 0 unless P = NP. This class is very natural for differential approximation, although has no sense for the standard one. Finally, we prove the existence of hard problems for a subclass of DPTAS, the differential counterpart of PTAS.

Software suite for determining the tilts of tower-type structures according to terrestrial laser scanning

2020 ◽  
Vol 961 (7) ◽  
pp. 2-7
Author(s):  
A.V. Zubov ◽  
N.N. Eliseeva
Keyword(s):  
Laser Scanning ◽  
Optimization Problems ◽  
Optimization Methods ◽  
User Participation ◽  
Software Suite ◽  
Current State ◽  
Visual Basic For Applications ◽  
Operational Data ◽  
Theoretical Developments

The authors describe a software suite for determining tilt degrees of tower-type structures according to ground laser scanning indication. Defining the tilt of the pipe is carried out with a set of measured data through approximating the sections by circumferences. They are constructed using one of the simplest search engine optimization methods (evolutionary algorithm). Automatic filtering the scan of the current section from distorting data is performed by the method of assessing the quality of models constructed with that of least squares. The software was designed using Visual Basic for Applications. It contains several blocks (subprograms), with each of them performing a specific task. The developed complex enables obtaining operational data on the current state of the object with minimal user participation in the calculation process. The software suite is the result of practical implementing theoretical developments on the possibilities of using search methods at solving optimization problems in geodetic practice.

scholarly journals Multi-Task Optimization and Multi-Task Evolutionary Computation in the Past Five Years: A Brief Review

Mathematics ◽  
2021 ◽  
Vol 9 (8) ◽  
pp. 864
Author(s):  
Qingzheng Xu ◽  
Na Wang ◽  
Lei Wang ◽  
Wei Li ◽  
Qian Sun
Keyword(s):  
Evolutionary Computation ◽  
Explicit Knowledge ◽  
Optimization Problems ◽  
Effective Means ◽  
Typical Application ◽  
The Past ◽  
Current State ◽  
Evolution Algorithms ◽  
Application Fields

Traditional evolution algorithms tend to start the search from scratch. However, real-world problems seldom exist in isolation and humans effectively manage and execute multiple tasks at the same time. Inspired by this concept, the paradigm of multi-task evolutionary computation (MTEC) has recently emerged as an effective means of facilitating implicit or explicit knowledge transfer across optimization tasks, thereby potentially accelerating convergence and improving the quality of solutions for multi-task optimization problems. An increasing number of works have thus been proposed since 2016. The authors collect the abundant specialized literature related to this novel optimization paradigm that was published in the past five years. The quantity of papers, the nationality of authors, and the important professional publications are analyzed by a statistical method. As a survey on state-of-the-art of research on this topic, this review article covers basic concepts, theoretical foundation, basic implementation approaches of MTEC, related extension issues of MTEC, and typical application fields in science and engineering. In particular, several approaches of chromosome encoding and decoding, intro-population reproduction, inter-population reproduction, and evaluation and selection are reviewed when developing an effective MTEC algorithm. A number of open challenges to date, along with promising directions that can be undertaken to help move it forward in the future, are also discussed according to the current state. The principal purpose is to provide a comprehensive review and examination of MTEC for researchers in this community, as well as promote more practitioners working in the related fields to be involved in this fascinating territory.

scholarly journals ACO with Intuitionistic Fuzzy Pheromone Updating Applied on Multiple-Constraint Knapsack Problem

Mathematics ◽  
2021 ◽  
Vol 9 (13) ◽  
pp. 1456
Author(s):  
Stefka Fidanova ◽  
Krassimir Todorov Atanassov
Keyword(s):  
Decision Making ◽  
Knapsack Problem ◽  
Propositional Logic ◽  
Optimization Problems ◽  
Real Life ◽  
Combinatorial Optimization Problems ◽  
Intuitionistic Fuzzy ◽  
Life Problems ◽  
Multiple Constraint

Some of industrial and real life problems are difficult to be solved by traditional methods, because they need exponential number of calculations. As an example, we can mention decision-making problems. They can be defined as optimization problems. Ant Colony Optimization (ACO) is between the best methods, that solves combinatorial optimization problems. The method mimics behavior of the ants in the nature, when they look for a food. One of the algorithm parameters is called pheromone, and it is updated every iteration according quality of the achieved solutions. The intuitionistic fuzzy (propositional) logic was introduced as an extension of Zadeh’s fuzzy logic. In it, each proposition is estimated by two values: degree of validity and degree of non-validity. In this paper, we propose two variants of intuitionistic fuzzy pheromone updating. We apply our ideas on Multiple-Constraint Knapsack Problem (MKP) and compare achieved results with traditional ACO.

scholarly journals Nanolaser-based emulators of spin Hamiltonians

Nanophotonics ◽  
2020 ◽  
Vol 9 (13) ◽  
pp. 4193-4198 ◽  
Author(s):  
Midya Parto ◽  
William E. Hayenga ◽  
Alireza Marandi ◽  
Demetrios N. Christodoulides ◽  
Mercedeh Khajavikhan
Keyword(s):  
Large Scale ◽  
Optimization Problems ◽  
Exchange Interactions ◽  
Np Hard ◽  
Spin Models ◽  
Geometric Frustration ◽  
Spin Hamiltonians ◽  
Hard Problems ◽  
On Chip ◽  
Classical Spin Models

AbstractFinding the solution to a large category of optimization problems, known as the NP-hard class, requires an exponentially increasing solution time using conventional computers. Lately, there has been intense efforts to develop alternative computational methods capable of addressing such tasks. In this regard, spin Hamiltonians, which originally arose in describing exchange interactions in magnetic materials, have recently been pursued as a powerful computational tool. Along these lines, it has been shown that solving NP-hard problems can be effectively mapped into finding the ground state of certain types of classical spin models. Here, we show that arrays of metallic nanolasers provide an ultra-compact, on-chip platform capable of implementing spin models, including the classical Ising and XY Hamiltonians. Various regimes of behavior including ferromagnetic, antiferromagnetic, as well as geometric frustration are observed in these structures. Our work paves the way towards nanoscale spin-emulators that enable efficient modeling of large-scale complex networks.

scholarly journals Coupling Elephant Herding with Ordinal Optimization for Solving the Stochastic Inequality Constrained Optimization Problems

2020 ◽  
Vol 10 (6) ◽  
pp. 2075 ◽  
Author(s):  
Shih-Cheng Horng ◽  
Shieh-Shing Lin
Keyword(s):  
Optimization Problems ◽  
Solution Space ◽  
Inequality Constraints ◽  
Optimization Methods ◽  
Ordinal Optimization ◽  
Np Hard ◽  
Constrained Optimization Problems ◽  
Inequality Constrained Optimization ◽  
Hard Problems ◽  
Np Hard Problems

The stochastic inequality constrained optimization problems (SICOPs) consider the problems of optimizing an objective function involving stochastic inequality constraints. The SICOPs belong to a category of NP-hard problems in terms of computational complexity. The ordinal optimization (OO) method offers an efficient framework for solving NP-hard problems. Even though the OO method is helpful to solve NP-hard problems, the stochastic inequality constraints will drastically reduce the efficiency and competitiveness. In this paper, a heuristic method coupling elephant herding optimization (EHO) with ordinal optimization (OO), abbreviated as EHOO, is presented to solve the SICOPs with large solution space. The EHOO approach has three parts, which are metamodel construction, diversification and intensification. First, the regularized minimal-energy tensor-product splines is adopted as a metamodel to approximately evaluate fitness of a solution. Next, an improved elephant herding optimization is developed to find N significant solutions from the entire solution space. Finally, an accelerated optimal computing budget allocation is utilized to select a superb solution from the N significant solutions. The EHOO approach is tested on a one-period multi-skill call center for minimizing the staffing cost, which is formulated as a SICOP. Simulation results obtained by the EHOO are compared with three optimization methods. Experimental results demonstrate that the EHOO approach obtains a superb solution of higher quality as well as a higher computational efficiency than three optimization methods.

scholarly journals Utilizing Model Knowledge for Design Developed Genetic Algorithm to Solving Problem

2018 ◽  
Vol 3 (2) ◽  
pp. 172
Author(s):  
Hamidreza Salmani mojaveri
Keyword(s):  
Genetic Algorithm ◽  
Genetic Algorithms ◽  
Parallel Machines ◽  
Job Shop ◽  
Optimization Problems ◽  
Premature Convergence ◽  
Local Optimum ◽  
Scheduling Problems ◽  
Algorithm Implementation

One of the discussed topics in scheduling problems is Dynamic Flexible Job Shop with Parallel Machines (FDJSPM). Surveys show that this problem because of its concave and nonlinear nature usually has several local optimums. Some of the scheduling problems researchers think that genetic algorithms (GA) are appropriate approach to solve optimization problems of this kind. But researches show that one of the disadvantages of classical genetic algorithms is premature convergence and the probability of trap into the local optimum. Considering these facts, in present research, represented a developed genetic algorithm that its controlling parameters change during algorithm implementation and optimization process. This approach decreases the probability of premature convergence and trap into the local optimum. The several experiments were done show that the priority of proposed procedure of solving in field of the quality of obtained solution and convergence speed toward other present procedure.

scholarly journals An improved arithmetic optimization algorithm with forced switching mechanism for global optimization problems

2022 ◽  
Vol 19 (1) ◽  
pp. 473-512
Author(s):  
Rong Zheng ◽  
◽  
Heming Jia ◽  
Laith Abualigah ◽  
Qingxin Liu ◽  
...  
Keyword(s):  
Optimization Algorithm ◽  
Optimization Problems ◽  
Heuristic Method ◽  
Population Diversity ◽  
Test Functions ◽  
Design Problems ◽  
Local Optima ◽  
Switching Mechanism ◽  
Engineering Design Problems

<abstract> <p>Arithmetic optimization algorithm (AOA) is a newly proposed meta-heuristic method which is inspired by the arithmetic operators in mathematics. However, the AOA has the weaknesses of insufficient exploration capability and is likely to fall into local optima. To improve the searching quality of original AOA, this paper presents an improved AOA (IAOA) integrated with proposed forced switching mechanism (FSM). The enhanced algorithm uses the random math optimizer probability (<italic>RMOP</italic>) to increase the population diversity for better global search. And then the forced switching mechanism is introduced into the AOA to help the search agents jump out of the local optima. When the search agents cannot find better positions within a certain number of iterations, the proposed FSM will make them conduct the exploratory behavior. Thus the cases of being trapped into local optima can be avoided effectively. The proposed IAOA is extensively tested by twenty-three classical benchmark functions and ten CEC2020 test functions and compared with the AOA and other well-known optimization algorithms. The experimental results show that the proposed algorithm is superior to other comparative algorithms on most of the test functions. Furthermore, the test results of two training problems of multi-layer perceptron (MLP) and three classical engineering design problems also indicate that the proposed IAOA is highly effective when dealing with real-world problems.</p> </abstract>

scholarly journals Semidefinite Programming and Nash Equilibria in Bimatrix Games

2020 ◽  
Author(s):  
Amir Ali Ahmadi ◽  
Jeffrey Zhang
Keyword(s):  
Nash Equilibrium ◽  
Semidefinite Programming ◽  
Nash Equilibria ◽  
Valid Inequalities ◽  
Bimatrix Games ◽  
Competitive Game ◽  
Approximate Nash Equilibria ◽  
Hard Problems ◽  
Rank 2

We explore the power of semidefinite programming (SDP) for finding additive ɛ-approximate Nash equilibria in bimatrix games. We introduce an SDP relaxation for a quadratic programming formulation of the Nash equilibrium problem and provide a number of valid inequalities to improve the quality of the relaxation. If a rank-1 solution to this SDP is found, then an exact Nash equilibrium can be recovered. We show that, for a strictly competitive game, our SDP is guaranteed to return a rank-1 solution. We propose two algorithms based on the iterative linearization of smooth nonconvex objective functions whose global minima by design coincide with rank-1 solutions. Empirically, we demonstrate that these algorithms often recover solutions of rank at most 2 and ɛ close to zero. Furthermore, we prove that if a rank-2 solution to our SDP is found, then a [Formula: see text]-Nash equilibrium can be recovered for any game, or a [Formula: see text]-Nash equilibrium for a symmetric game. We then show how our SDP approach can address two (NP-hard) problems of economic interest: finding the maximum welfare achievable under any Nash equilibrium, and testing whether there exists a Nash equilibrium where a particular set of strategies is not played. Finally, we show the connection between our SDP and the first level of the Lasserre/sum of squares hierarchy.

The Application of Fuzzification for Solving Quadratic Functions

2021 ◽  
Author(s):  
Lunshan Gao
Keyword(s):  
Approximate Solution ◽  
Approximation Algorithm ◽  
Critical Point ◽  
Numerical Experiments ◽  
Optimization Problems ◽  
Local Minimizer ◽  
Quadratic Functions ◽  
Computational Time ◽  
Computational Results ◽  
Average Computational Time

Abstract This paper describes an approximation algorithm for solving standard quadratic optimization problems(StQPs) over the standard simplex by using fuzzification technique. We show that the approximate solution of the algorithm is an epsilon -critical point and satisfies epsilon-delta condition. The algorithm is compared with IBM ILOG CPLEX (short for CPLEX). The computational results indicate that the new algorithm is faster than CPLEX. Especially for infeasible problems. Furthermore, we calculate 100 instances for different size StQP problems. The numerical experiments show that the average computational time of the new algorithm for calculating the first local minimizer is in BigO(n) when the size of the problems is less or equal to 450.

A multi-objective evolutionary algorithm based on niche selection in solving irregular Pareto fronts

2021 ◽  
pp. 1-21
Author(s):  
Xin Li ◽  
Xiaoli Li ◽  
Kang Wang
Keyword(s):  
Evolutionary Algorithm ◽  
Optimization Problems ◽  
Optimal Solution ◽  
Benchmark Problems ◽  
Multi Objective Optimization ◽  
Multi Objective ◽  
Environmental Selection ◽  
Optimal Solution Set ◽  
Pareto Fronts

The key characteristic of multi-objective evolutionary algorithm is that it can find a good approximate multi-objective optimal solution set when solving multi-objective optimization problems(MOPs). However, most multi-objective evolutionary algorithms perform well on regular multi-objective optimization problems, but their performance on irregular fronts deteriorates. In order to remedy this issue, this paper studies the existing algorithms and proposes a multi-objective evolutionary based on niche selection to deal with irregular Pareto fronts. In this paper, the crowding degree is calculated by the niche method in the process of selecting parents when the non-dominated solutions converge to the first front, which improves the the quality of offspring solutions and which is beneficial to local search. In addition, niche selection is adopted into the process of environmental selection through considering the number and the location of the individuals in its niche radius, which improve the diversity of population. Finally, experimental results on 23 benchmark problems including MaF and IMOP show that the proposed algorithm exhibits better performance than the compared MOEAs.

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