scholarly journals Single-based and Population-Based Metaheuristics Algorithms Performances in Solving NP-hard Problems

2021 ◽  
Author(s):  
Saman Almufti
Keyword(s):  
Real Life ◽  
Optimal Solution ◽  
Population Based ◽  
Performance Evaluations ◽  
Np Hard ◽  
Life Problems ◽  
Hard Problems ◽  
Optimum Solution ◽  
Over Time ◽  
Np Hard Problems

Metaheuristics is one of the most well-known field of researches uses to find optimum solution for Non-deterministic polynomial hard problems (NP-Hard), that are difficult to find an optimal solution in a polynomial time. Over time many algorithms have been developed based on the heuristics to solve difficult real-life problems, this paper will introduce Metaheuristic-based algorithms and its classifications, Non-deterministic polynomial hard problems. It also will compare the performance two metaheuristic-based algorithms (Elephant Herding optimization algorithm and Tabu Search) to solve Traveling Salesman Problem (TSP), which is one of the most known problem belongs to Non-deterministic polynomial hard problem and widely used in the performance evaluations for different metaheuristics-based optimization algorithms. the experimental results of the paper compare the results of EHO and TS for solving 10 different problems from the TSPLIB95.

Bio-Inspired Metaheuristics

2020 ◽  
Vol 10 (4) ◽  
pp. 1-18
Author(s):  
Rachid Kaleche ◽  
Zakaria Bendaoud ◽  
Karim Bouamrane
Keyword(s):  
Real Life ◽  
Optimal Solution ◽  
Np Hard ◽  
Exact Methods ◽  
Approximate Methods ◽  
Life Problems ◽  
Comprehensive Survey ◽  
Hard Problems ◽  
Exact And Approximate Methods ◽  
Np Hard Problems

In real life, problems becoming more complicated, among them NP-Hard problems. To resolve them, two families of methods exist, exact and approximate methods. When exact methods provide the optimal solution in an unacceptable amount of time, the approximate ones provide good solutions in a reasonable amount of time. Approximate methods are two kinds, heuristics and metaheuristics. The first ones are problem specific, while metaheuristics are independent from problems. A broad number of metaheuristics are inspired from nature, specially from biology. These bio-inspired metaheuristics are easy to implement and provide interesting results. This paper aims to provide a comprehensive survey of bio-inspired metaheuristics, their classification, principals, algorithms, their application domains, and a comparison between them.

scholarly journals Inverse Generalized Maximum Flow Problems

Mathematics ◽  
2019 ◽  
Vol 7 (10) ◽  
pp. 899 ◽  
Author(s):  
Javad Tayyebi ◽  
Adrian Deaconu
Keyword(s):  
Flow Problem ◽  
Natural Extension ◽  
Maximum Flow ◽  
Fast Method ◽  
Np Hard ◽  
Flow Problems ◽  
Maximum Flow Problem ◽  
Hard Problems ◽  
Optimum Solution ◽  
Np Hard Problems

A natural extension of maximum flow problems is called the generalized maximum flow problem taking into account the gain and loss factors for arcs. This paper investigates an inverse problem corresponding to this problem. It is to increase arc capacities as less cost as possible in a way that a prescribed flow becomes a maximum flow with respect to the modified capacities. The problem is referred to as the generalized maximum flow problem (IGMF). At first, we present a fast method that determines whether the problem is feasible or not. Then, we develop an algorithm to solve the problem under the max-type distances in O ( m n · log n ) time. Furthermore, we prove that the problem is strongly NP-hard under sum-type distances and propose a heuristic algorithm to find a near-optimum solution to these NP-hard problems. The computational experiments show the accuracy and the efficiency of the algorithm.

NP vs QMA_\log(2)

2010 ◽  
Vol 10 (1&2) ◽  
pp. 141-151
Author(s):  
S. Beigi
Keyword(s):  
Quantum Algorithms ◽  
Np Hard ◽  
Complete Problems ◽  
Hard Problems ◽  
Np Complete ◽  
Np Hard Problems

Although it is believed unlikely that $\NP$-hard problems admit efficient quantum algorithms, it has been shown that a quantum verifier can solve NP-complete problems given a "short" quantum proof; more precisely, NP\subseteq QMA_{\log}(2) where QMA_{\log}(2) denotes the class of quantum Merlin-Arthur games in which there are two unentangled provers who send two logarithmic size quantum witnesses to the verifier. The inclusion NP\subseteq QMA_{\log}(2) has been proved by Blier and Tapp by stating a quantum Merlin-Arthur protocol for 3-coloring with perfect completeness and gap 1/24n^6. Moreover, Aaronson et al. have shown the above inclusion with a constant gap by considering $\widetilde{O}(\sqrt{n})$ witnesses of logarithmic size. However, we still do not know if QMA_{\log}(2) with a constant gap contains NP. In this paper, we show that 3-SAT admits a QMA_{\log}(2) protocol with the gap 1/n^{3+\epsilon}} for every constant \epsilon>0.

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.

Social Insect Societies for the Optimization of Dynamic NP-Hard Problems

2011 ◽  
pp. 43-67 ◽  
Author(s):  
Stephan Hartmann ◽  
Pedro Pinto ◽  
Thomas Runkler ◽  
João Sousa
Keyword(s):  
Social Insect ◽  
Np Hard ◽  
Insect Societies ◽  
Hard Problems ◽  
Np Hard Problems

scholarly journals Scheduling two agents on a single machine: A parameterized analysis of NP-hard problems

Omega ◽  
2019 ◽  
Vol 83 ◽  
pp. 275-286 ◽  
Author(s):  
Danny Hermelin ◽  
Judith-Madeleine Kubitza ◽  
Dvir Shabtay ◽  
Nimrod Talmon ◽  
Gerhard J. Woeginger
Keyword(s):  
Single Machine ◽  
Np Hard ◽  
Two Agents ◽  
Hard Problems ◽  
Np Hard Problems
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