Solution of “Hard” Knapsack Instances Using Quantum Inspired Evolutionary Algorithm

2014 ◽  
Vol 5 (1) ◽  
pp. 52-68 ◽  
Author(s):  
C. Patvardhan ◽  
Sulabh Bansal ◽  
Anand Srivastav
Keyword(s):  
Evolutionary Algorithm ◽  
Exact Algorithm ◽  
Population Based ◽  
Exact Algorithms ◽  
Programming Technique ◽  
Worst Case ◽  
Problem Instances ◽  
Population Based Search ◽  
Made In

Knapsack Problem (KP) is a popular combinatorial optimization problem having application in many technical and economic areas. Several attempts have been made in past to solve the problem. Various exact and non-exact approaches exist to solve KP. Exact algorithms for KP are based on either branch and bound or dynamic programming technique. Heuristics exist which solve KP non-exactly in lesser time. Heuristic approaches do not provide any guarantee regarding the quality of solution whereas exact approaches have high worst case complexities. Quantum-inspired Evolutionary Algorithm (QEA) is a subclass of Evolutionary Algorithm, a naturally inspired population based search technique. QEA uses concepts of quantum computing. An engineered Quantum-inspired Evolutionary Algorithm (QEA-E), an improved version of QEA, is presented which quickly solves extremely large spanner problem instances (e.g. 290,000 items) that are very difficult for the state of the art exact algorithm as well as the original QEA.

Solution of “Hard” Knapsack Instances Using Quantum Inspired Evolutionary Algorithm

2015 ◽  
pp. 1108-1124
Author(s):  
C. Patvardhan ◽  
Sulabh Bansal ◽  
Anand Srivastav
Keyword(s):  
Evolutionary Algorithm ◽  
Exact Algorithm ◽  
Population Based ◽  
Exact Algorithms ◽  
Combinatorial Optimization Problem ◽  
Programming Technique ◽  
Worst Case ◽  
Problem Instances ◽  
Population Based Search

Knapsack Problem (KP) is a popular combinatorial optimization problem having application in many technical and economic areas. Several attempts have been made in past to solve the problem. Various exact and non-exact approaches exist to solve KP. Exact algorithms for KP are based on either branch and bound or dynamic programming technique. Heuristics exist which solve KP non-exactly in lesser time. Heuristic approaches do not provide any guarantee regarding the quality of solution whereas exact approaches have high worst case complexities. Quantum-inspired Evolutionary Algorithm (QEA) is a subclass of Evolutionary Algorithm, a naturally inspired population based search technique. QEA uses concepts of quantum computing. An engineered Quantum-inspired Evolutionary Algorithm (QEA-E), an improved version of QEA, is presented which quickly solves extremely large spanner problem instances (e.g. 290,000 items) that are very difficult for the state of the art exact algorithm as well as the original QEA.

Hybrid Evolutionary Optimization of Two-Stage Stochastic Integer Programming Problems: An Empirical Investigation

2009 ◽  
Vol 17 (4) ◽  
pp. 511-526 ◽  
Author(s):  
Thomas Tometzki ◽  
Sebastian Engell
Keyword(s):  
Evolutionary Algorithm ◽  
Empirical Investigation ◽  
Scale Up ◽  
Exact Algorithm ◽  
Integer Program ◽  
Mixed Integer ◽  
Two Stage ◽  
Integer Programming Problems ◽  
Problem Instances ◽  
Feasible Solutions

In this contribution, we consider decision problems on a moving horizon with significant uncertainties in parameters. The information and decision structure on moving horizons enables recourse actions which correct the here-and-now decisions whenever the horizon is moved a step forward. This situation is reflected by a mixed-integer recourse model with a finite number of uncertainty scenarios in the form of a two-stage stochastic integer program. A stage decomposition-based hybrid evolutionary algorithm for two-stage stochastic integer programs is proposed that employs an evolutionary algorithm to determine the here-and-now decisions and a standard mathematical programming method to optimize the recourse decisions. An empirical investigation of the scale-up behavior of the algorithms with respect to the number of scenarios exhibits that the new hybrid algorithm generates good feasible solutions more quickly than a state of the art exact algorithm for problem instances with a high number of scenarios.

scholarly journals Dynastic Potential Crossover Operator

2021 ◽  
pp. 1-35
Author(s):  
Francisco Chicano ◽  
Gabriela Ochoa ◽  
L. Darrell Whitley ◽  
Renato Tinós
Keyword(s):  
Polynomial Time ◽  
Population Based ◽  
Combinatorial Problems ◽  
Crossover Operator ◽  
Empirical Comparison ◽  
Worst Case ◽  
Optimal Recombination ◽  
Max Sat ◽  
Variable Interaction

Abstract An optimal recombination operator for two parent solutions provides the best solution among those that take the value for each variable from one of the parents (gene transmission property). If the solutions are bit strings, the offspring of an optimal recombination operator is optimal in the smallest hyperplane containing the two parent solutions. Exploring this hyperplane is computationally costly, in general, requiring exponential time in the worst case. However, when the variable interaction graph of the objective function is sparse, exploration can be done in polynomial time. In this paper, we present a recombination operator, called Dynastic Potential Crossover (DPX), that runs in polynomial time and behaves like an optimal recombination operator for low-epistasis combinatorial problems. We compare this operator, both theoretically and experimentally, with traditional crossover operators, like uniform crossover and network crossover, and with two recently defined efficient recombination operators: partition crossover and articulation points partition crossover. The empirical comparison uses NKQ Landscapes and MAX-SAT instances. DPX outperforms the other crossover operators in terms of quality of the offspring and provides better results included in a trajectory and a population-based metaheuristic, but it requires more time and memory to compute the offspring.

New algorithms for pattern matching with wildcards and length constraints

2015 ◽  
Vol 07 (03) ◽  
pp. 1550032 ◽  
Author(s):  
Abdullah N. Arslan ◽  
Betsy George ◽  
Kirsten Stor
Keyword(s):  
Pattern Matching ◽  
Polynomial Time ◽  
Original Problem ◽  
Heuristic Algorithms ◽  
Optimal Solution ◽  
Exact Algorithm ◽  
Exact Algorithms ◽  
Worst Case ◽  
Special Cases ◽  
New Algorithms

The pattern matching with wildcards and length constraints problem is an interesting problem in the literature whose computational complexity is still open. There are polynomial time exact algorithms for its special cases. There are heuristic algorithms, and online algorithms that do not guarantee an optimal solution to the original problem. We consider two special cases of the problem for which we develop offline solutions. We give an algorithm for one case with provably better worst case time complexity compared to existing algorithms. We present the first exact algorithm for the second case. This algorithm uses integer linear programming (ILP) and it takes polynomial time under certain conditions.

scholarly journals The Static Bike Sharing Rebalancing Problem with Forbidden Temporary Operations

2019 ◽  
Vol 53 (3) ◽  
pp. 882-896 ◽  
Author(s):  
Bruno P. Bruck ◽  
Fábio Cruz ◽  
Manuel Iori ◽  
Anand Subramanian
Keyword(s):  
Minimum Cost ◽  
Exact Algorithm ◽  
Exact Algorithms ◽  
Worst Case Analysis ◽  
Worst Case ◽  
Online Appendix ◽  
Bike Sharing ◽  
Courier Service ◽  
Demand And Capacity ◽  
Theoretical Results

This paper introduces and solves the static bike rebalancing problem with forbidden temporary operations. In this problem, one aims at finding a minimum cost route in which a vehicle performs a series of pickup and delivery operations while satisfying demand and capacity constraints. In addition, a vehicle can visit stations multiple times but cannot use them to temporarily store or provide bikes. Apart from bike rebalancing, the problem also models courier service transportation and repositioning of inventory between retail stores, where temporary operations are frequently disliked because they require additional manual work and service time. We present some theoretical results concerning problem complexity and worst-case analysis, and then propose three exact algorithms based on different mathematical formulations. Extensive computational results on instances involving up to 80 stations show that an exact algorithm based on a minimal extended network produces the best average results. The online appendix is available at https://doi.org/10.1287/trsc.2018.0859 .

Probabilistic quality estimations for combinatorial optimization problems

2018 ◽  
Vol 25 (1) ◽  
pp. 123-134 ◽  
Author(s):  
Nodari Vakhania
Keyword(s):  
Time Complexity ◽  
Case Analysis ◽  
Performance Measure ◽  
Accurate Estimation ◽  
Average Case Analysis ◽  
Worst Case ◽  
Average Case ◽  
Probabilistic Average ◽  
Problem Instances

AbstractThe computational complexity of an algorithm is traditionally measured for the worst and the average case. The worst-case estimation guarantees a certain worst-case behavior of a given algorithm, although it might be rough, since in “most instances” the algorithm may have a significantly better performance. The probabilistic average-case analysis claims to derive an average performance of an algorithm, say, for an “average instance” of the problem in question. That instance may be far away from the average of the problem instances arising in a given real-life application, and so the average case analysis would also provide a non-realistic estimation. We suggest that, in general, a wider use of probabilistic models for a more accurate estimation of the algorithm efficiency could be possible. For instance, the quality of the solutions delivered by an approximation algorithm may also be estimated in the “average” probabilistic case. Such an approach would deal with the estimation of the quality of the solutions delivered by the algorithm for the most common (for a given application) problem instances. As we illustrate, the probabilistic modeling can also be used to derive an accurate time complexity performance measure, distinct from the traditional probabilistic average-case time complexity measure. Such an approach could, in particular, be useful when the traditional average-case estimation is still rough or is not possible at all.

SCHEDULING FLEXIBLE JOB-SHOPS: A WORST CASE ANALYSIS AND AN EVOLUTIONARY ALGORITHM

2003 ◽  
Vol 03 (04) ◽  
pp. 437-452 ◽  
Author(s):  
IMED KACEM
Keyword(s):  
Evolutionary Algorithm ◽  
Job Shop ◽  
Job Shop Scheduling ◽  
Heuristic Method ◽  
Case Analysis ◽  
Worst Case Analysis ◽  
Job Shops ◽  
Flexible Job Shop Scheduling ◽  
Worst Case

In this paper, we deal with the flexible job shop scheduling problem. We propose an efficient heuristic method for solving the assignment problem. Indeed, we propose a worst case analysis to evaluate the performance of such a heuristic. The second specificity of the problem studied is the sequencing property. Our approach consists in the application of an evolutionary algorithm based on a set of adapted operators to solve the sequencing step. Some lower bounds for the problem (previously proposed in Ref. 1) will be used in order to evaluate the quality of our method and the solutions according to the different criteria.

Assessing the quality of public health in the Russian Federation and Israel: Main problems and solutions

2020 ◽  
Vol 19 (4) ◽  
pp. 618-632
Author(s):  
A.S. Panchenko
Keyword(s):  
Public Health ◽  
Russian Federation ◽  
Population Based ◽  
The Public ◽  
Disability Adjusted Life ◽  
Problems And Solutions ◽  
The Russian Federation ◽  
Disability Adjusted Life Year ◽  
Practical Recommendations

Subject. The article addresses the public health in the Russian Federation and Israel. Objectives. The focus is on researching the state of public health in Russia and Israel, using the Global Burden of Disease (GBD) project methodology, identifying problem areas and searching for possible ways to improve the quality of health of the Russian population based on the experience of Israel. Methods. The study draws on the ideology of the GBD project, which is based on the Disability-Adjusted Life-Year (DALY) metric. Results. The paper reveals the main causes of DALY losses and important risk factors for cancer for Russia and Israel. The findings show that the total DALY losses for Russia exceed Israeli values. The same is true for cancer diseases. Conclusions. Activities in Israel aimed at improving the quality of public health, the effectiveness of which has been proven, can serve as practical recommendations for Russia. The method of analysis, using the ideology of the GBD project, can be used as a tool for quantitative and comparative assessment of the public health.

Reuse of Sludge from Pulp and Paper Industry Pilot and Full Scale Applications

1993 ◽  
Vol 28 (2) ◽  
pp. 17-26 ◽  
Author(s):  
V. Eroǧlu ◽  
A. M. Saatçi
Keyword(s):  
Economic Analysis ◽  
Paper Industry ◽  
Pulp And Paper Industry ◽  
Pulp And Paper ◽  
Full Scale ◽  
Primary Sludge ◽  
Recent Advances ◽  
Made In

Recent advances made in the reuse of pulp and paper industry sludges in hardboard production are explained. Data obtained from pilot and full-scale plants using primary sludge of a pulp and paper industry as an additive in the production of hardboard is presented. An economic analysis of the reuse of pulp and paper primary sludge in hardboard manufacturing is given. The quality of the hardboard produced is tested and compared with the qualities of the hardboard produced by the same plant before the addition of primary sludge. The hardboard with primary sludge additive has been used in Turkey for about a year in the manufacturing of office and home furniture. The results are very satisfactory when the primary sludge is used at 1/4 ratio.

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