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.

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.

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.

scholarly journals Population-based rapid assessment of avoidable blindness survey in Sohag governorate in Egypt

BMJ Open ◽  
2020 ◽  
Vol 10 (10) ◽  
pp. e036337
Author(s):  
Heba AlSawahli ◽  
Ian McCormick ◽  
Caleb D Mpyet ◽  
Gamal Ezzelarab ◽  
Mohammad Shalaby
Keyword(s):  
Cataract Surgery ◽  
Census Data ◽  
Rapid Assessment ◽  
Population Based ◽  
Vision Impairment ◽  
Health System Strengthening ◽  
Secondary Outcome ◽  
Institutional Setting ◽  
Financial Barriers

ObjectivesTo determine the prevalence and causes of blindness and vision impairment, and the coverage and quality of cataract surgical services, among population aged 50 years and older in Sohag governorate in Egypt.DesignA population-based cross-sectional survey using two-stage cluster random sampling following the rapid assessment of avoidable blindness methodology.SettingA community-based survey conducted by six teams of ophthalmologists, assistants and local guides. Enrolment and examination were door-to-door in selected clusters.ParticipantsUsing 2016 census data, 68 population units were randomly selected as clusters (of 60 people) with probability proportionate to population size. Anyone aged 50 years and older, residing in a non-institutional setting in a cluster for at least 6 months, was eligible to participate.Primary and secondary outcome measuresThe prevalence and causes of blindness and vision impairment. Secondary outcomes were CSC and effectiveness and participant-reported barriers to cataract surgery.ResultsOf 4078 participants enrolled, 4033 (98.9%) were examined. The age-adjusted and sex-adjusted prevalence of blindness, severe vision impairment and moderate vision impairment were 5.9% (95% CI 4.8% to 6.9%), 4.7% (95% CI 3.8% to 5.7%) and 18.9% (95% CI 16.8% to 21.0%), respectively. Cataract caused most of blindness (41.6%), followed by non-trachomatous corneal opacity (15.7%) and posterior segment diseases (14.5%). Cataract surgical coverage (CSC) for persons for visual acuity <3/60 was 86.8%, the proportion of cataract surgeries with poor visual outcome was 29.5% and effective CSC (eCSC) was 44.9%. eCSC was lower in women than men. The most frequently reported barrier to surgery was cost (51.5%).ConclusionsThe prevalence of blindness in Sohag governorate is higher than districts in other middle-income countries in the region. CSC was high; however, women suffer worse quality-corrected CSC than men. The quality of cataract surgery needs to be addressed, while health system strengthening across government and private settings could alleviate financial barriers.

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