Journal of Computational and Applied Mathematics Volume 253, 1 December 2013, Pages 14–25 Reporter : Zong-Dian Lee A hybrid quantum inspired harmony search algorithm for 0–1 optimization problems Abdesslem Layeb

2014/02/252 Outline 23 Implementation and validation 4 Introduction 1 Conclusions 5 Quantum Inspired Harmony Search Algorithm (QIHSA) Personal remark 6 Knapsack problem, QC, HS

3 Introduction(1/2)  Harmony search (HS) algorithm, developed by Geem et al. is a new metaheuristic algorithm and it is based on natural musical performance process that arise when a musician examines for a better state of harmony.  Quantum Computing (QC) is a new research field that has induced intense researches in the last decade, and that covers investigations on quantum computers and quantum algorithms.  The parallelism that the quantum computing provides obviously reduces the algorithmic complexity.  Such an ability of parallel processing can be used to solve combinatorial optimization problems which require the exploration of large solutions spaces. 2014/02/25

4 Introduction(2/2)  We propose in this paper a new hybrid algorithm called Quantum Inspired Harmony Search Algorithm(QIHSA) to cope with combinatorial optimization problems.  The main features of the proposed is the integration of quantum representation scheme in the basic harmony search algorithm that allows applying successfully some quantum inspired operators like measurement and interference. 2014/02/25

5 Knapsack problem 2014/02/25  The knapsack problem can be defined as follows: we have a knapsack with maximum capacity equal to C and a set of N items. Each item i has a profit pi and a weight wi.  Maximize(1)  Subject(2)  Subject (3)  that depends of the knapsack.  Example: an item can have a weight 3 in knapsack 1, 5 in knapsack 2, etc. iWiPiXi Maximize

62014/02/25 Quantum Computing (4) (5)

72014/02/25 HS algorithms(1/3)  Step 1. Initialize the problem and algorithm parameters : lower bounds : upper bounds harmony memory size (HMS) harmony memory considering rate (HMCR) bandwidth (bw) pitch adjusting rate (PAR) number of improvisations (MaxItr)

82014/02/25 HS algorithms(2/3)  Step 2. Initialize the harmony memory The initial harmony memory is randomly generated in the region. This is done by using the following equation : (6) where rand() is a random number from a uniform distribution of.  Step 3. Improvise a new harmony In this step we generate a new harmony. The new harmony vector is created by using the three basic rules of harmony search algorithm: memory consideration, pitch adjustment and random selection.

92014/02/25 HS algorithms(3/3)  Step 4. Update harmony memory If the fitness value of the new harmony is better than that of the worst one in the HM, the HM will be updated. That is, the new generated harmony is included into the HM and the worst harmony is excluded from the HM.  Step 5. Check the stopping criterion If the maximum number of iterations K is reached, the process is terminated.Otherwise, goto step 3.

10 Quantum Inspired Harmony Search Algorithm (QIHSA) (1/7) 2014/02/25  In this section, we present the proposed algorithm called Quantum Inspired Harmony Search Algorithm (QIHSA) which integers the quantum computing principles such as qubit representation, measure operation and quantum mutation, in the core the harmony search algorithm.  This proposed model will focus on enhancing diversity and the performance of the harmony search algorithm.

11 Quantum Inspired Harmony Search Algorithm (QIHSA) (2/7) 2014/02/25 Architecture of the QIHCSA algorithm

12 Quantum Inspired Harmony Search Algorithm (QIHSA) (3/7) 2014/02/25 (a) Inter-qubit quantum mutation. (b) Intra-qubit quantum mutation.

13 Quantum Inspired Harmony Search Algorithm (QIHSA) (4/7) 2014/02/25 (b) Quantum representation of the quantum harmony memory(a) Quantum representation of the harmony solution

14 Quantum Inspired Harmony Search Algorithm (QIHSA) (5/7) 2014/02/25

15 Quantum Inspired Harmony Search Algorithm (QIHSA) (6/7) 2014/02/25 (7) (8)

16 Quantum Inspired Harmony Search Algorithm (QIHSA) (7/7) 2014/02/25 UpdateHM: update harmony memory schema. Finally, the whole process is repeated until reaching a stopping criterion.

17 Implementation and validation 2014/02/25

(9) 18 Implementation and validation 2014/02/25

19 Implementation and validation 2014/02/25

20 Implementation and validation 2014/02/25

(10) 21 Implementation and validation 2014/02/25

22 Implementation and validation 2014/02/25

23 Conclusions 2014/02/25  In this work, we have presented a new inspired algorithm based on the hybridization between harmony search algorithm and quantum computing called Quantum Inspired Harmony Search Algorithm (QIHSA).  The effectiveness of our approach is explained by the good combination between the performances of the quantum computing and the harmony search algorithm, which leads the proposed algorithm to effectively explore the search space and locate a good solution.  The main contributions in this work are the introduction of some quantum computing principles in the core of the harmony search algorithm like quantum representation, measure, interference, and mutation operators.  The proposed algorithm reduces efficiently the harmony memory size and the number of improvisation to have the optimal solution.

24 Personal remark 2014/02/25  Authors do not provide the detail procedures of the two phase repair operator.  Performance of QIHSA-R is not better than ANT and PSO-R, although QIHSA-R is better than QIHSA.