Josu Ceberio

Previously…  EDAs for integer domains.  EDAs for real value domains.  Few efficient designs for permutation- based problems. POOR PERFORMANCE EHBSA and NHBSA (Tsutsui et al.)

Distance-based ranking models  The Mallows model is a distance-based exponential model.  Two parameters Consensus ranking, Spread parameter,  Probability distribution

Distance-based ranking models  Kendall’s tau distance  Decomposition of the distance  Factorization of the probability distribution

Distance-based ranking EDA  Generalized Mallows EDA is proposed.  A generalization of the Mallows model.  spread parameters.  Probability distribution

The problem  To check the performance we approach: Permutation Flowshop Scheduling Problem.  Extensively studied.  The Mallows EDA demonstrated good performance.

Permutation Flowshop Scheduling Problem  Given a set of n jobs and m machines and processing times p ij.  Find the sequence for scheduling jobs optimally.  Optimization criterion: Total Flow Time (TFT). Codification m1m1 m2m2 m3m3 m4m4 j1j1 j3j3 j2j2 j5j5 j4j4 Example Objective function

Generalized Mallows EDA Preliminary experiments Spread parameters

Generalized Mallows EDA Preliminary experiments GM model convergence

Generalized Mallows EDA Approximating spread parameters Newton-Raphson An upper bound for the spread parameters is fixed!!

Generalized Mallows EDA Approximating spread parameters

Standart evolutionary shape Restart mechanism shape Generalized Mallows EDA Preliminary experiments Restart mechanism Improvement !

PFSP state-of-the-art LR(n/m) GA VNS Crossover VNS Asynchronus Genetic Algorithm (AGA) – Xu et al Local Search (Swap) Local Search (Insert) Shake

PFSP state-of-the-art LR(n/m) Local Search (Swap) Local Search (Insert) Shake Variable Neighborhood Search 4 (VNS 4 ) – Costa et al. 2012

PFSP state-of-the-art  Fundamentalist approaches rarely achieve optimum solutions.  Hybridization is the path to follow.  High presence of VNS algorithms.

First approach to the PFSP  GM-EDA does not succeed.  An hybrid approach is considered: Hybrid Generalized Mallows EDA (HGM-EDA)

Hybrid Generalized Mallows EDA Generalized Mallows EDA Local Search (Swap) Local Search (Insert) Orbit Shake VNS

Experimentation  Algorithms: AGA, VNS 4, GM-EDA, VNS and HGM-EDA. 20 repetitions  Taillard’s PFSP benchmarks: 100 instances 20 x x x x x x x x x x x x 20

Experimentation  Spread parameters upper bound. Select the upper-theta that provides the best solutions for GM-EDA  Stopping criterion: maximum number of evaluations. Evaluations performed by AGA in n x m x 0.4s.

Experimentation  Taillards benchmark 20 x 520 x 1020 x 20 AGA VNS GM-EDA VNS HGM-EDA

Experimentation  Taillards benchmark 50 x 550 x 1050 x 20 AGA VNS GM-EDA VNS HGM-EDA

Experimentation  Taillards benchmark 100 x 5100 x x 20 AGA VNS GM-EDA VNS HGM-EDA

Experimentation  Taillards benchmark 200 x x x 20 AGA VNS GM-EDA VNS HGM-EDA

Experimentation  Taillard’s benchmark - Summary 20x0520x1020x2050x0550x1050x20100x05100x10100x20200x10200x20500x20 AGA ✔✔✔✔✔✔✔✔ VNS 4 ✔✔✔ GM-EDA VNS ✔✔✔ HGM-EDA ✔✔✔✔✔✔✔

Experimentation  Taillard’s benchmark – Results analysis HGM-EDA outperforms state-of-the-art results in some cases. ○ Which is the reason for the performance fall given in instances of 500x20? Biased instances? -A tabu search algorithm was used for to choose the hardest instances. We generate a random benchmark

Experimentation  Random benchmark New configurations between 200 and 500. Total: 100 instances. 250 x x x x x x x x x x 20

Experimentation  Random benchmark - Summary 250x10250x20300x10300x20350x x20400x10400x20450x10450x20 AGA ✔✔✔ VNS 4 GM-EDA VNS HGM-EDA ✔✔✔✔✔✔✔

Experimentation  Random benchmark – Results analysis Statistical Analysis confirms experimentation. ○ Friedman test + Shaffer’s static. HGM-EDA and AGA are definitely the best algorithms. VNS 4 results do not match with those reported. The performance falls onwards 400x20. What’s wrong with largest instances?

Analysis – Hybrid approach Improvement ratio EDA vs. VNS

Analysis – Generalized Mallows EDA AGA vs. GM-EDA

Analysis – Generalized Mallows EDA Thetas convergence

Stops prematurely!!!

Analysis – HGM-EDA vs. AGA More evaluations Max eval.AGAHGM-EDA x x x x x x x x  One instance of 500x20

Analysis – Generalized Mallows EDA LR vs. GM-EDA

Analysis – HGM-EDA vs. AGA More evaluations Max eval.AGAHGM-EDA x x x x x x x x  One instance of 500x20

Analysis – HGM-EDA vs. AGA More evaluations Max eval.AGAHGM-EDAGuided HGM-EDA x x x x x x x x  One instance of 500x20

Analysis – HGM-EDA vs. AGA More evaluations  One instance of 500x20

Conclusions  Hybrid Generalized Mallows EDA is a efficient algorithm for solving the PFSP. Succeed in 152/220 instances.  The participation of the GM-EDA is essential.

Future Work - PFSP  Test other parameters: evaluations, population size, theta bounds, selection size…  Include information of the instance.  Guided Initialization Shake the solution of the LR(n/m) to build up the population?

Future Work – GM-EDA  Set different upper bounds to the spread parameters  Study other distances.  Is suitable Kendall’s-tau distance?  Other distances: Cayley, Ulam, Hamming Study the problem.  Other problems: TSP QAP LOP (work in progress)

Eskerrik asko Josu Ceberio Eskerrik asko Josu Ceberio

Distance-based ranking EDA  Mallows EDA Learning and Sampling 0...n n - 1