• TODO

  • Overview

    • multiple EMOAs available
    • many empirical tests available
    • no conclusions on ease-of-programming
    • no comparison against HGS
    • we implemented some and compared by time of fitness calls
    • comparison by time—-no, since fitness could be very expensive

    Keywords: search strategies, multiobjective optimization, evolutionary algorithms

  • Strategies

  • Problems

  • Results

  • Results analysis

  • Conclusions

  • Various

  • Problems

  • Introduction

    • multiple objectives -> single criterion by utility function
    • what is EMOA
    • objective of EMOAs is the approximation of Pareto set
    • advantages of Pareto-optimal set against single solution (insight into problem)
  • EMOAs

    • main concepts (“intuition behind“)
    • math definitions for dominance, Pareto front/set

    Key-words:

    • decision/parameter vector in parameter space (m)
    • objective vector in objective space(n)
  • SPEA-II

    • scalarization inside (ranking + ?)
  • NSGA-II

    • non-dominated sorting genetic algorithm improved
    • NSGA—-one of the first MOEAs
  • IBEA

    • formalizes preferences (diversity vs distance to the Pareto-optimal set)
  • HGS

  • COEMOA—family

  • Kursawe

  • fast non-dominated sorting approach

    • described in “A fast elitist non-diminated sorting genetic algorithm…“, p. 4
  • Do we share source-codes

    • if so, then git-history shall be collapsed, right?
    • if so, then probably all traces to p4r4noj4/evolutionary-pareto shall be ereased
  • MOEA or EMOA?

  • Discrete optimization problems

    LOTZ

    • leading ones, trailing zeroes
    • from “Running time analysis of a multi-objective evolutionary…

    LOTZ: {0,1}^n -> N^2
    LOTZ(x1,…,xn) = [f1, f2]
    f1 = sum{i=1}^n prod{j=1}^i xj
    f2 = sum
    {i=1}^n prod_{j=1}^i (1-x_j)

  • Showing paths towards the target?

  • Do we present simple problems like Ackley?

    • math-detail: we minimize fitnesses
  • EMOAs difficulties

    • diversity
    • how to guide selection to Pareto-optimal set so to accomplish fitness
  • Tuning

  • Criticism of NSGA

    • high computational complexity of non-dominated sorting
    • lack of elitism
    • need for specyfying the sharing parameter
{"cards":[{"_id":"387ade93f178b6576800005f","treeId":"387920bef178b65768000036","seq":1,"position":1,"parentId":null,"content":"# TODO"},{"_id":"387afa39f178b65768000064","treeId":"387920bef178b65768000036","seq":1,"position":0.5,"parentId":"387ade93f178b6576800005f","content":"## Various"},{"_id":"387afa71f178b65768000065","treeId":"387920bef178b65768000036","seq":1,"position":1,"parentId":"387afa39f178b65768000064","content":"### fast non-dominated sorting approach\n\n* described in \"*A fast elitist non-diminated sorting genetic algorithm...*\", p. 4"},{"_id":"387b126df178b65768000069","treeId":"387920bef178b65768000036","seq":1,"position":2,"parentId":"387afa39f178b65768000064","content":"### Do we share source-codes\n\n* if so, then git-history shall be collapsed, right?\n* if so, then probably all traces to p4r4noj4/evolutionary-pareto shall be ereased"},{"_id":"387b1c8df178b6576800006c","treeId":"387920bef178b65768000036","seq":1,"position":3,"parentId":"387afa39f178b65768000064","content":"MOEA or EMOA?"},{"_id":"387aded9f178b65768000060","treeId":"387920bef178b65768000036","seq":1,"position":1,"parentId":"387ade93f178b6576800005f","content":"## Problems"},{"_id":"387adf27f178b65768000061","treeId":"387920bef178b65768000036","seq":1,"position":1,"parentId":"387aded9f178b65768000060","content":"### Discrete optimization problems\n\n#### LOTZ\n\n* leading ones, trailing zeroes\n* from \"*Running time analysis of a multi-objective evolutionary...*\"\n\nLOTZ: {0,1}^n -> N^2\nLOTZ(x1,...,xn) = [f1, f2]\nf1 = sum_{i=1}^n prod_{j=1}^i x_j\nf2 = sum_{i=1}^n prod_{j=1}^i (1-x_j)"},{"_id":"387b1b79f178b6576800006b","treeId":"387920bef178b65768000036","seq":1,"position":2,"parentId":"387aded9f178b65768000060","content":"Showing paths towards the target?"},{"_id":"387b26a6f178b6576800006e","treeId":"387920bef178b65768000036","seq":1,"position":3,"parentId":"387aded9f178b65768000060","content":"Do we present simple problems like Ackley?"},{"_id":"387a3f23f178b65768000045","treeId":"387920bef178b65768000036","seq":1,"position":2,"parentId":null,"content":"# Overview\n\n* multiple EMOAs available\n* many empirical tests available\n* no conclusions on ease-of-programming\n* no comparison against HGS\n* we implemented some and compared by time of fitness calls\n* comparison by time---no, since fitness could be **very** expensive\n\nKeywords: search strategies, multiobjective optimization, evolutionary algorithms"},{"_id":"387ab0b8f178b6576800005d","treeId":"387920bef178b65768000036","seq":1,"position":2,"parentId":"387a3f23f178b65768000045","content":"## Introduction\n\n* multiple objectives -> single criterion by *utility function*\n* what is EMOA\n* objective of EMOAs is the approximation of Pareto set\n* advantages of Pareto-optimal set against single solution (insight into problem)"},{"_id":"387af00ff178b65768000062","treeId":"387920bef178b65768000036","seq":1,"position":3,"parentId":"387a3f23f178b65768000045","content":"## EMOAs\n\n* main concepts (\"*intuition behind*\")\n* math definitions for dominance, Pareto front/set\n\n#### Key-words:\n* decision/parameter vector in parameter space (m)\n* objective vector in objective space(n)"},{"_id":"387b0819f178b65768000067","treeId":"387920bef178b65768000036","seq":1,"position":1,"parentId":"387af00ff178b65768000062","content":"* math-detail: we minimize fitnesses"},{"_id":"387b0f72f178b65768000068","treeId":"387920bef178b65768000036","seq":1,"position":2,"parentId":"387af00ff178b65768000062","content":"### EMOAs difficulties\n\n* diversity\n* how to guide selection to Pareto-optimal set so to accomplish fitness"},{"_id":"387a4270f178b65768000047","treeId":"387920bef178b65768000036","seq":1,"position":4,"parentId":null,"content":"# Strategies"},{"_id":"387a661cf178b6576800004d","treeId":"387920bef178b65768000036","seq":1,"position":1,"parentId":"387a4270f178b65768000047","content":"## SPEA-II\n\n* scalarization inside (ranking + ?)"},{"_id":"387b1615f178b6576800006a","treeId":"387920bef178b65768000036","seq":1,"position":1,"parentId":"387a661cf178b6576800004d","content":"### Tuning"},{"_id":"387a6674f178b6576800004e","treeId":"387920bef178b65768000036","seq":1,"position":2,"parentId":"387a4270f178b65768000047","content":"## NSGA-II\n\n* non-dominated sorting genetic algorithm improved\n* NSGA---one of the first MOEAs"},{"_id":"387af5abf178b65768000063","treeId":"387920bef178b65768000036","seq":1,"position":1,"parentId":"387a6674f178b6576800004e","content":"### Criticism of NSGA\n\n* high computational complexity of non-dominated sorting\n* lack of elitism\n* need for specyfying the sharing parameter"},{"_id":"387a66faf178b6576800004f","treeId":"387920bef178b65768000036","seq":1,"position":3,"parentId":"387a4270f178b65768000047","content":"## IBEA\n\n* formalizes preferences (diversity vs distance to the Pareto-optimal set)"},{"_id":"387a6727f178b65768000050","treeId":"387920bef178b65768000036","seq":1,"position":4,"parentId":"387a4270f178b65768000047","content":"## HGS"},{"_id":"387a429ff178b65768000048","treeId":"387920bef178b65768000036","seq":1,"position":5,"parentId":null,"content":"# Problems"},{"_id":"387a6ab0f178b65768000052","treeId":"387920bef178b65768000036","seq":1,"position":1,"parentId":"387a429ff178b65768000048","content":"## COEMOA--family"},{"_id":"387a6b13f178b65768000053","treeId":"387920bef178b65768000036","seq":1,"position":2,"parentId":"387a429ff178b65768000048","content":"## Kursawe"},{"_id":"387a437bf178b6576800004a","treeId":"387920bef178b65768000036","seq":1,"position":7,"parentId":null,"content":"# Results"},{"_id":"387a43b7f178b6576800004b","treeId":"387920bef178b65768000036","seq":1,"position":8,"parentId":null,"content":"# Results analysis"},{"_id":"387a6567f178b6576800004c","treeId":"387920bef178b65768000036","seq":1,"position":9,"parentId":null,"content":"# Conclusions"}],"tree":{"_id":"387920bef178b65768000036","name":"EvoGIL","publicUrl":"evo-gil"}}