Using Timer on a Paint Component

Basically, the Timer becomes you for-loop, so each time it ticks, you need to increment it's iteration and update the state of the model before it's painted.

This means you will HAVE to separate the initialisation and update phases of your code, for example...

class MyPanel extends JPanel implements ActionListener{

    private final static int POINTWIDTH = 8;
    private final static Color POINTCOLOR = Color.RED;
    private final static Color LINECOLOR = Color.GREEN;
    private JLabel label =  new JLabel();
    private City city,city2,city3,city4,city5,city6,city7,city8,city9,city10,city11,city12,city13,city14,city15,city16,city17,city18,city19,city20;
    private Population population;
    private ArrayList tempCity = new ArrayList<City>();
    private ArrayList tempCity2 = new ArrayList<City>();

    int delay = 5000;
    private int iteration = 0;

    Timer timer = new Timer(delay, this);


    public void start(){
        iteration = 0;
        timer.start();
    }

    public void initGA() {
        city = new City(60, 200);
        TourManager.addCity(city);
        city2 = new City(180, 200);
        TourManager.addCity(city2);
        city3 = new City(80, 180);
        TourManager.addCity(city3);
        city4 = new City(140, 180);
        TourManager.addCity(city4);
        city5 = new City(20, 160);
        TourManager.addCity(city5);
        city6 = new City(100, 160);
        TourManager.addCity(city6);
        city7 = new City(200, 160);
        TourManager.addCity(city7);
        city8 = new City(140, 140);
        TourManager.addCity(city8);
        city9 = new City(40, 120);
        TourManager.addCity(city9);
        city10 = new City(100, 120);
        TourManager.addCity(city10);
        city11 = new City(180, 100);
        TourManager.addCity(city11);
        city12 = new City(60, 80);
        TourManager.addCity(city12);
        city13 = new City(120, 80);
        TourManager.addCity(city13);
        city14 = new City(180, 60);
        TourManager.addCity(city14);
        city15 = new City(20, 40);
        TourManager.addCity(city15);
        city16 = new City(100, 40);
        TourManager.addCity(city16);
        city17 = new City(200, 40);
        TourManager.addCity(city17);
        city18 = new City(20, 20);
        TourManager.addCity(city18);
        city19 = new City(60, 20);
        TourManager.addCity(city19);
        city20 = new City(160, 20);
        TourManager.addCity(city20);
        population = new Population(50, true);
    }

    public void doGA(){
        population = GA.evolvePopulation(population);
        repaint();
        System.out.println(population.getFittest().getFitness());
    }

    public void paintComponent(Graphics g){
        super.paintComponent(g);
        Graphics2D g2 = (Graphics2D) g;
        g2.setStroke(new BasicStroke(3));
        for(int x = 0; x<19;x++){
            g2.setColor(LINECOLOR);
            //g2.drawLine(tempCity.get(x).getX(), tempCity.get(x).getY(), tempCity2.get(x).getX(), tempCity2.get(x).getY());
            g2.drawLine(population.getFittest().getCity(x).getX(), population.getFittest().getCity(x).getY(), population.getFittest().getCity(x+1).getX(), population.getFittest().getCity(x+1).getY());
            g2.setColor(POINTCOLOR);
            g2.fillOval(population.getFittest().getCity(x).getX() - POINTWIDTH/2, population.getFittest().getCity(x).getY() - POINTWIDTH/2, POINTWIDTH, POINTWIDTH);

        }
        g2.setColor(LINECOLOR);
        g2.drawLine(population.getFittest().getCity(19).getX(), population.getFittest().getCity(19).getY(), population.getFittest().getCity(0).getX(), population.getFittest().getCity(0).getY());
        g2.setColor(POINTCOLOR);
        g2.fillOval(population.getFittest().getCity(0).getX() - POINTWIDTH/2, population.getFittest().getCity(0).getY() - POINTWIDTH/2, POINTWIDTH, POINTWIDTH);

    }

    public void actionPerformed(ActionEvent e){
        iteration++;
        if (iteration < 100) {
            doGA();
        } else {
            ((Timer)e.getSource()).stop();
        }
    }
}

The short answer would be, no, you can't keep your doGA method as it is, it must be changed, there simply is no other way to achieve it, but the longer answer is, it's not that hard if you simply think of the Timer as a fancy type of loop...