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Computational Intelligence: An Introduction, Second Edition AP Engelbrecht c 2007 John Wiley & Sons, Ltd

parameters are discussed in Section 1316 A geometric illustration of the DE variation approach is given in Section 1317

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//Get the date, hours and minutes myDate=new Date(); myHours=myDategetHours(); myMinutes = myDategetMinutes(); //Convert to 12 hours instead of 24 if (myHours>=12) { myHours = myHours-12; } mySeconds = myDategetSeconds(); //Rotate the hours by 30 degrees, the //minutes by 6 degrees //and the seconds by 6 degrees setProperty("hours1",_rotation, myHours*30+(myMinutes/2)); setProperty("minutes1",_rotation, myMinutes*6); setProperty("seconds1",_rotation, mySeconds*6); //Convert the number returned by the //getDay function to the //actual weekday weekdays = ["Sunday","Monday","Tuesday", "Wednesday","Thursday","Friday", "Saturday"];

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The positions of individuals provide valuable information about the tness landscape Provided that a good uniform random initialization method is used to construct the initial population, the initial individuals will provide a good representation of the entire search space, with relatively large distances between individuals Over time, as the search progresses, the distances between individuals become smaller, with all individuals converging to the same solution Keep in mind that the magnitude of the initial distances between individuals is in uenced by the size of the population The more individuals in a population, the smaller the magnitude of the distances Distances between individuals are a very good indication of the diversity of the current population, and of the order of magnitude of the step sizes that should be taken in order for the population to contract to one point If there are large distances between individuals, it stands to reason that individuals should make large step sizes in order to explore as much of the search space as possible On the other hand, if the distances between individuals are small, step sizes should be small to exploit local areas It is this behaviour that is achieved by DE in calculating mutation step sizes as weighted di erences between randomly selected individuals The rst step of mutation is therefore to rst calculate one or more di erence vectors, and then to use these di erence vectors to determine the magnitude and direction of step sizes Using vector di erentials to achieve variation has a number of advantages Firstly, information about the tness landscape, as represented by the current population, is used to direct the search Secondly, due to the central limit theorem [177], mutation step sizes approaches a Gaussian (Normal) distribution, provided that the population is su ciently large to allow for a good number of di erence vectors [811]1 The mean of the distribution formed by the di erence vectors are always zero, provided that individuals used to calculate di erence vectors are selected uniformly from the population [695, 164] Under the condition that individuals are uniformly selected, this characteristic follows from the fact that di erence vectors (xi1 xi2 ) and (xi2 xi1 ) occur with equal frequency, where xi1 and xi2 are two randomly selected individuals The zero mean of the resulting step sizes ensures that the population will not su er from genetic drift It should also be noted that the deviation of this distribution is determined by the magnitude of the di erence vectors Eventually, di erentials will become in nitesimal, resulting in very small mutations Section 132 shows that more than one di erential can be used to determine the mutation step size If nv is the number of di erentials used, and ns is the population size, then the total number of di erential perturbations is given by [429] ns 2nv 2nv ! O(n2nv ) s (131).

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1 The central limit theorem states that the probability distribution governing a random variable approaches the Normal distribution as the number of samples of that random variable tends to in nity

months = ["January","February", "March","April","May","June","July", "August", "September","October","November", "December"]; myDate1 = weekdays[myDategetDay()] + ", " + months[myDategetMonth()] + "" + myDategetDate() + "," + " " + myDategetfullYear(); gotoAndPlay(1);

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