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copied!<p>It is not possible to find parents if you do not know the inverse-crossover function (so that AxB => (a,b) & (any a) => (A,B)). </p> <p>Usually the 1-point crossover function is:</p> <pre><code>a = A1 + B2 b = B1 + A2 </code></pre> <p>Even if you know <em>a</em> and <em>b</em> you <strong>cannot solve</strong> the system (system of 2 equations with 4 variables).</p> <p>If you know any 2 parts of any A or/and B then it <strong>can be solved</strong> (system of 2 equations with 2 variables). This is the case for your question as you provide both A and B.</p> <p>Generally crossover function does not have inverse function and you just need to find the solution logically or, <strong>if you know parents, perform the crossover and compare</strong>.</p> <p>So to make a generic formula for you we should know 2 things:</p> <ol> <li>Crossover function.</li> <li>Inverse-crossover function.</li> </ol> <p>The 2nd one is not usually used in GAs as it is not required. </p> <hr> <p>Now, I'll just answer your questions.</p> <blockquote> <p>Q1: In a genetic algorithm given the two parents A and B with the chromosomes 001110 and 101101, respectively, which of the following offspring could have resulted from a one-point crossover?</p> </blockquote> <p>Looking at the <em>a</em> and <em>b</em> I can see the crossover point is here:</p> <pre><code> 1 2 A: 00 | 1110 B: 10 | 1101 </code></pre> <p>Usually the crossover is done using <strong>this formula</strong>:</p> <pre><code>a = A1 + B2 b = B1 + A2 </code></pre> <p>so that possible children are:</p> <pre><code>a: 00 | 1101 b: 10 | 1110 </code></pre> <p>which excludes option b from the question.<br> <strong>So the answer to Q1 is the result child is a: 001101 assuming given <em>crossover function</em></strong></p> <blockquote> <p>Q2: Which of the above offspring could have resulted from a two-point crossover? and why?</p> </blockquote> <p>Looking at the a and b I can see the crossover points can be here:</p> <pre><code> 1 2 3 A: 00 | 11 | 10 B: 10 | 11 | 01 </code></pre> <p>Usual <strong>formula</strong> for 2-point crossover is:</p> <pre><code>a = A1 + B2 + A3 b = B1 + A2 + B3 </code></pre> <p>So the children would be:</p> <pre><code>a = 00 | 11 | 10 b = 10 | 11 | 01 </code></pre> <p>Comparing them to the options you asked (small <em>a</em> and <em>b</em>) we can say the answer:</p> <p><strong>Q2. A:</strong> <strong>Neither of <em>a</em> or <em>b</em> could be result of 2-point crossover with <em>AxB</em> <em>according to the given crossover function</em>.</strong> </p> <hr> <p>Again it is <strong>not possible</strong> to answer your questions without knowing the <strong>crossover function</strong>.</p> <p>The functions I provided are common in GA, but you can invent so many of them so they could answer the question (see the comment below):</p>

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