We propose a genetic algorithm -- MckpGen -- for rate scaling and adaptive streaming of layered video streams from multiple sources in a bandwidth-constrained environment. A genetic algorithm (GA) consists of several components: a representation scheme; a generator for creating an initial population; a crossover operator for producing offspring solutions from parents; a mutation operator to promote genetic diversity and a repair operator to ensure feasibility of solutions produced. We formulated the problem as a Multiple-Choice Knapsack Problem (MCKP), a variant of Knapsack Problem (KP) and a decision problem in combinatorial optimization. MCKP has many successful applications in fault tolerance, capital budgeting, resource allocation for conserving energy on mobile devices, etc. Genetic algorithms have been used to solve NP-complete problems effectively, such as the KP, however, to the best of our knowledge, there is no GA for MCKP. We utilize a binary chromosome representation scheme for MCKP and design and implement the components, utilizing problem-specific knowledge for solving MCKP. In addition, for the repair operator, we propose two schemes (RepairSimple and RepairBRP ). Results show that RepairBRP yields significantly better performance. We further show that the average fitness of the entire population converges towards the best fitness (optimal) value and compare the performance at various bit-rates.