Abstract
Multi-choice programming (MCP) problem is a type of combinatorial optimization problem where the decision maker has to choose a value for a parameter from many alternative values. Genetic algorithm (GA) is a very popular approach used for solving combinatorial optimization problems. If some or all parameters present in the MCP problem are random, then it is known as multi-choice stochastic programming or multi-choice probabilistic programming (MCPP) problem. Chance-constrained programming (CCP) and two-stage stochastic programming (TSSP) are widely used to solve problems involving randomness. In this paper, we have considered an MCPP problem where some parameters are multi-choice types, and some are random variables. First, we apply the CCP technique to convert it to a deterministic MCP problem. While solving MCP problems, generally, some transformation techniques are used to transform the MCP problem into a mixed-integer programming (MIP) problem. After that, a standard mathematical programming approach is followed to solve the transformed MIP problem. These transformation techniques generate some extra variables and extra constraints which complicates the problem. But here we have proposed a GA to solve the MCP problem directly (without using any transformation technique). At last, a numerical example is provided to demonstrate the proposed algorithm and the solution approach.
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