Many interesting optimization problems have no known fast solution algorithms either because their objective functions are complicated (and possibly discontinuous) or because they contain difficult constraint structures. For such problems, in practice, any near-optimal solution would be desirable if obtained with a reasonable effort. For many problems with difficult objective functions this can be done using probabilistic search methods; however, such methods have no general way of handling constraints.In general, constraints are an integral part of the formulation of any problem. In [6] the authors wrote: "β¦Virtually all decision making situations involve constraints. What distinguish various types of problems is the form of these constraints. Depending on how the problem is visualized, they can arise as rules, data dependencies, algebraic expressions, or other forms.Constraint satisfaction problems (CSPs) have been studied extensively in the operations research (OR) and artificial intelligence (AI) literature. In OR formulations constraints are quantitative, and the solver (such as the Simplex algorithm) optimizes (maximizes or minimizes) the value of a specified objective function subject to the constraints. In contrast, AI research has focused on inference-based approaches with mostly symbolic constraints. The inference mechanism employed include theorem provers, production rule interpreters, and various labeling procedures such as those used in truth maintenance systems."In this article we present a new approach to solving numerical optimization problems with linear constraints, based on genetic algorithms. Our new methodology seems to fit between the OR and AI approaches. First, it uses the OR technique for problem representation, i.e. the formulation of constraints is quantitative. On the other hand, our method uses a genetic algorithm, which is considered as an AI based search method.Genetic algorithms ([14], [5], [4], ) are a class of stochastic algorithms which simulate both the natural inheritance by genetics and the Darwinian strive for survival. As stated in [4]: "β¦the metaphor underlying genetic algorithms is that of natural evolution. In evolution, the problem each species faces is one of searching for beneficial adaptations to a complicated and changing environment. The 'knowledge' that each species has gained is embodied in the makeup of the chromosomes of its members.