Aggregate Blending Using Genetic Algorithms

Abstract

Aggregate blending consists of finding the proportions of fractions to form a final blend satisfying predefined specifications. It is a problem which is posed in many ways, and solved by using different techniques. These techniques range from simple graphical methods to advanced computer methods such as nonlinear pro- gramming or dynamic programming. In this article, an aggregate-blending problem is formulated as a multiob- jective optimization problem and solved by using genetic algorithms (GAs). It is shown that in this way all existing formulations of an aggregate-blending problem can be covered and solved. The effectiveness of this new appli- cation is demonstrated through numerical examples. The technique is shown to be quite versatile in tackling multiple objectives including cost minimization, and approaching at best a given target curve. Linear and nonlinear cost functions can be dealt with equal ease; additional objec- tives may be inserted into the problem with no difficulty. The user has the possibility of defining and finding the best solutions with Pareto optimality considerations. Problems associated with aggregate blending are very common in the construction industry. Mixing aggregate fractions is necessary when making concrete, mortar, as- phalt concrete, and any soil recomposition, and when constructing granular bases and sub-bases. In fact, the problem can easily be generalized to any blending prob- lem that can be encountered in the food, chemical, pharmaceutical, and petrochemical industries and the like. Before the common use of computers, trial-and-error (TE) type and graphical methods were used extensively ∗ To whom correspondence should be addressed. E-mail: yct001@ yahoo.com. for solving aggregate-blending problems. These methods were all characterized by choosing a subset of sieve sizes to make the calculations easier. In the TE type calcula- tions, an iterative procedure was followed for obtaining an acceptable solution. In the graphical methods, some triangular and rectangular charts were designed where each side corresponded to one sieve size. The solution was highly dependent on the sizes chosen and also the experience of the engineer. These methods were effec- tive for at most three or four fractions and for the only objective of finding a mix within the prescribed limits. Fo ra higher number of fractions, other graphical meth- ods were proposed where straight lines approximated the grading curves. Analytical methods, which consisted of solving a system of equations of a number equal to the number of fractions considered, were also being used. Then came more sophisticated methods, which were adapted for computer applications. With the advances in computer technologies and using the advantages of these methods, more and more complex blending problems have been solved, such as multiobjective or chance-constrained problems or problems with nonlin- ear constraints. A summary of these methods with a com- prehensive literature analysis is given by Toklu (2002b). The common disadvantage of these methods is that all of them are especially designed for the formulation con- sidered. If a problem has different properties, then the method should be changed accordingly. In the present study, the problem is formulated as a multiobjective optimization problem. It has been shown that this formulation is capable of covering all formula- tions studied before and actually can be considered as the most general approach. The problem is then solved by using a metaheuristic method, namely, a genetic algo- rithm (GA). Certain aspects are checked by applying a combinatory approach, scanning the range of all feasible solutions using a step size sufficiently small. Optimality