Many optimal decision problems in scientific, engineering, and public sector applications involve both discrete decisions and nonlinear system dynamics that affect the quality of the final design or plan. These decision problems lead to mixed-integer nonlinear programming (MINLP) problems that combine the combinatorial difficulty of optimizing over discrete variable sets with the challenges of ...

Integer optimization problems are concerned with the efficient allocation of limited resources to meet a desired objective when some of the resources in question can only be divided into discrete parts. In such cases, the divisibility constraints on these resources, which may be people, machines, or other discrete inputs, may restrict the possible alternatives to a finite set. Nevertheless, the...

although lot streaming scheduling is an active research field, lot streaming flexible flow lines problems have received far less attention than classical flow shops. this paper deals with scheduling jobs in lot streaming flexible flow line problems. the paper mathematically formulates the problem by a mixed integer linear programming model. this model solves small instances to optimality. moreo...

Global optimization of mixed-integer nonlinear bilevel optimization problems is addressed using a novel technique. For problems where integer variables participate in both inner and outer problems, the outer level may involve general mixed-integer nonlinear functions. The inner level may involve functions that are mixed-integer nonlinear in outer variables, linear, polynomial, or multilinear in...

the markowitz’s optimization problem is considered as a standard quadratic programming problem that has exact mathematical solutions. considering real world limits and conditions, the portfolio optimization problem is a mixed quadratic and integer programming problem for which efficient algorithms do not exist. therefore, the use of meta-heuristic methods such as neural networks and evolutionar...

Motivated by the significant advances in integer optimization in the past decade, we introduce mixed-integer optimization methods to the classical statistical problems of classification and regression and construct a software package called CRIO (classification and regression via integer optimization). CRIO separates data points into different polyhedral regions. In classification each region i...

Evolutionary algorithms (EAs) are population-based global search methods. They have been successfully applied to many complex optimization problems. However, EAs are frequently incapable of finding a convergence solution in default of local search mechanisms. Memetic Algorithms (MAs) are hybrid EAs that combine genetic operators with local search methods. With global exploration and local explo...