Integer heuristic programming

Since the program (DEP) represents a mixed-integer linear program (MILP), it can be solved by commercially available state-of-the-art MILP solvers like CPLEX [3] or XPRESS-MP [4], These solvers are based on implementations of modem branch-and-bound search algorithms with cuts and heuristics. 

AI = artificial intelligence GUI = graphical user interface HAZOP = hazard and operability HEN = heat exchanger network HNS = heuristic-numeric System KBS = knowledge-based system MILP = mixed integer linear programming XPS = expert system. 

This design problem can be understood as a large optimization problem where the best constellation has to be selected out of a large number of possible solutions. Therefore, usually pure mathematical methods are used to work out a solution (e.g., MILP Mixed Integer Linear Programming). But not all conditions can be described using a mathematical model. Therefore, heuristic rules are applied to fill this gap. Rules of thumb lead to a minimization of the optimization effort. 

Since scope economies are especially hard to quantify, a separate class of optimization models solely dealing with plant loading decisions can be found. For example, Mazzola and Schantz (1997) propose a non-linear mixed integer program that combines a fixed cost charge for each plant-product allocation, a fixed capacity consumption to reflect plant setup and a non-linear capacity-consumption function of the total product portfolio allocated to the plant. To develop the capacity consumption function the authors build product families with similar processing requirements and consider effects from intra- and inter-product family interactions. Based on a linear relaxation the authors explore both tabu-search heuristics and branch-and-bound algorithms to obtain solutions. 

S. Panek, S. Engell, and C. Eessner, 2005, Scheduling of a pipele.s.s multi-product batch plant using mixed-integer programming combined with heuristics, Proe. ESCAPE. 

Dobson, G. (1982), Worst-Case Analysis of Greedy Heuristics for Integer Programming with Nonnegative Data, Mathematics of Operations Research, Vol. 7, pp. 515-531. 

Since integer programming models are hard to solve, it might be efficient to use heuristics to find a reasonable— not optimal solution to a lot sizing problem. Here are some of the widely used ones ... 

The second category includes hybrids resulting from the combination of meta-heuristics with constraint programming, integer programming, tree-based search methods, data mining techniques, etc. [26]. 

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