Optimization heuristic methods

In this chapter, we discuss solution approaches for MILP and MINLP that are capable of finding an optimal solution and verify that they have done so. Specifically, we consider branch-and-bound (BB) and outer linearization (OL) methods. BB can be applied to both linear and nonlinear problems, but OL is used for nonlinear problems by solving a sequence of MILPs. Chapter 10 further considers branch-and-bound methods, and also describes heuristic methods, which often find very good solutions but are unable to verify optimality. 

Heuristics are reliable, well-established rules for reducing the number of potential alternative sequences with minimum effort, and often lead to near-optimal separation system designs. Most of the heuristics for distillation sequencing were originally formulated from parametric studies. A number of Heuristics have been suggested, some of which contradict each other (5—8). Heuristic methods have also been extended to sequencing nonsharp distillation separations and to combinations of distillation, mixing, and stream bypass operations (9—11). 

A Hybrid Meta-heuristic Method for Logistics Optimization Associated with Production Planning... 

Finally, before leaving this section on preliminary process synthesis, the limitations of the heuristic approaches should not be overlooked. Many algorithmic methods are very effective for the synthesis of alternative flowsheets, their analysis, and optimization. These methods are usually used by design teams in parallel with their work on the development of the base-case design, which is the subject of the next section. The algorithmic methods are easily implemented and are illustrated with many examples in Part Two of this text (Chapters 6-12). 

Unconstrained optimization methods are discussed in Chapter 3. Heuristic methods, gradient methods and the conjugate direction methods are introduced together with Newton s method and modified Newton and quasi-Newton methods. Convergence and stop criteria are discussed, implemented in generalized classes, and used to optimize the design and operation of batch and fixed-bed reactors. 

Volkanovski A., Optimization of reactive power injections in distribution networks using heuristic methods and deterministic initializations. Final seminar work Computational physics. Faculty of Mathematics and Physics, University of Ljubljana, Slovenia, 2007, Pages 25. 

Keywords Sustainability Green logistics optimization Hybrid meta-heuristic method Emission trading Modal shift... 

The aim of the fourth example is to illustrate the optimal position of dampers on stmcture when dampers are modelled using the fractional Kelvin model and the fractional Maxwell model. Moreover, it is shown that results obtained using the sequential optimization method (which is a heuristic method) and using the PSO method are very similar. It justifies that it is possible to find, using the sequential optimization method, a solution which is near the global optimum of the optimization problem at hand. 

Particle Swarm Optimization (PSO) The optimization method based on the study of social behaviour in a self-organized population system (i.e., ant colonies, fish schools). Itisanon-gradient, heuristic method which requires calculation of the objective function only. This method is able to find a global solution to non-convex optimization problem and problems which have many local minima. 

Abstract. Finding the optimal solution to NP-hard problems requires at least exponential time. Thus, heuristic methods are usually applied to obtain acceptable solntions to this kind of problems. In this paper we propose a new type of heuristic algorithms to solve this kind of complex problems. Our algorithm is based on river formation dynamics and provides some advantages over other heuristic methods, like ant colony optimization methods. We present our basic scheme and we illustrate its usefulness applying it to a concrete example The Traveling Salesman Problem. 

In this paper we have presented a new heuristic method to solve complex problems. The method is inspired on the way rivers are created in nature. By using it, we can obtain acceptable solutions to NP-hard problems in reasonable times. Our method obtains competitive results when compared with other more matured schemes, like ants colonies. In the TSP case study, our current experimental results shows that the RFD method is preferable to AGO if the optimality of the solution is the main requirement. The fast reinforcement of shortcuts, the avoidance of local cycles, the punishment of wrong paths, and the creation of global direction tendencies motivate these results. 

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