Search results for "Graph theory"
showing 10 items of 784 documents
The distributed assembly permutation flowshop scheduling problem
2013
Nowadays, improving the management of complex supply chains is a key to become competitive in the twenty-first century global market. Supply chains are composed of multi-plant facilities that must be coordinated and synchronised to cut waste and lead times. This paper proposes a Distributed Assembly Permutation Flowshop Scheduling Problem (DAPFSP) with two stages to model and study complex supply chains. This problem is a generalisation of the Distributed Permutation Flowshop Scheduling Problem (DPFSP). The first stage of the DAPFSP is composed of f identical production factories. Each one is a flowshop that produces jobs to be assembled into final products in a second assembly stage. The o…
Multi-Start Methods
2006
Heuristic search procedures that aspire to find global optimal solutions to hard combinatorial optimization problems usually require some type of diversification to overcome local optimality. One way to achieve diversification is to re-start the procedure from a new solution once a region has been explored. In this chapter we describe the best known multi-start methods for solving optimization problems. We propose classifying these methods in terms of their use of randomization, memory and degree of rebuild. We also present a computational comparison of these methods on solving the linear ordering problem in terms of solution quality and diversification power.
Advanced Multi-start Methods
2010
Heuristic search procedures that aspire to find globally optimal solutions to hard combinatorial optimization problems usually require some type of diversification to overcome local optimality. One way to achieve diversification is to re-start the procedure from a new solution once a region has been explored. In this chapter we describe the best known multi-start methods for solving optimization problems. We propose classifying these methods in terms of their use of randomization, memory, and degree of rebuild. We also present a computational comparison of these methods on solving the maximum diversity problem in terms of solution quality and diversification power.
Optimal positioning of irregular shapes in stamping die strip
2010
The nesting of two-dimensional shapes is a common problem, where raw material has to be economically cut. As for the single-pass single-row strip layout, several algorithms, based on established methods, have been proposed. Moreover, it should be noticed that the optimum layout should also consider a few constraints, like grain orientation for subsequent forming operation, correct bridge width, and the commercial roll of metal width in order to make solutions applicable in real industrial environments. Most of the procedures until now shown in literature are quite complex and often ignore these real constraints. They usually make use of sliding techniques and are not able to effectively wor…
Feasibility of finite and infinite paths in data dependent programs
2005
This paper considers the feasibility of finite and infinite paths in programs in two simple programming languages. The language LBASE allows to express the dependencies of real time systems on integer data, the language LTIM can model quantitative timing constraints in r.t.s. specifications. It is proven that the problem of whether a given LBASE or LTIM program has an infinite feasible path (i.e. whether it can exhibit an infinite behaviour) is decidable. The possibilities to characterise the sets of all feasible finite and infinite paths in LBASE and LTIM programs are also discussed. The infinite feasible path existence problem is proven decidable also for the language LTIBA which has both…
Time optimization and state-dependent constraints in the quantum optimal control of molecular orientation
2014
We apply two recent generalizations of monotonically convergent optimization algorithms to the control of molecular orientation by laser fields. We show how to minimize the control duration by a step-wise optimization and maximize the field-free molecular orientation using state-dependent constraints. We discuss the physical relevance of the different results.
Scatter Search and Path Relinking
2011
Scatter search (SS) and path relinking (PR) are evolutionary methods that have been successfully applied to a wide range of hard optimization problems. The fundamental concepts and principles of the methods were first proposed in the 1970s and 1980s, and were based on formulations, dating back to the 1960s, for combining decision rules and problem constraints. The methods use strategies for search diversification and intensification that have proved effective in a variety of optimization problems and that have sometimes been embedded in other evolutionary methods to yield improved performance. This paper examines the scatter search and path relinking methodologies from both conceptual and p…
On the Bias and Performance of the Edge-Set Encoding
2009
The edge-set encoding of trees directly represents trees as sets of their edges. Nonheuristic operators for edge-sets manipulate trees' edges without regard for their weights, while heuristic operators consider edges' weights when including or excluding them. In the latter case, the operators generally favor edges with lower weights, and they tend to generate trees that resemble minimum spanning trees. This bias is strong, which suggests that evolutionary algorithms (EAs) that employ heuristic operators will succeed when optimum solutions resemble minimum spanning trees (MSTs) but fail otherwise. The one-max tree problem is a scalable test problem for trees where the optimum solution can be…
Solution to nonlinear MHDS arising from optimal growth problems
2011
Abstract In this paper we propose a method for solving in closed form a general class of nonlinear modified Hamiltonian dynamic systems (MHDS). This method is used to analyze the intertemporal optimization problem from endogenous growth theory, especially the cases with two controls and one state variable. We use the exact solutions to study both uniqueness and indeterminacy of the optimal path when the dynamic system has not a well-defined isolated steady state. With this approach we avoid the linearization process, as well as the reduction of dimension technique usually applied when the dynamic system offers a continuum of steady states or no steady state at all.
Scatter Search and Path Relinking: Advances and Applications
2006
Scatter search (SS) is a population-based method that has recently been shown to yield promising outcomes for solving combinatorial and nonlinear optimization problems. Based on formulations originally proposed in the 1960s for combining decision rules and problem constraints, SS uses strategies for combining solution vectors that have proved effective in a variety of problem settings. Path relinking (PR) has been suggested as an approach to integrate intensification and diversification strategies in a search scheme. The approach may be viewed as an extreme (highly focused) instance of a strategy that seeks to incorporate attributes of high quality solutions, by creating inducements to favo…