Complete solution of a constrained tropical optimization problem with application to location analysis

We present a multidimensional optimization problem that is formulated and solved in the tropical mathematics setting. The problem consists of minimizing a nonlinear objective function defined on vectors over an idempotent semifield by means of a conjugate transposition operator, subject to constraints in the form of linear vector inequalities. A complete direct solution to the problem under fairly general assumptions is given in a compact vector form suitable for both further analysis and practical implementation. We apply the result to solve a multidimensional minimax single facility location problem with Chebyshev distance and with inequality constraints imposed on the feasible location area.Comment: 20 pages, 3 figure

An improved constraint satisfaction adaptive neural network for job-shop scheduling

Copyright @ Springer Science + Business Media, LLC 2009This paper presents an improved constraint satisfaction adaptive neural network for job-shop scheduling problems. The neural network is constructed based on the constraint conditions of a job-shop scheduling problem. Its structure and neuron connections can change adaptively according to the real-time constraint satisfaction situations that arise during the solving process. Several heuristics are also integrated within the neural network to enhance its convergence, accelerate its convergence, and improve the quality of the solutions produced. An experimental study based on a set of benchmark job-shop scheduling problems shows that the improved constraint satisfaction adaptive neural network outperforms the original constraint satisfaction adaptive neural network in terms of computational time and the quality of schedules it produces. The neural network approach is also experimentally validated to outperform three classical heuristic algorithms that are widely used as the basis of many state-of-the-art scheduling systems. Hence, it may also be used to construct advanced job-shop scheduling systems.This work was supported in part by the Engineering and Physical Sciences Research Council (EPSRC) of UK under Grant EP/E060722/01 and in part by the National Nature Science Fundation of China under Grant 60821063 and National Basic Research Program of China under Grant 2009CB320601

Solving Fuzzy Job-Shop Scheduling Problems with a Multiobjective Optimizer

International audienceIn real-world manufacturing environments, it is common to face a job-shop scheduling problem (JSP) with uncertainty. Among different sources of uncertainty, processing times uncertainty is the most common. In this paper, we investigate the use of a multiobjective genetic algorithm to address JSPs with uncertain durations. Uncertain durations in a JSP are expressed by means of triangular fuzzy numbers (TFNs). Instead of using expected values as in other work, we consider all vertices of the TFN representing the overall completion time. As a consequence, the proposed approach tries to obtain a schedule that optimizes the three component scheduling problems (corresponding to the lowest, most probable, and largest durations) all at the same time. In order to verify the quality of solutions found by the proposed approach, an experimental study was carried out across different benchmark instances. In all experiments, comparisons with previous approaches that are based on a single-objective genetic algorithm were also performed

When Model Bias is Stronger than Selection Pressure

We investigate the inuence of model bias in model-based search. As an example we choose Ant Colony Optimization as a well-known model-based search algorithm. We present the eect of two dierent pheromone models for an Ant Colony Optimization algorithm to tackle a general scheduling problem. The results show that a pheromone model can introduce a strong bias toward certain regions of the search space, stronger than the selection pressure introduced by the updating rule for the model. This potentially leads to an algorithm where over time the probability to produce good quality solutions decreases