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

A Memory Enhanced Evolutionary Algorithm for Dynamic Scheduling Problems

Abstract. This paper describes a memory enhanced evolutionary algorithm (EA) approach to the dynamic job shop scheduling problem. Memory enhanced EAs have been widely investigated for other dynamic optimization problems with changing fitness landscapes, but only when associated with a fixed search space. In dynamic scheduling, the search space shifts as jobs are completed and new jobs arrive, so memory entries that describe specific points in the search space will become infeasible over time. The relative importances of jobs in the schedule also change over time, so previously good points become increasingly irrelevant. We describe a classifier-based memory for abstracting and storing information about schedules that can be used to build similar schedules at future times. We compared the memory enhanced EA with a standard EA and several common EA diversity techniques both with and without memory. The memory enhanced EA improved performance over the standard EA, while diversity techniques decreased performance.