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  • 1
    Electronic Resource
    Electronic Resource
    Convex two-level optimization (1988)
    Springer
    Mathematical programming 40 (1988), S. 15-27 
    Details
    ISSN: 1436-4646
    Keywords: Bilevel programming ; Stackelberg games ; branch and bound ; active set strategy
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract In this paper a model for a two-level planning problem is presented in the form of a static Stackelberg game. By assumption, play is sequential and noncooperative; however, the leader can influence the actions of the followers through a set of coordination variables while the followers' responses may partly determine the leader's payoff. Under certain convexity assumptions, it is shown that the feasible region induced by the leader is continuous in the original problem variables. This observation, coupled with two corollary results, are used as a basis for a hybrid algorithm which clings to the inducible region until a local optimum is found. A branching scheme is then employed to located other segments of the region, eventually terminating with the global optimum. A number of examples are given to highlight the results, while the algorithm's performance is tested in a comparison with two other procedures.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01580720
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  • 2
    Electronic Resource
    Electronic Resource
    Single machine scheduling with flow time and earliness penalties (1993)
    Springer
    Journal of global optimization 3 (1993), S. 289-309 
    Details
    ISSN: 1573-2916
    Keywords: Single machine scheduling ; dynamic programming ; greedy heuristics ; bicriteria optimization ; branch and bound
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract This paper considers the problem of schedulingn jobs on a single machine to minimize the total cost incurred by their respective flow time and earliness penalties. It is assumed that each job has a due date that must be met, and that preemptions are not allowed. The problem is formulated as a dynamic program (DP) and solved with a reaching algorithm that exploits a series of dominance properties and efficiently generated bounds. A major factor underlying the effectiveness of the approach is the use of a greedy randomized adaptive search procedure (GRASP) to construct high quality feasible solutions. These solutions serve as upper bounds on the optimum, and permit a predominant portion of the state space to be fathomed during the DP recursion. To evaluate the performance of the algorithm, an experimental design involving over 240 randomly generated problems was followed. The test results indicate that problems with up to 30 jobs can be readily solved on a microcomputer in less than 12 minutes. This represents a significant improvement over previously reported results for both dynamic programming and mixed integer linear programming approaches.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01096772
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