A linear two-level programming problem

Candler, Wilfred; Townsley, Robert

doi:10.1016/0305-0548(82)90006-5

Cited by 344 publications

(128 citation statements)

References 2 publications

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“…Ben-Ayed and Blair [11] demonstrated the failure of both the Parametric Complementarity Pivot Algorithm [13] and the Grid Search Algorithm [5] to locate the optimal solution. Since then, progress has been made in solving the linear-BLPP and techniques including implicit enumeration [21], penalty based methods [2] and methods based on Karush -Kuhn-Tucker (KKT) conditions [41] have been developed. (See [117] for a detailed review of the algorithms available for the linear-BLPP).…”

Section: Solution Algorithms For the Blppmentioning

confidence: 99%

A Metaheuristic Framework for Bi-level Programming Problems with Multi-disciplinary Applications

Koh

2013

Metaheuristics for Bi-Level Optimization

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Bi-level programming problems arise in situations when the decision maker has to take into account the responses of the users to his decisions. Several problems arising in engineering and economics can be cast within the bi-level programming framework. The bi-level programming model is also known as a Stackleberg or leader-follower game in which the leader chooses his variables so as to optimise his objective function, taking into account the response of the follower(s) who separately optimise their own objectives, treating the leader's decisions as exogenous. In this chapter, we present a unified framework fully consistent with the Stackleberg paradigm of bi-level programming that allows for the integration of meta-heuristic algorithms with traditional gradient based optimisation algorithms for the solution of bi-level programming problems. In particular we employ Differential Evolution as the main meta-heuristic in our proposal. We subsequently apply the proposed method (DEBLP) to a range of problems from many fields such as transportation systems management, parameter estimation and game theory. It is demonstrated that DEBLP is a robust and powerful search heuristic for this class of problems characterised by non smoothness and non convexity.

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Section: Solution Algorithms For the Blppmentioning

confidence: 99%

A Metaheuristic Framework for Bi-level Programming Problems with Multi-disciplinary Applications

Koh

2013

Metaheuristics for Bi-Level Optimization

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“…Since it caught the attention in the 1970s, there have been many algorithms proposed for solving bilevel linear programming problems (e.g. [24,25,26]). A popular way to solve such a problem, e.g.…”

Section: Introductionmentioning

confidence: 99%

Complexity of fuzzy answer set programming under Łukasiewicz semantics

Blondeel

Schockaert

Vermeir

et al. 2014

International Journal of Approximate Reasoning

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Fuzzy answer set programming (FASP) is a generalization of answer set programming (ASP) in which propositions are allowed to be graded. Little is known about the computational complexity of FASP and almost no techniques are available to compute the answer sets of a FASP program. In this paper, we analyze the computational complexity of FASP under Lukasiewicz semantics. In particular we show that the complexity of the main reasoning tasks is located at the first level of the polynomial hierarchy, even for disjunctive FASP programs for which reasoning is classically located at the second level. Moreover, we show a reduction from reasoning with such FASP programs to bilevel linear programming, thus opening the door to practical applications. For definite FASP programs we can show P-membership. Surprisingly, when allowing disjunctions to occur in the body of rules -a syntactic generalization which does not affect the expressivity of ASP in the classical case -the picture changes drastically. In particular, reasoning tasks are then located at the second level of the polynomial hierarchy, while for simple FASP programs, we can only show that the unique answer set can be found in pseudo-polynomial time. Moreover, the connection to an existing open problem about integer equations suggests that the problem of fully

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“…The bilevel programming (BLP) approaches to hierarchical decision problems have been studied widely since Candler and Townsley [4] demonstrated the use of BLP to large hierarchical decision making and planning organizations.…”

Section: Introductionmentioning

confidence: 99%

Mixed 0−1 Goal Programming Approach to Interval-Valued Bilevel Programming Problems Via Bio-Inspired Computational Algorithm

Chakraborti¹,

Biswas²

2013

Computer Science &Amp; Information Technology ( CS &Amp; IT )

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This paper presents how the mixed 0-1 programming in the framework of goal programming (GP) can be used to solve interval-valued fractional bilevel programming (IVFBLP) problems by employing genetic algorithm (GA) in a hierarchical decision making system. In the model formulation of the problem, a goal achievement function for minimizing the lower-bounds of the necessary regret intervals defined for the target intervals of achieving the goals and thereby arriving at a compromise decision is constructed by using both the aspects of 'minsum ' and 'minmax' approaches in GP. In the decision process, an GA scheme is employed for execution of the problems at the two stages, target interval specification and optimal decision determination, for distribution of decision powers to the decision makers (DMs) in the order of hierarchy. A numerical example is provided to illustrate the potential use of the approach.

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A linear two-level programming problem

Cited by 344 publications

References 2 publications

A Metaheuristic Framework for Bi-level Programming Problems with Multi-disciplinary Applications

A Metaheuristic Framework for Bi-level Programming Problems with Multi-disciplinary Applications

Complexity of fuzzy answer set programming under Łukasiewicz semantics

Mixed 0−1 Goal Programming Approach to Interval-Valued Bilevel Programming Problems Via Bio-Inspired Computational Algorithm

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