Note on Multiple Objective Dynamic Programming

Daellenbach, Hans; Kluyver, Cornelis A. de

doi:10.1057/jors.1980.114

Cited by 62 publications

(24 citation statements)

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“…The origin node number assigned to each nondominated path helps identify the low and high risk zones within the house. The paths originating at node 2 (of cost (11,13) ) and node 1 (of cost (16,6) ) belong to the high risk zone due to the large values of time and distance to traveL The paths from node 5 and 6 are, of course, in the lowest risk zone. When node 5 becomes impassable, the path from node 6 stays in the lowest risk zone, but the only two paths leaving node 4 (of cost (11,10) and (17,8) ) are in the high risk zone.…”

Section: Discussion and Analysismentioning

confidence: 99%

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Optimization Models In Fire Egress Analysis For Residential Buildings

Kostreva¹,

Wiecek²,

Getachew³

1991

Fire Safety Science - Proceedings of the Third International Sy

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Fire hazard analysis often includes the use of mathematical models of the egress of the individual occupants of a structure which is involved in a fire. In this paper, we introduce some mathematical optimization models which produce as output at least one path for each occupant which is optimal with respect to some measurement. Network based models of increasing levels of complexity and realism are demonstrated by means of a sequence of examples. These examples include single attribute constant costs, single attribute timevarying costs, two attribute constant costs, and finally two attribute time-varying costs imposed on network links. Dynamic programming functional equations which are based on the principle of optimality are presented. A multi-attribute analysis is proposed to evaluate a building design with respect to evacuation paths.

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Section: Discussion and Analysismentioning

confidence: 99%

“…Since the steps are so similar to the scalar case, they will not be repeated here. The method of dynamic programming for a similar multiple attribute network problem is discussed in [13].…”

Section: Mathematical Foundationsmentioning

confidence: 99%

Optimization Models In Fire Egress Analysis For Residential Buildings

Kostreva¹,

Wiecek²,

Getachew³

1991

Fire Safety Science - Proceedings of the Third International Sy

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“…Multi-objective optimal control problems have multiple criteria (performance measures) which can be defined as follows [7,8]: In the case of dynamic multi-objective optimal control the following formulation is applicable:…”

Section: Definition Of the Multi-objective Optimal Control Problemmentioning

confidence: 99%

Discrete dynamic system control using multi-objective dynamic programming

Lutvica

Konjicija

2014

2014 X International Symposium on Telecommunications (BIHTEL)

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This paper deals with the design and implementation of a discrete dynamic control system using multiobjective dynamic programming. A discrete dynamic system along with the constraints regarding the values of the system's state (output) and the applicable control input has been introduced. Using multi-objective dynamic programming, a control system has been designed which minimizes two objectives while satisfying introduced constraints. The implemented control solution is explained. Experiments have been performed to test the quality of the implemented solution. A single-objective version of the control problem has been tested to provide reference for analysis regarding the quality of the implemented multi-objective control solution. The comparison of the obtained experimental results confirms the effectiveness of the proposed control solution and demonstrates the benefits of the multiobjective approach.

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“…Many algorithms for solving both problems are known, and they fall into the following categories: label correcting algorithms (Brumbaugh-Smith and Shier, 1989;Corley and Moon, 1985;Daellenbach and De Kluyver, 1980;Skriver and Andersen, 2000b), label setting algorithms (Hansen, 1980;Martins, 1984;Tung and Chew, 1988), k-th shortest path algorithms (Climaco and Martins, 1982), two-phase algorithms (Mote et al, 1991) and others (Chen and Nie, 2013;Dell'Olmo et al, 2005;Machuca et al, 2009;Mandow and Pérez de la Cruz, 2008;Martí et al, 2009;Raith and Ehrgott, 2009). The MSP problem is also solved using the weighed linear scalarization method, where a single-objective function is formulated and an optimal solution to a single-objective function is determined (Carraway et al, 1990).…”

Section: Introductionmentioning

confidence: 99%

A Relation of Dominance for the Bicriterion Bus Routing Problem

Widuch

2017

International Journal of Applied Mathematics and Computer Science

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A bicriterion bus routing (BBR) problem is described and analysed. The objective is to find a route from the start stop to the final stop minimizing the time and the cost of travel simultaneously. Additionally, the time of starting travel at the start stop is given. The BBR problem can be resolved using methods of graph theory. It comes down to resolving a bicriterion shortest path (BSP) problem in a multigraph with variable weights. In the paper, differences between the problem with constant weights and that with variable weights are described and analysed, with particular emphasis on properties satisfied only for the problem with variable weights and the description of the influence of dominated partial solutions on non-dominated final solutions. This paper proposes methods of estimation a dominated partial solution for the possibility of obtaining a non-dominated final solution from it. An algorithm for solving the BBR problem implementing these estimation methods is proposed and the results of experimental tests are presented.

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Note on Multiple Objective Dynamic Programming

Cited by 62 publications

References 0 publications

Optimization Models In Fire Egress Analysis For Residential Buildings

Optimization Models In Fire Egress Analysis For Residential Buildings

Discrete dynamic system control using multi-objective dynamic programming

A Relation of Dominance for the Bicriterion Bus Routing Problem

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