A direct memetic approach to the solution of multi-objective optimal control problems

Massimiliano Vasile; Lorenzo Ricciardi

doi:10.1109/SSCI.2016.7850103

A direct memetic approach to the solution of multi-objective optimal control problems

Massimiliano Vasile, Lorenzo Ricciardi

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution book

6 Citations (Scopus)

89 Downloads (Pure)

Abstract

This paper proposes a memetic direct transcription algorithm to solve Multi-Objective Optimal Control Problems (MOOCP). The MOOCP is first transcribed into a Non-linear Programming Problem (NLP) with Direct Finite Elements in Time (DFET) and then solved with a particular formulation of the Multi Agent Collaborative Search (MACS) framework. Multi Agent Collaborative Search is a memetic algorithm in which a population of agents combines local search heuristics, exploring the neighbourhood of each agent, with social actions exchanging information among agents. A collection of all Pareto optimal solutions is maintained in an archive that evolves towards the Pareto set. In the approach proposed in this paper, individualistic actions run a local search, from random points within the neighbourhood of each agent, solving a normalised Pascoletti-Serafini scalarisation of the multi-objective NLP problem. Social actions, instead, solve a bi-level problem in which the lower level handles only the constraint equations while the upper level handles only the objective functions. The proposed approach is tested on the multi-objective extensions of two well-known optimal control problems: the Goddard Rocket problem, and the maximum energy orbit rise problem.

Original language	English
Title of host publication	2016 IEEE Symposium Series on Computational Intelligence, SSCI 2016
Place of Publication	Piscataway
ISBN (Electronic)	9781509042401
DOIs	https://doi.org/10.1109/SSCI.2016.7850103
Publication status	Published - 13 Feb 2017
Event	2016 IEEE Symposium Series on Computational Intelligence, SSCI 2016 - Royal Olympic Hotel, Athens, Greece Duration: 6 Dec 2016 → 9 Dec 2016 http://ssci2016.cs.surrey.ac.uk/

Conference

Conference	2016 IEEE Symposium Series on Computational Intelligence, SSCI 2016
Abbreviated title	SSCI 2016
Country/Territory	Greece
City	Athens
Period	6/12/16 → 9/12/16
Internet address	http://ssci2016.cs.surrey.ac.uk/

Keywords

optimal control
linear programming
optimization
memetics
collaboration
finite element analysis
sociology
search problems
nonlinear programming
pareto optimisation

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10.1109/SSCI.2016.7850103

Vasile-etal-SSCI-2016-A-direct-memetic-approach-to-the-solution-of-multi-objective-optimal-control-problemsAccepted author manuscript, 442 KB

Cite this

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title = "A direct memetic approach to the solution of multi-objective optimal control problems",

abstract = "This paper proposes a memetic direct transcription algorithm to solve Multi-Objective Optimal Control Problems (MOOCP). The MOOCP is first transcribed into a Non-linear Programming Problem (NLP) with Direct Finite Elements in Time (DFET) and then solved with a particular formulation of the Multi Agent Collaborative Search (MACS) framework. Multi Agent Collaborative Search is a memetic algorithm in which a population of agents combines local search heuristics, exploring the neighbourhood of each agent, with social actions exchanging information among agents. A collection of all Pareto optimal solutions is maintained in an archive that evolves towards the Pareto set. In the approach proposed in this paper, individualistic actions run a local search, from random points within the neighbourhood of each agent, solving a normalised Pascoletti-Serafini scalarisation of the multi-objective NLP problem. Social actions, instead, solve a bi-level problem in which the lower level handles only the constraint equations while the upper level handles only the objective functions. The proposed approach is tested on the multi-objective extensions of two well-known optimal control problems: the Goddard Rocket problem, and the maximum energy orbit rise problem.",

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N2 - This paper proposes a memetic direct transcription algorithm to solve Multi-Objective Optimal Control Problems (MOOCP). The MOOCP is first transcribed into a Non-linear Programming Problem (NLP) with Direct Finite Elements in Time (DFET) and then solved with a particular formulation of the Multi Agent Collaborative Search (MACS) framework. Multi Agent Collaborative Search is a memetic algorithm in which a population of agents combines local search heuristics, exploring the neighbourhood of each agent, with social actions exchanging information among agents. A collection of all Pareto optimal solutions is maintained in an archive that evolves towards the Pareto set. In the approach proposed in this paper, individualistic actions run a local search, from random points within the neighbourhood of each agent, solving a normalised Pascoletti-Serafini scalarisation of the multi-objective NLP problem. Social actions, instead, solve a bi-level problem in which the lower level handles only the constraint equations while the upper level handles only the objective functions. The proposed approach is tested on the multi-objective extensions of two well-known optimal control problems: the Goddard Rocket problem, and the maximum energy orbit rise problem.

AB - This paper proposes a memetic direct transcription algorithm to solve Multi-Objective Optimal Control Problems (MOOCP). The MOOCP is first transcribed into a Non-linear Programming Problem (NLP) with Direct Finite Elements in Time (DFET) and then solved with a particular formulation of the Multi Agent Collaborative Search (MACS) framework. Multi Agent Collaborative Search is a memetic algorithm in which a population of agents combines local search heuristics, exploring the neighbourhood of each agent, with social actions exchanging information among agents. A collection of all Pareto optimal solutions is maintained in an archive that evolves towards the Pareto set. In the approach proposed in this paper, individualistic actions run a local search, from random points within the neighbourhood of each agent, solving a normalised Pascoletti-Serafini scalarisation of the multi-objective NLP problem. Social actions, instead, solve a bi-level problem in which the lower level handles only the constraint equations while the upper level handles only the objective functions. The proposed approach is tested on the multi-objective extensions of two well-known optimal control problems: the Goddard Rocket problem, and the maximum energy orbit rise problem.

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KW - collaboration

KW - finite element analysis

KW - sociology

KW - search problems

KW - nonlinear programming

KW - pareto optimisation

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CY - Piscataway

T2 - 2016 IEEE Symposium Series on Computational Intelligence, SSCI 2016

Y2 - 6 December 2016 through 9 December 2016

ER -

A direct memetic approach to the solution of multi-objective optimal control problems

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