proposed such a hybrid approach in which a memory-based adaptive partitioning algorithm was embedded into an archive-based multi-objective evolutionary algorithm, developed relying on the structure of NSGA II [18].
3.3 Surrogate Model-Based Optimizers
This research line consists in building tailored computationally cheap surrogate
models of the optimization problem, aiming to accelerate the convergence and
reduce the computational burden. Two approaches have been developed [8, 9] in
which the surrogate model of the optimization problem is based on:
(1) mixed-integer linear programming (MILP) [8,16]. This surrogate model relies
on piecewise linear approximations, via brute-force sensitivity computation, of
the objective functions and inequality constraints. Additionally, the use of
constraint programming [19] for solving the MILP problem at the core of the
surrogate model has been explored in [9].
(2) nonlinear programming (NLP). This surrogate model relies on curve fitting of
objectives and inequality constraints via either quadratic polynomial functions
or higher order polynomial functions (e.g. cubic) [9].
In both proposed methodologies which include such surrogate models, the
approximation of the Pareto front is generated upon applying the well-known
e-constraint method [20] to the MOO surrogate problems.
3.4 Local Search
The last optimization research strand investigated in this project concerns the local
search [10]. The latter is useful not only in the context of hybrid algorithms (see
Sect. 3.2) but also in many real-world computationally expensive simulation-based
applications, where the aim is to improve a given system state locally with limited
computational budget. To this end, a new neighborhood-based iterative local search
method has been proposed [10]. This method aims at steering the search along any
desired direction in the objectives space and resorting to first derivatives approximation and linear programming optimization.
A Synthesis of Optimization Approaches …
25
3.3 Surrogate Model-Based Optimizers
This research line consists in building tailored computationally cheap surrogate
models of the optimization problem, aiming to accelerate the convergence and
reduce the computational burden. Two approaches have been developed [8, 9] in
which the surrogate model of the optimization problem is based on:
(1) mixed-integer linear programming (MILP) [8,16]. This surrogate model relies
on piecewise linear approximations, via brute-force sensitivity computation, of
the objective functions and inequality constraints. Additionally, the use of
constraint programming [19] for solving the MILP problem at the core of the
surrogate model has been explored in [9].
(2) nonlinear programming (NLP). This surrogate model relies on curve fitting of
objectives and inequality constraints via either quadratic polynomial functions
or higher order polynomial functions (e.g. cubic) [9].
In both proposed methodologies which include such surrogate models, the
approximation of the Pareto front is generated upon applying the well-known
e-constraint method [20] to the MOO surrogate problems.
3.4 Local Search
The last optimization research strand investigated in this project concerns the local
search [10]. The latter is useful not only in the context of hybrid algorithms (see
Sect. 3.2) but also in many real-world computationally expensive simulation-based
applications, where the aim is to improve a given system state locally with limited
computational budget. To this end, a new neighborhood-based iterative local search
method has been proposed [10]. This method aims at steering the search along any
desired direction in the objectives space and resorting to first derivatives approximation and linear programming optimization.
A Synthesis of Optimization Approaches …
25