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11.5 Real-World Optimisation
Real-world optimisation problems occur in many applications such as engineering
design, scientific modelling, image processing, etc. In general, these problems
contain non-linear objective functions of mixed design variables i.e. continuous and
discrete, with linear as well as non-linear constraints. These problems might have
several local optima, causing trouble to heuristic methods, as these methods do not
guarantee to locate the global optimum. For a wide range of real-world optimisation
problems, though, a near-optimal or a better-than-known solution is considered a
satisfactory result of an optimisation problem.
Real-world systems are, in general, large and very complex. They require to
process a large amount of data, to perform complex optimisation and make decisions
fast [55]. Real-world optimisation problems consist of several characteristics that
increase the complexity of the optimum solution search. Some of the characteristics
of the problems for which parameter control in optimisation could appear advantageous are the following:
• Number and type of variables: Large number of decision variables, with problems
that are known as large-scale global optimisation (LSGO) problems [56]. Also,
mixed-integer problems, where different types of variables are optimised.
• Dynamic problems: Problems that are changing over time.
• Problems under uncertainty: The variables of the problem have some uncertainty.
• Number of objectives: Problems that require optimising more than one objective
function simultaneously and need to be solved by a multi/many-objective
approach.
• Nested problems: Multi-/bilevel optimisation, where one optimisation problem
has another optimisation problem as a constraint.
As mentioned before properly defined control parameters play a crucial role
in effectively handling the above characteristics and solving such problems. For
example, with increasing dimensionality of the problem, its landscape complexity
grows and the search space increases exponentially. However, an optimisation
algorithm must be able to explore the entire search space efficiently.
11.5.1 Large-Scale Global Optimisation
LSGO, where the problem dimension D (the number of variables to be optimised)
has an order of magnitude of around D = 1000, is an active research field
due to the growing number of large-scale optimisation problems in engineering,
manufacturing and economy applications (such as bio-computing, data or web
mining, scheduling, vehicle routing, etc.) [57, 58]. Most engineering problems
have an exponential increase in the number of required decision variables [59].
Advances in machine learning and the wide use of deep artificial neural networks
M. Antoniou et al.
11.5 Real-World Optimisation
Real-world optimisation problems occur in many applications such as engineering
design, scientific modelling, image processing, etc. In general, these problems
contain non-linear objective functions of mixed design variables i.e. continuous and
discrete, with linear as well as non-linear constraints. These problems might have
several local optima, causing trouble to heuristic methods, as these methods do not
guarantee to locate the global optimum. For a wide range of real-world optimisation
problems, though, a near-optimal or a better-than-known solution is considered a
satisfactory result of an optimisation problem.
Real-world systems are, in general, large and very complex. They require to
process a large amount of data, to perform complex optimisation and make decisions
fast [55]. Real-world optimisation problems consist of several characteristics that
increase the complexity of the optimum solution search. Some of the characteristics
of the problems for which parameter control in optimisation could appear advantageous are the following:
• Number and type of variables: Large number of decision variables, with problems
that are known as large-scale global optimisation (LSGO) problems [56]. Also,
mixed-integer problems, where different types of variables are optimised.
• Dynamic problems: Problems that are changing over time.
• Problems under uncertainty: The variables of the problem have some uncertainty.
• Number of objectives: Problems that require optimising more than one objective
function simultaneously and need to be solved by a multi/many-objective
approach.
• Nested problems: Multi-/bilevel optimisation, where one optimisation problem
has another optimisation problem as a constraint.
As mentioned before properly defined control parameters play a crucial role
in effectively handling the above characteristics and solving such problems. For
example, with increasing dimensionality of the problem, its landscape complexity
grows and the search space increases exponentially. However, an optimisation
algorithm must be able to explore the entire search space efficiently.
11.5.1 Large-Scale Global Optimisation
LSGO, where the problem dimension D (the number of variables to be optimised)
has an order of magnitude of around D = 1000, is an active research field
due to the growing number of large-scale optimisation problems in engineering,
manufacturing and economy applications (such as bio-computing, data or web
mining, scheduling, vehicle routing, etc.) [57, 58]. Most engineering problems
have an exponential increase in the number of required decision variables [59].
Advances in machine learning and the wide use of deep artificial neural networks