Multi-Objective Optimization
• NP-Hard
• Conflicting objectives
– Flow shop with both minimum makespan and tardiness objective
– TSP problem with minimum distance, time and cost objective
– Container management – balancing volume, weight and value
• Has no single solution but a set of solutions called Pareto
Optimal Solutions
– A solution is Pareto optimal if it not possible to improve a single
objective without deteriorating another objective
• The objective is to find the Pareto optimal set and the Pareto
front
• Metaheuristics can be used to approximate the Pareto
optimal set
– Both S and P – metaheuristics are used
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Metaheuristics for Multiobjective Optimization
• Fitness assignment – assign a scalar value to the quality of the
solution
• Diversity preserving – generate a diverse set of solutions
• Elitism – Select the best set of solutions at every step
General strategies
• Aggregation – use an aggregation method to covert the problem
into mono-objective
• Weighted Metric – preselect a reference value of the objective
function and measure the distance of the other solutions from this
reference and minimize this distance
• Parallel approach- treat each objective individually. Then crossover
and mutate the solutions from each objective to find a compromise
• Sequential approach- search in a preference order of objectives
• Dominance based- search using a dominant criteria set by the final
user
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Hybrid Metaheuristics
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Combining S and P or a S and S metaheuristics
Combining with other math programming methods
Metaheuristics and AI
Main classification
– Relay - sequential
– Teamwork – cooperative search
– Example
– Branch and bound – the upper bound of a node can be obtained using
metaheuristic which also yields a partial solution upto the given node
– Dynamic programming- if the state-action space is large,
metaheuristics can reduce the action space by performing a local
search among a set of all possible actions for a state
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Parallel Metaheuristics
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Speed up search
Improve quality
Solve large NP hard problems
Parallel designs
– Algorithmic level – Independent or cooperative self-contained
metaheuristics approaches are used in parallel
– Iterative level – At an iteration search is done in several
neighborhoods by different computers to speed up search
– Solution level- the generation of the objective function value and the
check for any constraint violations is done in parallel for a set of
solutions generated by one search
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Single-Metaheuristics
• Accept nonimproving neighbors
– Tabu search and simulated annealing
• Iterating with different initial solutions
– Multistart local search, greedy randomized adaptive search procedure
(GRASP), iterative local search
• Changing the neighborhood
– Variable neighborhood search
• Changing the objective function or the input to the problem in
a effort to solve the original problem more effectively.
– Guided local search
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Population-based metaheuristics
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Nature-inspired
Initialize a population
A new population of solutions is generated
Integrate the new population into the current one using one these
methods – by replacement which is a selection process from the new and
current solutions
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Evolutionary Algorithms – genetic algorithm
Estimation of distribution algorithm (EDA)
Scatter search
Evolutionary programming- genetic programming
Swarm Intelligence
• Ant colony
• Particle swarm optimization (PSO)
• Bee colony
– Artificial Immune system AIS
• Continue until a stopping criteria is reached
• The generation and replacement process could be memoryless or some
search memory is used
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What was covered
1) S metaheuristics
Applications
• Some methods in detail and some
1) Standard OR problems: TSP, knapsack,
only introduction
Setcovering
2) P metaheuristics
2) Scheduling and Manufacturing
• Some methods in detail and some
Job-shop
only introduction
Flowshop
3) Metaheuristics for multi-objective
Flexible flowshop
Optimization –only intro
Lot-sizing
4) Hybrid- only intro
PERT CPM
5) Parallel -only intro
Reservation and timetabling
Several Special heuristics
Workforce scheduling
1) Dispatch rules
2) Composite dispatch rules – ATC
3) Shifting bottleneck
4) Profile fitting
5) Flexible flow line loading FFLL
6) ELSP- frequency fixing and sequencing FFS
7) Maximizing number of jobs processed
8) Barriers algorithm for reservation
9) Graph coloring heuristic
10) FF and FFD First fit decreasing
11) Day-off scheduling and crew scheduling
12) Tournament scheduling
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What was covered
1) S metaheuristics
Applications
• Some methods in detail and some
1) Standard OR problems: TSP, knapsack,
only introduction
Setcovering
2) P metaheuristics
2) Scheduling in Manufacturing
• Some methods in detail and some
Job-shop
only introduction
Flowshop
3) Metaheuristics for multi-objective
Flexible flowshop
Optimization –only intro
Lot-sizing
4) Hybrid- only intro
PERT CPM
5) Parallel -only intro
3) Scheduling in Service
Several Special heuristics
Reservation and timetabling
1) Dispatch rules
Workforce scheduling
2) Composite dispatch rules – ATC
3) Shifting bottleneck
4) Profile fitting
5) Flexible flow line loading FFLL
6) ELSP- frequency fixing and sequencing FFS
7) Maximizing number of jobs processed
8) Barriers algorithm for reservation
9) Graph coloring heuristic
10) FF and FFD First fit decreasing
11) Day-off scheduling and crew scheduling
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12) Tournament scheduling