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 1

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 2

Hybrid Metaheuristics 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 3

Parallel Metaheuristics 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 4

Single-Metaheuristics 5 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

Population-based metaheuristics 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 – 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 6

What was covered 7 1) S metaheuristics Some methods in detail and some only introduction 2) P metaheuristics Some methods in detail and some only introduction 3) Metaheuristics for multi-objective Optimization –only intro 4) Hybrid- only intro 5) Parallel -only intro Applications 1) Standard OR problems: TSP, knapsack, Setcovering 2) Scheduling and Manufacturing Job-shop Flowshop Flexible flowshop Lot-sizing PERT CPM Reservation and timetabling Workforce scheduling Several Special heuristics 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

What was covered 8 1) S metaheuristics Some methods in detail and some only introduction 2) P metaheuristics Some methods in detail and some only introduction 3) Metaheuristics for multi-objective Optimization –only intro 4) Hybrid- only intro 5) Parallel -only intro Applications 1) Standard OR problems: TSP, knapsack, Setcovering 2) Scheduling in Manufacturing Job-shop Flowshop Flexible flowshop Lot-sizing PERT CPM 3) Scheduling in Service Reservation and timetabling Workforce scheduling Several Special heuristics 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