Multi-Objective Optimization

1. 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

2. 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

3. 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

4. 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

5. 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

6. 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

7. What was covered • 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 Dispatch rules Composite dispatch rules – ATC Shifting bottleneck Profile fitting Flexible flow line loading FFLL ELSP- frequency fixing and sequencing FFS Maximizing number of jobs processed Barriers algorithm for reservation Graph coloring heuristic FF and FFD First fit decreasing Day-off scheduling and crew scheduling Tournament scheduling

8. What was covered • 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 Dispatch rules Composite dispatch rules – ATC Shifting bottleneck Profile fitting Flexible flow line loading FFLL ELSP- frequency fixing and sequencing FFS Maximizing number of jobs processed Barriers algorithm for reservation Graph coloring heuristic FF and FFD First fit decreasing Day-off scheduling and crew scheduling Tournament scheduling