Approximation algorithms for solving multi-objective optimization problems

This paper tries to cover the main aspects/properties related to scheduling problems, approximation algorithms, and multi-objective combinatorial optimization. Then, we try to describe the main techniques that can be used to solve such problems. In this paper, the reviews results relate to multi-objective optimization problems, exact and approximation search, with the aim of getting all Pareto optimal solutions for some NP-hard problems

Multiobjective Order Acceptance and Scheduling on Unrelated Parallel Machines with Machine Eligibility Constraints

This paper studies the order acceptance and scheduling problem on unrelated parallel machines with machine eligibility constraints. Two objectives are considered to maximize total net profit and minimize the makespan, and the mathematical model of this problem is formulated as multiobjective mixed integer linear programming. Some properties with respect to the objectives are analysed, and then a classic list scheduling (LS) rule named the first available machine rule is extended, and three new LS rules are presented, which focus on the maximization of the net profit, the minimization of the makespan, and the trade-off between the two objectives, respectively. Furthermore, a list-scheduling-based multiobjective parthenogenetic algorithm (LS-MPGA) is presented with parthenogenetic operators and Pareto-ranking and selection method. Computational experiments on randomly generated instances are carried out to assess the effectiveness and efficiency of the four LS rules under the framework of LS-MPGA and discuss their application environments. Results demonstrate that the performance of the LS-MPGA developed for trade-off is superior to the other three algorithms

A Multiple Criteria Genetic Algorithm Scheduling Tool for Production Scheduling in the Capital Goods Industry

Production planners usually aim to satisfy multiple objectives. This paper describes the development of a genetic algorithm tool that finds optimum trade-offs among delivery performance, resource utilisation, and workin-progress inventory. The tool was specifically developed to meet the requirements of capital goods companies that manufacture products with deep and complex product structures with components that have long and complicated routings. The model takes into account operation and assembly precedence relationships and finite capacity constraints. The tool was tested using various production problems that were obtained from a collaborating company. A series of experiments showed the tool provides a set of non-dominated solutions that enable the planner to choose an optimum trade-off according to their preferences. Previous research had optimised a single objective function. This is the first scheduling tool of its type that has simultaneously optimised delivery performance, resource utilisation and work-in-progress inventory. The quality of the schedules produced was significantly better than the approaches used by the collaborating company