Multi-objective Optimisation of Multi-robot Task Allocation with Precedence Constraints

Efficacy of the multi-robot systems depends on proper sequencing and optimal allocation of robots to the tasks. Focuses on deciding the optimal allocation of set-of-robots to a set-of-tasks with precedence constraints considering multiple objectives. Taguchi’s design of experiments based parameter tuned genetic algorithm (GA) is developed for generalised task allocation of single-task robots to multi-robot tasks. The developed methodology is tested for 16 scenarios by varying the number of robots and number of tasks. The scenarios were tested in a simulated environment with a maximum of 20 robots and 40 multi-robot foraging tasks. The tradeoff between performance measures for the allocations obtained through GA for different task levels was used to decide the optimal number of robots. It is evident that the tradeoffs occur at 20 per cent of performance measures and the optimal number of robot varies between 10 and 15 for almost all the task levels. This method shows good convergence and found that the precedence constraints affect the optimal number of robots required for a particular task level

Genetic algorithm for process sequencing modelled as the travelling salesman problem with precedence constraints

This thesis addresses process sequencing subject to precedence constraints which arises as a subproblem in scheduling, planning and routing problems. The process sequencing problem can be modelled as the Travelling Salesman Problem with Precedence Constraints (TSPPC). In the general Travelling Salesman Problem (TSP) scenario, the salesman must travel from city to city; visiting each city exactly once and wishes to minimize the total distance travelled during the tour of all cities. TSPPC is similar in concept to TSP, except that it has a set of precedence constraints to be followed by the salesman. The exact methods that are used to find an optimal solution of the problem are only capable of handling small and medium sizes of instances. Genetic algorithms (GA) are heuristic optimization techniques based on the principles and mechanisms of natural evolution and can be used to solve larger instances and numerous side constraints with optimal or near-optimal solutions. However, the use of a conventional genetic algorithm procedure for TSP, with an order-based representation, might generate invalid candidate solutions when precedence constraints are involved. In this thesis, a new GA procedure is developed which includes chromosome’s repairing strategy based topological sort to handle the precedence constraints and to generate only feasible solution during the evolutionary process. The procedure to select the task in sequence is based on the “earliest position” techniques. This procedure is combined with a roulette wheel selection, linear order crossover and inversion mutation. The effectiveness and the stability of the proposed GA are then evaluated against a wide range of benchmark problems and the solutions are compared with the results obtained from research results published in the relevant literature. The results from the computational experiments demonstrate that the proposed GA procedure developed in this thesis is capable to tackle large-size problem and reach for optimal solutions. The developed GA procedure improved the performance of the algorithm with less number of generations and less convergence time in achieving optimal solutions. The genetic operators used are capable to always introduce new fitter offspring and free from being trapped in a local optimum. Therefore it can be stated that the proposed genetic algorithm is efficient to solve process sequencing modelled as the travelling salesman problem with precedence constraints. This result will greatly help to solve many real world sequencing problems especially in the field of assembly line design and management

Restricted Dynamic Programming Heuristic for Precedence Constrained Bottleneck Generalized TSP

We develop a restricted dynamical programming heuristic for a complicated traveling salesman problem: a) cities are grouped into clusters, resp. Generalized TSP; b) precedence constraints are imposed on the order of visiting the clusters, resp. Precedence Constrained TSP; c) the costs of moving to the next cluster and doing the required job inside one are aggregated in a minimax manner, resp. Bottleneck TSP; d) all the costs may depend on the sequence of previously visited clusters, resp. Sequence-Dependent TSP or Time Dependent TSP. Such multiplicity of constraints complicates the use of mixed integer-linear programming, while dynamic programming (DP) benefits from them; the latter may be supplemented with a branch-and-bound strategy, which necessitates a “DP-compliant” heuristic. The proposed heuristic always yields a feasible solution, which is not always the case with heuristics, and its precision may be tuned until it becomes the exact DP

Combining Heuristics in Assembly Sequence Planning

Assembly Sequence Planning is tackled by modelling and solving a planning problem that considers the execution of the plan in a system with multiple assembly machines. The objective of the plan is the minimization of the total assembly time (makespan). To meet this objective, the model takes into account the durations and resources for the assembly tasks, the change of configuration in the machines, and the transportation of intermediate subassemblies between different workstations. In order to solve the problem, different heuristics has been defined from two relaxed model of it, one considering only the precedence constraints among tasks, and the other one considering only the use of shared resources. From these basic heuristics, other ones have been defined, combining both types of information from the problem, so that the refinement produces substantial improvements over the initial heuristics.Ministerio de Ciencia y TecnologíaDPI2003-07146-C02-0

How the structure of precedence constraints may change the complexity class of scheduling problems

This survey aims at demonstrating that the structure of precedence constraints plays a tremendous role on the complexity of scheduling problems. Indeed many problems can be NP-hard when considering general precedence constraints, while they become polynomially solvable for particular precedence constraints. We also show that there still are many very exciting challenges in this research area

Models and Strategies for Variants of the Job Shop Scheduling Problem

Recently, a variety of constraint programming and Boolean satisfiability approaches to scheduling problems have been introduced. They have in common the use of relatively simple propagation mechanisms and an adaptive way to focus on the most constrained part of the problem. In some cases, these methods compare favorably to more classical constraint programming methods relying on propagation algorithms for global unary or cumulative resource constraints and dedicated search heuristics. In particular, we described an approach that combines restarting, with a generic adaptive heuristic and solution guided branching on a simple model based on a decomposition of disjunctive constraints. In this paper, we introduce an adaptation of this technique for an important subclass of job shop scheduling problems (JSPs), where the objective function involves minimization of earliness/tardiness costs. We further show that our technique can be improved by adding domain specific information for one variant of the JSP (involving time lag constraints). In particular we introduce a dedicated greedy heuristic, and an improved model for the case where the maximal time lag is 0 (also referred to as no-wait JSPs).Comment: Principles and Practice of Constraint Programming - CP 2011, Perugia : Italy (2011

A CSP model for simple non-reversible and parallel repair plans

Thiswork presents a constraint satisfaction problem (CSP) model for the planning and scheduling of disassembly and assembly tasks when repairing or substituting faulty parts. The problem involves not only the ordering of assembly and disassembly tasks, but also the selection of them from a set of alternatives. The goal of the plan is the minimization of the total repairing time, and the model considers, apart from the durations and resources used for the assembly and disassembly tasks, the necessary delays due to the change of configuration in the machines, and to the transportation of intermediate subassemblies between different machines. The problem considers that sub-assemblies that do not contain the faulty part are nor further disassembled, but allows non-reversible and parallel repair plans. The set of all feasible repair plans are represented by an extended And/Or graph. This extended representation embodies all of the constraints of the problem, such as temporal and resource constraints and those related to the selection of tasks for obtaining a correct plan.Ministerio de Educación y Ciencia DIP2006-15476-C02-0

A Constraint-based Model for Multi-objective Repair Planning

This work presents a constraint based model for the planning and scheduling of disconnection and connection tasks when repairing faulty components in a system. Since multi-mode operations are considered, the problem involves the ordering and the selection of the tasks and modes from a set of alternatives, using the shared resources efficiently. Additionally, delays due to change of configurations and transportation are considered. The goal is the minimization of two objective functions: makespan and cost. The set of all feasible plans are represented by an extended And/Or graph, that embodies all of the constraints of the problem, allowing non reversible and parallel plans. A simple branch-and-bound algorithm has been used for testing the model with different combinations of the functions to minimize using the weighted-sum approach.Ministerio de Educación y Ciencia DIP2006-15476-C02-0

Parallel algorithms for two processors precedence constraint scheduling

The final publication is available at link.springer.comPeer ReviewedPostprint (author's final draft

Profit-oriented disassembly-line balancing

As product and material recovery has gained importance, disassembly volumes have increased, justifying construction of disassembly lines similar to assembly lines. Recent research on disassembly lines has focused on complete disassembly. Unlike assembly, the current industry practice involves partial disassembly with profit-maximization or cost-minimization objectives. Another difference between assembly and disassembly is that disassembly involves additional precedence relations among tasks due to processing alternatives or physical restrictions. In this study, we define and solve the profit-oriented partial disassembly-line balancing problem. We first characterize different types of precedence relations in disassembly and propose a new representation scheme that encompasses all these types. We then develop the first mixed integer programming formulation for the partial disassembly-line balancing problem, which simultaneously determines (1) the parts whose demand is to be fulfilled to generate revenue, (2) the tasks that will release the selected parts under task and station costs, (3) the number of stations that will be opened, (4) the cycle time, and (5) the balance of the disassembly line, i.e. the feasible assignment of selected tasks to stations such that various types of precedence relations are satisfied. We propose a lower and upper-bounding scheme based on linear programming relaxation of the formulation. Computational results show that our approach provides near optimal solutions for small problems and is capable of solving larger problems with up to 320 disassembly tasks in reasonable time