An architecture for solving sequencing and resource allocation problems using approximation methods

In the search for better optimisation techniques, new methods that mix artificial intelligence and operations research have emerged. Search heuristics are integrated with optimisation algorithms. Approximation methods, like Hill Climbing, Simulated Annealing, and Tabu Search, that have been used with success in combinatorial optimisation problems, are one of such research lines. This paper presents the key elements of approximation methods and combines them in a tool appropriate for solving sequencing and resource allocation problems. The system permits a clear division between problem specification and problem solving, allowing a declarative representation and therefore minimising developing costs. The key issues discussed in this work are a model for representing this class of problems in a standard form, a set of strategies for applying the approximation methodology, and an expert system that dynamically manipulates the strategies' parameters.     

Tabu Search directed by direct search methods for nonlinear global optimization

In recent years, there has been a great deal of interest in metaheuristics in the optimization community. Tabu Search (TS) represents a popular class of metaheuristics. However, compared with other metaheuristics like genetic algorithm and simulated annealing, contributions of TS that deals with continuous problems are still very limited. In this paper, we introduce a continuous TS called Directed Tabu Search (DTS) method. In the DTS method, direct-search-based strategies are used to direct a tabu search. These strategies are based on the well-known Nelder–Mead method and a new pattern search procedure called adaptive pattern search. Moreover, we introduce a new tabu list conception with anti-cycling rules called Tabu Regions and Semi-Tabu Regions. In addition, Diversification and Intensification Search schemes are employed. Numerical results show that the proposed method is promising and produces high quality solutions.     

An Interactive Method for 0-1 Multiobjective Problems Using Simulated Annealing and Tabu Search

This paper presents an interactive method for solving general 0-1 multiobjective linear programs using Simulated Annealing and Tabu Search. The interactive protocol with the decision maker is based on the specification of reservation levels for the objective function values. These reservation levels narrow the scope of the search in each interaction in order to identify regions of major interest to the decision maker. Metaheuristic approaches are used to generate potentially nondominated solutions in the computational phases. Generic versions of Simulated Annealing and Tabu Search for 0-1 single objective linear problems were developed which include a general routine for repairing unfeasible solutions. This routine improves significantly the results of single objective problems and, consequently, the quality of the potentially nondominated solutions generated for the multiobjective problems. Computational results and examples are presented.     

Solving Vehicle Routing Problems Using Constraint Programming and Metaheuristics

Constraint Programming typically uses the technique of depth-first branch and bound as the method of solving optimization problems. Although this method can give the optimal solution, for large problems, the time needed to find the optimal can be prohibitive. This paper introduces a method for using local search techniques within a Constraint Programming framework, and applies this technique to vehicle routing problems. We introduce a Constraint Programming model for vehicle routing, and a system for integrating Constraint Programming and local search techniques. We then describe how the method can be accelerated by handling core constraints using fast local checks, while other more complex constraints are left to the constraint propagation system. We have coupled our local search method with a meta-heuristic to avoid the search being trapped in local minima. Several meta-heuristics are investigated ranging from a simple Tabu Search method to Guided Local Search. An empirical study over benchmark problems shows the relative merits of these techniques. Investigations indicate that the specific long-term memory technique used by Guided Local Search can be used as a diversification method for Tabu Search, resulting in significant benefit. Several new best solutions on the Solomon problems are found in relatively few iterations of our algorithm.     

Managing the tabu list length using a fuzzy inference system: an application to examination timetabling

In this paper, we present an application of Tabu Search (TS) to the examination timetabling problem. One of the drawbacks of this meta-heuristic is related to the need of tuning some parameter (like tabu tenure) whose value affects the performance of the algorithm. The importance of developing an automatic procedure is clear considering that most of the users of timetabling software, like academic staff, do not have the expertise to conduct such tuning. The goal of this paper is to present a method to automatically manage the memory in the TS using a Decision Expert System. More precisely a Fuzzy Inference Rule Based System (FIRBS) is implemented to handle the tabu tenure based on two concepts, “Frequency” and “Inactivity”. These concepts are related respectively with the number of times a move is introduced in the tabu list and the last time (in number of iterations) the move was attempted and prevented by the tabu status. Computational results show that the implemented FIRBS handles well the tuning of the tabu status duration improving, as well, the performance of Tabu Search.     

Comparison of metaheuristic algorithms for Examination Timetabling Problem

SA, TS, GA and ACS are four of the main algorithms for solving challenging problems of intelligent systems. In this paper we consider Examination Timetabling Problem that is a common problem for all universities and institutions of higher education. There are many methods to solve this problem, In this paper we use Simulated Annealing, Tabu Search, Genetic Algorithm and Ant Colony System in their basic frameworks for solving this problem and compare results of them with each other.     

The development of a multi-objective Tabu Search algorithm for continuous optimisation problems

While there have been many adaptations of some of the more popular meta-heuristics for continuous multi-objective optimisation problems, Tabu Search has received relatively little attention, despite its suitability and effectiveness on a number of real-world design optimisation problems. In this paper we present an adaptation of a single-objective Tabu Search algorithm for multiple objectives. Further, inspired by path relinking strategies common in discrete optimisation problems, we enhance our algorithm to allow it to handle problems with large numbers of design variables. This is achieved by a novel parameter selection strategy that, unlike a full parametric analysis, avoids the use of objective function evaluations, thus keeping the overall computational cost of the procedure to a minimum. We assess the performance of our two Tabu Search variants on a range of standard test functions and compare it to a leading multi-objective Genetic Algorithm, NSGA-II. The path relinking-inspired parameter selection scheme gives a clear performance improvement over the basic multi-objective Tabu Search adaptation and both variants perform comparably with the NSGA-II.     

Tabu Search with Simple Ejection Chains for Coloring Graphs

We present a Tabu Search (TS) method that employs a simple version of ejection chains for coloring graphs. The procedure is tested on a set of benchmark problems. Empirical results indicate that the proposed TS implementation outperforms other metaheuristic methods, including Simulated Annealing, a previous version of Tabu Search and a recent implementation of a Greedy Randomized Adaptive Search Procedure (GRASP).     

Solving large scale Max Cut problems via tabu search

In recent years many algorithms have been proposed in the literature for solving the Max-Cut problem. In this paper we report on the application of a new Tabu Search algorithm to large scale Max-cut test problems. Our method provides best known solutions for many well-known test problems of size up to 10,000 variables, although it is designed for the general unconstrained quadratic binary program (UBQP), and is not specialized in any way for the Max-Cut problem.     

Hashing vectors for tabu search

Tabu search as proposed by Glover [3,4] has proven to be a very effective metaheuristic for hard problems. In this paper we propose that hash functions be used to record the solutions encountered during recent iterations of the search in a long list. Hash values of potential solutions can be compared to the values on the list for the purpose of avoiding cycling. This frees the algorithm designer of the need to consider cycling when creating tabu restrictions based on move attributes. We suggest specific functions that result in very good performance.     

Hybrid scatter tabu search for unconstrained global optimization

The problem of finding a global optimum of an unconstrained multimodal function has been the subject of intensive study in recent years, giving rise to valuable advances in solution methods. We examine this problem within the framework of adaptive memory programming (AMP), focusing particularly on AMP strategies that derive from an integration of Scatter Search and Tabu Search. Computational comparisons involving 16 leading methods for multimodal function optimization, performed on a testbed of 64 problems widely used to calibrate the performance of such methods, disclose that our new Scatter Tabu Search (STS) procedure is competitive with the state-of-the-art methods in terms of the average optimality gap achieved.     

Comparing local search metaheuristics for the maximum diversity problem

The Maximum Diversity Problem (MDP) requires to extract a subset M of given cardinality from a set N, maximising the sum of the pair-wise diversities between the extracted elements. The MDP has recently been the subject of much research, and several sophisticated heuristics have been proposed to solve it. The present work compares four local search metaheuristics for the MDP, all based on the same Tabu Search procedure, with the aim to identify what additional elements provide the strongest improvement. The four metaheuristics are an Exploring Tabu Search, a Scatter Search, a Variable Neighbourhood Search and a simple Random Restart algorithm. All of them prove competitive with the best algorithms proposed in the literature. Quite surprisingly, the best ones are the simple Random Restart algorithm and a Variable Neighbourhood Search algorithm with an unusual parameter setting, which makes it quite close to random restart. Although this is probably related to the elementary structure of the MDP, it also suggests that, more often than expected, simpler algorithms might be better.     

Nonlinear and Geometric Programming – Current Status

Great strides have been made in nonlinear programming (NLP) in the last 5 years. In smooth NLP, there are now several reliable and efficient codes capable of solving large problems. Most of these implement GRG or SQP methods, and new software using interior point algorithms is under development. NLP software is now much easier to use, as it is interfaced with many modeling systems, including MSC/NASTRAN, and ANSYS for structural problems, GAMS and AMPL for general optimization, Matlab and Mathcad for general mathematical problems, and the widely used Microsoft Excel spreadsheet. For mixed integer problems, branch and bound and outer approximation codes are now available and are coupled to some of the above modeling systems, while search methods like Tabu Search and Genetic algorithms permit combinatorial, nonsmooth, and nonconvex problems to be attacked.     

A General Meta-Heuristic Based Solver for Combinatorial Optimisation Problems

In recent years, there have been many studies in which tailored heuristics and meta-heuristics have been applied to specific optimisation problems. These codes can be extremely efficient, but may also lack generality. In contrast, this research focuses on building a general-purpose combinatorial optimisation problem solver using a variety of meta-heuristic algorithms including Simulated Annealing and Tabu Search. The system is novel because it uses a modelling environment in which the solution is stored in dense dynamic list structures, unlike a more conventional sparse vector notation. Because of this, it incorporates a number of neighbourhood search operators that are normally only found in tailored codes and it performs well on a range of problems. The general nature of the system allows a model developer to rapidly prototype different problems. The new solver is applied across a range of traditional combinatorial optimisation problems. The results indicate that the system achieves good performance in terms of solution quality and runtime.     

Continuous ant colony system and tabu search algorithms hybridized for global minimization of continuous multi-minima functions

A new hybrid optimization method, combining Continuous Ant Colony System (CACS) and Tabu Search (TS) is proposed for minimization of continuous multi-minima functions. The new algorithm incorporates the concepts of promising list, tabu list and tabu balls from TS into the framework of CACS. This enables the resultant algorithm to avoid bad regions and to be guided toward the areas more likely to contain the global minimum. New strategies are proposed to dynamically tune the radius of the tabu balls during the execution and also to handle the variable correlations. The promising list is also used to update the pheromone distribution over the search space. The parameters of the new method are tuned based on the results obtained for a set of standard test functions. The results of the proposed scheme are also compared with those of some recent ant based and non-ant based meta-heuristics, showing improvements in terms of accuracy and efficiency.     

A simple Tabu Search method to solve the mixed-integer linear bilevel programming problem

Multilevel programming is characterized as mathematical programming to solve decentralized planning problems. The models partition control over decision variables among ordered levels within a hierarchical planning structure of which the linear bilevel form is a special case of a multilevel programming problem. In a system with such a hierarchical structure, the high-level decision making situations generally require inclusion of zero-one variables representing ‘yes-no’ decisions. We provide a mixed-integer linear bilevel programming formulation in which zero-one decision variables are controlled by a high-level decision maker and real-value decision variables are controlled by a low-level decision maker. An algorithm based on the short term memory component of Tabu Search, called Simple Tabu Search, is developed to solve the problem, and two supplementary procedures are proposed that provide variations of the algorithm. Computational results disclose that our approach is effective in terms of both solution quality and efficiency.     

A Hybrid Meta-Heuristic for Multi-Objective Optimization: MOSATS

Real optimization problems often involve not one, but multiple objectives, usually in conflict. In single-objective optimization there exists a global optimum, while in the multi-objective case no optimal solution is clearly defined but rather a set of solutions, called the Pareto-optimal front. Thus, the goal of multi-objective strategies is to generate a set of non-dominated solutions as an approximation to this front. However, the majority of problems of this kind cannot be solved exactly because they have very large and highly complex search spaces. In recent years, meta-heuristics have become important tools for solving multi-objective problems encountered in industry as well as in the theoretical field. This paper presents a novel approach based on hybridizing Simulated Annealing and Tabu Search. Experiments on the Graph Partitioning Problem show that this new method is a better tool for approximating the efficient set than other strategies also based on these meta-heuristics.