Heuristic for solving capacitor allocation problems in electric energy radial distribution networks

The goal of the capacitor allocation problem in radial distribution networks is to minimize technical losses with consequential positive impacts on economic and environmental areas. The main objective is to define the size and location of the capacitors while considering load variations in a given horizon. The mathematical formulation for this planning problem is given by an integer nonlinear mathematical programming model that demands great computational effort to be solved. With the goal of solving this problem, this paper proposes a methodology that is composed of heuristics and Tabu Search procedures. The methodology presented explores network system characteristics of the network system reactive loads for identifying regions where procedures of local and intensive searches should be performed. A description of the proposed methodology and an analysis of computational results obtained which are based on several test systems including actual systems are presented. The solutions reached are as good as or better than those indicated by well referenced methodologies. The technique proposed is simple in its use and does not require calibrating an excessive amount of parameters, making it an attractive alternative for companies involved in the planning of radial distribution networks

Combinatorial optimization and metaheuristics

Today, combinatorial optimization is one of the youngest and most active areas of discrete mathematics. It is a branch of optimization in applied mathematics and computer science, related to operational research, algorithm theory and computational complexity theory. It sits at the intersection of several fields, including artificial intelligence, mathematics and software engineering. Its increasing interest arises for the fact that a large number of scientific and industrial problems can be formulated as abstract combinatorial optimization problems, through graphs and/or (integer) linear programs. Some of these problems have polynomial-time (“efficient”) algorithms, while most of them are NP-hard, i.e. it is not proved that they can be solved in polynomial-time. Mainly, it means that it is not possible to guarantee that an exact solution to the problem can be found and one has to settle for an approximate solution with known performance guarantees. Indeed, the goal of approximate methods is to find “quickly” (reasonable run-times), with “high” probability, provable “good” solutions (low error from the real optimal solution). In the last 20 years, a new kind of algorithm commonly called metaheuristics have emerged in this class, which basically try to combine heuristics in high level frameworks aimed at efficiently and effectively exploring the search space. This report briefly outlines the components, concepts, advantages and disadvantages of different metaheuristic approaches from a conceptual point of view, in order to analyze their similarities and differences. The two very significant forces of intensification and diversification, that mainly determine the behavior of a metaheuristic, will be pointed out. The report concludes by exploring the importance of hybridization and integration methods

Simulated Annealing Algorithm for the Linear Ordering Problem: The Case of Tanzania Input Output Tables

Linear Ordering is a problem of ordering the rows and columns of a matrix such that the sum of the upper triangle values is as large as possible. The problem has many applications including aggregation of individual preferences, weighted ancestry relationships and triangulation of input-output tables in economics. As a result, many researchers have been working on the problem which is known to be NP-hard. Consequently, heuristic algorithms have been developed and implemented on benchmark data or specific real-world applications. Simulated Annealing has seldom been used for this problem. Furthermore, only one attempt has been done on the Tanzanian input output table data. This article presents a Simulated Annealing approach to the problem and compares results with previous work on the same data using Great Deluge algorithm. Three cooling schedules are compared, namely linear, geometric and Lundy & Mees. The results show that Simulated Annealing and Great Deluge provide similar results including execution time and final solution quality. It is concluded that Simulated Annealing is a good algorithm for the Linear Ordering problem given a careful selection of required parameters. Keywords: Combinatorial Optimization; Linear Ordering Problem; Simulated Annealing; Triangulation; Input Output table

A Group Theoretic Tabu Search Methodology for Solving the Theater Distribution Vehicle Routing and Scheduling Problem

The application of Group Theory to Tabu Search is a new and exciting field of research. This dissertation applies and extends some of Colletti\u27s (1999) seminal work in group theory and metaheuristics in order to solve the theater distribution vehicle routing and scheduling problem (TDVRSP). This research produced a robust, efficient, effective and flexible generalized theater distribution model that prescribes the routing and scheduling of multi-modal theater transportation assets to provide economically efficient time definite delivery of cargo to customers. In doing so, advances are provided in the field of group theoretic tabu search and its application to difficult combinatorial optimization problems, e.g., the multiple trip multiple services vehicle routing and scheduling problem with hubs and other defining constraints

An Adaptive Tabu Search Heuristic for the Location Routing Pickup and Delivery Problem with Time Windows with a Theater Distribution Application

The time constrained pickup and delivery problem (PDPTW) is a problem of finding a set of routes for a fleet of vehicles in order to satisfy a set of transportation requests. Each request represents a user-specified pickup and delivery location. The PDPTW may be used to model many problems in logistics and public transportation. The location routing problem (LRP) is an extension of the vehicle routing problem where the solution identifies the optimal location of the depots and provides the vehicle schedules and distribution routes. This dissertation seeks to blend the PDPTW and LRP areas of research and formulate a location scheduling pickup and delivery problem with time windows (LPDPTW) in order to model the theater distribution problem and find excellent solutions. This research utilizes advanced tabu search techniques, including reactive tabu search and group theory applications, to develop a heuristic procedure for solving the LPDPTW. Tabu search is a metaheuristic that performs an intelligent search of the solution space. Group theory provides the structural foundation that supports the efficient search of the neighborhoods and movement through the solution space

An examination of heuristics for the shelf space allocation problem.

Wong, Mei Ting.Thesis (M.Phil.)--Chinese University of Hong Kong, 2010.Includes bibliographical references (p. 115-120).Abstracts in English and Chinese.Chapter 1. --- Introduction --- p.1Chapter 1.1 --- Background --- p.1Chapter 1.2 --- Our Contributions --- p.4Chapter 1.3 --- Framework of Shelf Space Allocation Problem --- p.4Chapter 1.4 --- Organization --- p.6Chapter 2. --- Literature Review --- p.7Chapter 2.1 --- Introduction --- p.7Chapter 2.2 --- Commercial Approaches --- p.7Chapter 2.3 --- Experimental Approaches --- p.8Chapter 2.4 --- Optimization Approaches --- p.11Chapter 2.4.1 --- Exact Approaches --- p.11Chapter 2.4.2 --- Heuristics Approaches --- p.16Chapter 2.5 --- Summary --- p.19Chapter 3. --- Overview of Shelf Space Allocation Problem --- p.21Chapter 3.1 --- Introduction --- p.21Chapter 3.2 --- Problem description --- p.22Chapter 3.2.1 --- Mathematical Model --- p.24Chapter 3.2.1.1 --- Notations --- p.25Chapter 3.2.1.2 --- Model --- p.25Chapter 3.2.1.3 --- Assumption --- p.26Chapter 3.2.1.4 --- Notations of final model --- p.27Chapter 3.2.1.5 --- Final model --- p.27Chapter 3.3 --- Original Heuristic --- p.28Chapter 3.3.1 --- Yang (2001) Method --- p.28Chapter 3.3.2 --- Remarks on Original Heuristic --- p.29Chapter 3.4 --- Original Heuristic with Yang's Adjustment --- p.30Chapter 3.4.1 --- Remarks on Yang's Adjustment --- p.32Chapter 3.5 --- New Neighborhood Movements --- p.33Chapter 3.5.1 --- New Adjustment Phase --- p.33Chapter 3.6 --- Network Flow Model --- p.35Chapter 3.6.1 --- ULSSAP --- p.35Chapter 3.6.2 --- Transforming shelf space allocation problem (SSAP) --- p.38Chapter 3.7 --- Tabu Search --- p.41Chapter 3.7.1 --- Tabu Search Algorithm --- p.42Chapter 3.7.1.1 --- Neighborhood search moves --- p.42Chapter 3.7.1.2 --- Candidate list strategy --- p.45Chapter 3.7.1.3 --- Tabu list --- p.46Chapter 3.7.1.4 --- Aspiration criteria.........................................: --- p.47Chapter 3.7.1.5 --- Intensification and Diversification --- p.48Chapter 3.7.1.6 --- Stopping criterion --- p.49Chapter 3.7.1.7 --- Probabilistic choice --- p.50Chapter 3.7.2 --- General Process of Tabu Search --- p.51Chapter 3.7.3 --- Application of Tabu Search to SSAP --- p.54Chapter 3.7.4 --- Analysis of Tabu Search --- p.58Chapter 4. --- Tabu Search with Path Relinking --- p.60Chapter 4.1 --- Introduction --- p.60Chapter 4.2 --- Foundations of path relinking --- p.62Chapter 4.3 --- Path Relinking Template --- p.65Chapter 4.4 --- Identification of Reference set --- p.69Chapter 4.5 --- Choosing initial and guiding solution --- p.73Chapter 4.6 --- Neighborhood structure --- p.74Chapter 4.7 --- Moving along paths --- p.81Chapter 4.8 --- Application of Tabu Search with Path Relinking --- p.87Chapter 4.9 --- Conclusion --- p.90Chapter 5. --- Computational Studies --- p.92Chapter 5.1 --- Introduction --- p.92Chapter 5.2 --- General Parameter Setting --- p.92Chapter 5.3 --- Parameter values for Tabu search --- p.94Chapter 5.4 --- Sensitivity test for Tabu search with Path Relinking --- p.95Chapter 5.4.1 --- Reference Set Strategies and Initial and Guiding Solution Criteria --- p.96Chapter 5.4.2 --- Frequency of Path Relinking --- p.99Chapter 5.4.3 --- Size of reference set --- p.101Chapter 5.4.4 --- Comparison with Tabu Search --- p.102Chapter 5.5 --- Comparison with other heuristics --- p.105Chapter 5.6 --- Conclusion --- p.109Chapter 6. --- Conclusion --- p.111Chapter 6.1 --- Summary of achievements --- p.112Chapter 6.2 --- Future Works --- p.113Bibliography --- p.11