List of Figures. List of Tables. Preface. Foreword. 1. Basic Concepts. 2. Evolutionary Algorithm MOP Approaches. 3. MOEA Test Suites. 4. MOEA Testing and Analysis. 5. MOEA Theory and Issues. 3. MOEA Theoretical Issues. 6. Applications. 7. MOEA Parallelization. 8. Multi-Criteria Decision Making. 9. Special Topics. 10. Epilog. Appendix A: MOEA Classification and Technique Analysis. Appendix B: MOPs in the Literature. Appendix C: Ptrue & PFtrue for Selected Numeric MOPs. Appendix D: Ptrue & PFtrue for Side-Constrained MOPs. Appendix E: MOEA Software Availability. Appendix F: MOEA-Related Information. Index. References.

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Evolutionary algorithms for solving multi-objective problems

This paper provides a survey of the research in and an annotated bibliography of multiple objective combinatorial optimization, MOCO. We present a general formulation of MOCO problems, describe the main characteristics of MOCO problems, and review the main properties and theoretical results for these problems. The main parts of the paper are a section on the review of the available solution methodology, both exact and heuristic, and a section on the annotation of the existing literature in the field organized problem by problem. We conclude the paper by stating open questions and areas of future research.

A survey and annotated bibliography of multiobjective combinatorial optimization

Research in metaheuristics for combinatorial optimization problems has lately experienced a noteworthy shift towards the hybridization of metaheuristics with other techniques for optimization. At the same time, the focus of research has changed from being rather algorithm-oriented to being more problem-oriented. Nowadays the focus is on solving the problem at hand in the best way possible, rather than promoting a certain metaheuristic. This has led to an enormously fruitful cross-fertilization of different areas of optimization. This cross-fertilization is documented by a multitude of powerful hybrid algorithms that were obtained by combining components from several different optimization techniques. Hereby, hybridization is not restricted to the combination of different metaheuristics but includes, for example, the combination of exact algorithms and metaheuristics. In this work we provide a survey of some of the most important lines of hybridization. The literature review is accompanied by the presentation of illustrative examples.

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Hybrid metaheuristics in combinatorial optimization: A survey

This note contains two fully polynomial approximation schemes for the shortest path problem with an additional constraint. The main difficulty in constructing such algorithms arises since no trivial lower and upper bounds on the solution value, whose ratio is polynomially bounded, are known. In spite of this difficulty, one of the algorithms presented here is strongly polynomial. Applications to other problems are also discussed.

Approximation Schemes for the Restricted Shortest Path Problem

Bicriterion path problems in directed graphs are systematically studied. A series of ten problems are defined and their computational complexity examined. Algorithms are provided for some of them, including polynomial algorithms for the MAXMIN-MAXMIN problem and the MINSUM-MAXMIN problem, and a pseudo-polynomial exact algorithm as well as a fully polynomial approximation scheme for the MINSUM-MINSUM problem.

Bicriterion Path Problems

In a transportation problem, generally, a single criterion of minimizing the total cost is considered. But in certain practical situations two or more objectives are relevant. For example, the objectives may be minimizations of total cost, consumption of certain scarce resources such as energy, total deterioration of goods during transportation, etc. Clearly, this problem can be solved using any of the multiobjective linear programming techniques; but the computational efforts needed would be prohibitive in many cases. The computational complexity in these techniques arises from the fact that each of the methods finds the set of nondominated extreme points in the solution space where such extreme points are, generally, many. Therefore, this paper develops a method of finding the nondominated extreme points in the criteria space. Such extreme points in the criteria space would be generally less and only these are needed while choosing a nondominated solution for implementation. The method involves a parame...

Bicriteria transportation problem

Certain properties of a shortest chain subject to several side constraints are established. Based on these an implicit enumeration algorithm, that is, a generalization of the one given by Dijkstra for the case without any side constraint, is presented. Validation of the algorithm and an illustrative example are included.

Shortest chain subject to side constraints

Fuzzy models for single-period inventory problem

Minimal spanning tree subject to a side constraint

The shortest path problem between two specified nodes in a general network possesses the unimodularity property and, therefore, can be solved by efficient labelling algorithms. However, the introduction of an additional linear constraint would, in general, destroy this property and the existing algorithms are not applicable in this case. This paper presents a parametric approach for solving this problem. The algorithm presented would require, on the average, a number of iterations which is polynomially bounded. The similarity of this approach to that of the generalized Lagrange multiplier technique is demonstrated and a numerical example is presented.

K. P. K. Nair

Papers

Bicriteria transportation problem

Shortest chain subject to side constraints

Fuzzy models for single-period inventory problem

Minimal spanning tree subject to a side constraint

The constrained shortest path problem