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Combinatorial optimization problems appear in a wide range of applications in operations research, engineering, biological sciences and computer science. Many combinatorial optimization approaches have been developed that link the discrete universe to the continuous universe through geometric, analytic, and algebraic techniques.
Optimization problems with multi-objective arise in a natural fashion in most disciplines and their solution has been a challenge to researchers for a long time. Despite the considerable variety of techniques developed in Operations Research (OR) and other disciplines to tackle these problems, the complexities of their solution calls for alternative approaches.
In this book, we will discuss the results of a recent multi-objective combinatorial optimization achievement considering metaheuristic, mathematical programming, heuristic, hyper heuristic, and hybrid approaches. In other words, this book intends to show a diversity of various multi-objective combinatorial optimization issues that may benefit from different methods in theory and practice.
-A non-exhaustive list of topics we invite to be considered for inclusion in this book are as follows:
1. Basic concepts of combinatorial optimization
Chapter 1 presents and motivates MOP terminology and the nomenclature used in successive chapters including a lengthy discussion on theimpact of computational limitations on finding the Pareto front along with insight to MOP concepts.
2. Random methods for combinatorial optimization problems
2.1. Metaheuristic
2.1.1. Population-based methods
2.1.1.1. Multi-objective Evolutionary Algorithm (MOEA) Approaches
MOEA developmental history has proceeded in a number of ways from aggregated forms of single-objective Evolutionary Algorithms (EAs) to true multiobjective approaches and their extensions. Each MOEA is presented with historical and algorithmic insight. Being aware of the many facets of historical multiobjective problem solving provides a foundational understanding of the discipline.
2.1.1.2. Multi-objective swarm intelligence algorithms
Multi-objective particle swarm optimization, multi-objective ant colony optimization,…
2.1.2. Trajectory methods
Simulated annealing, Tabu search,…
2.1.3. Coevolution and hybrid of MOEA Local Search
Both coevolutionary MOEAs and hybridizations of MOEAs with local search procedures are covered.
2.2. Heuristic algorithms
2.2.1. Improvement heuristics
2.2.2. Constructive heuristics
2.3. Relaxation algorithms
E.g. Lagrangian relaxation
2.4. Decomposition algorithms
Benders decomposition algorithm
2.5. Column generation
3. Enumerate methods for combinatorial optimization problems
E.g. Dynamic programming
4. Deterministic methods for combinatorial optimization problems
4.1. Linear programming methods
Goal programming,…
4.2. Branching algorithms
This chapter presents well-known branching algorithms such as branch&cut, branch&price, branch& bound.
5. Many-objective combinatorial optimization problems
This chapter presents multi-objective combinatorial optimization in the case of more than three objectives along with solution approaches.
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