Lexicographic Goal Programming and Assessment Tools for a Combinatorial Production Problem

NP-complete combinatorial problems often necessitate the use of near-optimal solution techniques including heuristics and metaheuristics. The addition of multiple optimization criteria can further complicate comparison of these solution techniques due to the decision-maker’s weighting schema potentially masking search limitations. In addition, many contemporary problems lack quantitative assessment tools, including benchmark data sets. This chapter proposes the use of lexicographic goal programming for use in comparing combinatorial search techniques. These techniques are implemented here using a recently formulated problem from the area of production analysis. The development of a benchmark data set and other assessment tools is demonstrated, and these are then used to compare the performance of a genetic algorithm and an H-K general-purpose heuristic as applied to the production-related application.

An Introduction to Multi-Objective Optimization

This chapter is devoted to summarize common concepts related to multi-objective optimization (MO). An overview of “traditional” as well as CI-based MO is given. Further, all aspects of performance assessment for MO techniques are discussed. Finally, challenges facing MO techniques are addressed. All of these description and analysis give the readers basic knowledge for understandings the rest of the book.

Evolutionary Population Dynamics and Multi-Objective Optimisation Problems

Problems for which many objective functions are to be simultaneously optimised are widely encountered in science and industry. These multi-objective problems have also been the subject of intensive investigation and development recently for metaheuristic search algorithms such as ant colony optimisation, particle swarm optimisation and extremal optimisation. In this chapter, a unifying framework called evolutionary programming dynamics (EPD) is examined. Using underlying concepts of self organised criticality and evolutionary programming, it can be applied to many optimisation algorithms as a controlling metaheuristic, to improve performance and results. We show this to be effective for both continuous and combinatorial problems.

Evolutionary Multi-Objective Optimization in Military Applications

Evolutionary methods are used in many fields to solve multi-objective optimization problems. Military problems are no exception. This chapter looks at a variety of military applications that have utilized evolutionary techniques for solving their problem.

Multi-Objective Optimization Using Artificial Immune Systems

The human immune system (HIS) is a highly evolved, parallel and distributed adaptive system. The information processing abilities of HIS provide important aspects in the field of computation. This emerging field is referring to as the Artificial Immune Systems (AIS). In recent years, AIS have received significant amount of interest from researchers and industrial sponsors. Applications of AIS include such areas as machine learning, fault diagnosis, computer security and optimization. In this chapter, after surveying the AIS for multi-objective optimization, we will describe two multi-objective optimization algorithms using AIS, the Immune Dominance Clonal Multi-objective Algorithm (IDCMA), and the Nondominated Neighbor Immune Algorithm (NNIA). IDCMA is unique in that its fitness values of current dominated individuals are assigned as the values of a custom distance measure, termed as Ab-Ab affinity, between the dominated individuals and one of the nondominated individuals found so far. According to the values of Ab-Ab affinity, all dominated individuals (antibodies) are divided into two kinds, subdominant antibodies and cryptic antibodies. And local search only applies to the subdominant antibodies while the cryptic antibodies are redundant and have no function during local search, but they can become subdominant (active) antibodies during the subsequent evolution. Furthermore, a new immune operation, Clonal Proliferation is provided to enhance local search. Using the Clonal Proliferation operation, IDCMA reproduces individuals and selects their improved maturated progenies after local search, so single individuals can exploit their surrounding space effectively and the newcomers yield a broader exploration of the search space. The performance comparison of IDCMA with MISA, NSGA-II, SPEA, PAES, NSGA, VEGA, NPGA and HLGA in solving six well-known multi-objective function optimization problems and nine multi-objective 0/1 knapsack problems shows that IDCMA has a good performance in converging to approximate Pareto-optimal fronts with a good distribution. NNIA solves multi-objective optimization problems by using a nondominated neighbor-based selection technique, an immune inspired operator, two heuristic search operators and elitism. The unique selection technique of NNIA only selects minority isolated nondominated individuals in population. The selected individuals are then cloned proportionally to their crowding-distance values before heuristic search. By using the nondominated neighbor-based selection and proportional cloning, NNIA pays more attention to the less-crowded regions of the current trade-off front. We compare NNIA with NSGA-II, SPEA2, PESA-II, and MISA in solving five DTLZ problems, five ZDT problems and three low-dimensional problems. The statistical analysis based on three performance metrics including the Coverage of two sets, the Convergence metric, and the Spacing, show that the unique selection method is effective, and NNIA is an effective algorithm for solving multi-objective optimization problems.

Evolutionary Multi-Objective Optimization in Energy Conversion Systems

The research field on energy conversion systems presents a large variety of multi-objective optimization problems that can be solved taking full advantage of the features of evolutionary algorithms. In fact, design and operation of energy systems can be considered in several different perspectives (e.g., performance, efficiency, costs, environmental aspects). This results in a number of objective functions that should be simultaneously optimized, and the knowledge of the Pareto optimal set of solutions is of fundamental importance to the decision maker. This chapter proposes a brief survey of typical applications at different levels, ranging from the design of component detail to the challenge about the synthesis of the configuration of complex energy conversion systems. For sake of simplicity, the proposed examples are grouped into three main categories: design of components/component details, design of overall energy system, operation of energy systems. Each multi-objective optimization problem is presented with a short background and some details about the formulation. Future research directions in the field of energy systems are also discussed at the end of the chapter.

Multi-Objective Particles Swarm Optimization Approaches

The multiple criteria nature of most real world problems has boosted research on multi-objective algorithms that can tackle such problems effectively, with the smallest possible computational burden. Particle Swarm Optimization has attracted the interest of researchers due to its simplicity, effectiveness and efficiency in solving numerous single-objective optimization problems. Up-to-date, there are a significant number of multi-objective Particle Swarm Optimization approaches and applications reported in the literature. This chapter aims at providing a review and discussion of the most established results on this field, as well as exposing the most active research topics that can give initiative for future research.

Towards a More Efficient Multi-Objective Particle Swarm Optimizer

This chapter presents a hybrid between a particle swarm optimization (PSO) approach and scatter search. The main motivation for developing this approach is to combine the high convergence rate of the PSO algorithm with a local search approach based on scatter search, in order to have the main advantages of these two types of techniques. We propose a new leader selection scheme for PSO, which aims to accelerate convergence by increasing the selection pressure. However, this higher selection pressure reduces diversity. To alleviate that, scatter search is adopted after applying PSO, in order to spread the solutions previously obtained, so that a better distribution along the Pareto front is achieved. The proposed approach can produce reasonably good approximations of multi-objective problems of high dimensionality, performing only 4,000 fitness function evaluations. Test problems taken from the specialized literature are adopted to validate the proposed hybrid approach. Results are compared with respect to the NSGA-II, which is an approach representative of the state-of-the-art in the area.

Walking with EMO

This chapter will demonstrate the various robotics applications that can be achieved using evolutionary multi-objective optimization (EMO) techniques. The main objective of this chapter is to demonstrate practical ways of generating simple legged locomotion for simulated robots with two, four and six legs using EMO. The operational performance as well as complexities of the resulting evolved Pareto solutions that act as controllers for these robots will then be analyzed. Additionally, the operational dynamics of these evolved Pareto controllers in noisy and uncertain environments, limb dynamics and effects of using a different underlying EMO algorithm will also be discussed.

Evolutionary Multi-Objective Optimization for DNA Sequence Design

Finding reliable and efficient DNA sequences is one of the most important tasks for successful DNArelated experiments such as DNA computing, DNA nano-assembly, DNA microarrays and polymerase chain reaction. Sequence design involves a number of heterogeneous and conflicting design criteria. Also, it is proven as a class of NP problems. These suggest that multi-objective evolutionary algorithms (MOEAs) are actually good candidates for DNA sequence optimization. In addition, the characteristics of MOEAs including simple addition/deletion of objectives and easy incorporation of various existing tools and human knowledge into the final decision process could increase the reliability of final DNA sequence set. In this chapter, we review multi-objective evolutionary approaches to DNA sequence design. In particular, we analyze the performance of e-multi-objective evolutionary algorithms on three DNA sequence design problems and validate the results by showing superior performance to previous techniques.