Since the publication of the first edition of Probability-Based Multi-objective Optimization for Material Selection, some subsequent works have been done, which promote us to have the possibility to publish the second edition of the book with new complements. Especially, the viewpoint of system theory in considering “simultaneous optimization of multiple objectives” is put forward. 

In addition to the original materials of the first edition, the fuzzy-based probabilistic multi-objective optimization, cluster analysis of multiple objectives, treatments of portfolio investment, and multi-objective shortest path problem by means of probability-based multi-objective optimization are all developed in the second edition. Adjustment of arrangement of some chapters is involved. Besides, some minor supplements and error corrections of the first edition are conducted. Nevertheless, the aim of this book is still to cast a brick to attract jade and would make its contributions to relevant fields as a paving stone.

The main purpose of this book is to provide a rational way for material selection in viewpoint of system theory and in the spirit of probability theory with reasonable physical essence. It is our great pleasure if the readers including scientists, engineers, postgraduate, and advanced undergraduate in the relevant fields could gain valuable information from this book. 
The contents of the second edition are as following: 

Chapter 1 describes the history and current status of material selection with multi-objective optimization briefly; 

Chapter 2 reviews and summarizes the previous methods for material selection with multi-objective optimization mainly, including Farag comprehensive method, analytic hierarchy process (AHP), Vlšekriterijumsko KOmpromisno Rangiranje (VIKOR), technique of ranking preferences by similarity to the ideal solution (TOPSIS), multi-objective optimization (MOO) on the basis of ratio analysis (MOORA), Ashby’s method, etc.; 

Chapter 3 illuminates the fundamental principle and concepts of probability-based multi-objective optimization for material selection in viewpoint of system theory and in the spirit of probability theory;

Chapter 4 presents the robustness evaluation with probability-based multi-objective optimization in condition of the utility of response with uncertainty; 

Chapter 5 describes the extension of probability-based multi-objective optimization in condition of the utility with desirable value; 

Chapter 6 explains the hybrids of probability-based multi-objective optimization with experiment design methodologies, i.e., orthogonal experimental design, response surface design, and uniform experimental design; 

Chapter 7 illuminates discretization of simplified evaluation in probability-based multi-objective optimization by means of GLP and uniform experimental design; 

Chapter 8 presents the fuzzy-based probabilistic multi-objective optimization; 

Chapter 9 describes the cluster analysis of multiple objectives in probability-based multi-objective optimization; 

Chapter 10 states the applications of probability-based multi-objective optimization beyond material selection; 

Chapter 11 shows the treatment of portfolio investment by means of probability-based multi-objective optimization; 

Chapter 12 displays the treatment of multi-objective shortest path problem by means of probability-based multi-objective optimization; 

Chapter 13 discusses on preferable probability, discretization, error analysis, hybrid of sequential uniform design with PMOO, and weighting factor evaluation; 

Chapter 14 gives a comprehensive summary of the probability-based multi-objective optimization.