Polygeneration is a concept where multiple energy products are generated in a single plant by tightly integrating multiple processes into one system. Compared to conventional single-product systems, polygeneration systems have many economic advantages, such as potentially high profitability and high viability when exposed to market fluctuations. The optimal design of an energy polygeneration system that converts coal and biomass to electricity, liquid fuels (naphtha and diesel) and chemical products (methanol) with carbon dioxide (CO2) capture under different economic scenarios is investigated. In this system, syngas is produced by gasification of coal and/or biomass; purified by a cleaning process to remove particles, mercury, sulfur and CO2; and then split to different downstream sections such as the gas turbine, FT process and the methanol process. In this thesis, the optimal design with the highest net present value (NPV) is determined by optimizing equipment capacities, stream flow rates and stream split fractions. The case study results for static polygeneration systems reveal that the optimal design of polygeneration systems is strongly influenced by economic conditions such as feedstock prices, product prices, and potential emissions penalties for CO2. Over the range of economic scenarios considered, it can be optimal to produce a mixture of electricity, liquid fuels, and methanol; only one each; or mixtures in-between. The optimal biomass/coal feed ratio significantly increases when the carbon tax increases or the biomass price decreases. An economic analysis of the optimal static polygeneration designs yielded a slightly higher NPV than comparable single-product plants. The flexible operation is then considered for the energy polygeneration system. In real applications, product prices can fluctuate significantly seasonally or even daily. The profitability of the polygeneration system can potentially be increased if some operational flexibility is introduced, such as adjusting the product mix in response to changing market prices. The major challenge of this flexible design is the determination of the optimal trade-off between flexibility and capital cost because higher flexibility typically implies both higher product revenues and larger equipment sizes. A two-stage optimization formulation for is used for the optimal design and operation of flexible energy polygeneration systems, which simultaneously optimizes design decision variables (e.g., equipment sizes) and operational decision variables (e.g., production rate schedules) in several different market scenarios to achieve the best expected economic performance. Case study results for flexible polygeneration systems show that for most of market scenarios, flexible polygeneration systems achieved higher expected NPVs than static polygeneration systems. Furthermore, even higher expected NPVs could be obtained with increases in flexibility. The flexible polygeneration optimization problem is a potentially large-scale nonconvex mixed-integer nonlinear program (MINLP) and cannot be solved to global optimality by state-of-the-art global optimization solvers, such as BARON, within a reasonable time. The nonconvex generalized Benders decomposition (NGBD) method can exploit the special structure of this mathematical programming problem and enable faster solution. In this method, the nonconvex MINLP is relaxed into a convex lower bounding problem which can be further reformulated into a relaxed master problem according to the principles of projection, dualization and relaxation. The relaxed master problem yields an nondecreasing sequence of lower bounds for the original problem. And an nonincreasing sequence of upper bounds is obtained by solving primal problems, which are generated by fixing the integer variables in the original problem. A global optimal objective is obtained when the lower and upper bounds coincide. The decomposition algorithm guarantees to find an E-optimal solution in a finite number of iterations. In this thesis, several enhanced decomposition methods with improved relaxed master problems are developed, including enhanced NGBD with primal dual information (NGBD-D), piecewise convex relaxation (NGBD-PCR) and lift-and-project cuts (NGBD-LAP). In NGBD-D, additional dual information is introduced into the relaxed master problem by solving the relaxed dual of primal problem. The soobtained primal dual cuts can significantly improve the convergence rate of the algorithm. In NGBD-PCR, the piecewise McCormick relaxation technique is integrated into the NGBD algorithm to reduce the gap between the original problem and its convex relaxation. The domains of variables in bilinear functions can be uniformly partitioned before solution or dynamically partitioned in the algorithm by using the intermediate solution information. In NGBD-LAP, lift-and-project cuts are employed for solving the piecewise lower bounding problem. In all three enhanced decomposition algorithms, there is a trade-off between tighter relaxations and more solution times for subproblems. The computational advantages of the enhanced decomposition methods are demonstrated via case studies on the flexible polygeneration problems. The computational results show that, while NGBD can solve problems that are intractable for a state-ofthe- art global optimization solver (BARON), the enhanced NGBD algorithms help to reduce the solution time by up to an order of magnitude compared to NGBD. And enhanced NGBD algorithms solved the large-scale nonconvex MINLPs to [epsilon]-optimality in practical times (e.g., a problem with 70 binary variables and 44136 continuous variables was solved within 19 hours).