The gasification of highly watered waste residues may help to reduce fossil fuels consumption, as well as emissions, all the while improving efficiency. The integration of supercritical gasification with solar energy may improve the performances of both new and existing plants. The design and optimization of such kinds of energy conversion plants requires to take into account the following aspects: renewable sources are intermittent, prices of fuels and materials are continuously fluctuating and are uncertain, the energy efficiency should be maximized and the capital and opeating costs should be minimized. The main goal of this thesis is to develop mathematical programming frameworks in order to solve the design, the scheduling and the Heat Exchanger Network Synthesis (HENS) of any industrial plant. In particular, the final goal is to apply the proposed methods to the design of a solar-assisted supercritical gasification plant. The methods are developed in order to propose strategies to account for uncertainty, sizing constraints, scheduling options and multi-period HENS. In order to apply the frameworks elaborated in this dissertation, a set of mathematical models is suggested. The goal is to describe the thermodynamics of the considered process units: supercritical water gasification, gas separation, solar energy conversion technologies and storage utilities are studied. The pre-design problem is first tackled by coupling an energy targeting model with a Global Sensitivity Analysis (GSA) method and a Monte Carlo (MC) simulation. Given a set of energy conversion options, the most promising energy conversion paths with respect to a set of uncertain parameters are identified while applying energy integration principles. The design problem is then tackled and the design, the scheduling, as well as HENS for multi-period operations are investigated. The result is a sequential mathematical programming algorithm for solving the problem. A decomposition approach is applied using a bi-level optimization strategy, where derivative-free optimization algorithms are coupled with derivative based, mixed integer linear and non linear models. The framework is tested on a literature example and on a large scale example in order to prove its effectiveness. The integration of thermal storage options is included in order to highlight the improvements that can be achieved with process heat recovery. The computation time problem is addressed and an alternative strategy to solve the same problem is put forward. Finally, the developed methods are coupled with a Multi-Objective Optimization algorithm and the multi-period design problem for designing a solar-assisted super-critical gasification plant is solved. It is thus demonstrated how the proposed methods can be successfully applied to industrial-scale problems. It remains that computational issues are problem-dependent and sensitive to the problem definition.